diff --git "a/mr-ca/Quantitative Aptitude_indic_translation.jsonl" "b/mr-ca/Quantitative Aptitude_indic_translation.jsonl"
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+{"en":"Ratio and proportion are fundamental concepts in mathematics.","translation":"गुणोत्तर आणि प्रमाण हे गणितातील मूलभूत संकल्पना आहेत.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"If a sum of money is divided in the ratio 2:3, what are the parts?","translation":"जर काही रक्कम २:३ या प्रमाणात विभागली, तर त्याचे भाग काय असतील?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The ratio of boys to girls in the school is 5:4.","translation":"शाळेतील मुलामुलींचे प्रमाण ५:४ आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"We can find the number of girls if the total number of students and the ratio of boys to girls are known.","translation":"जर विद्यार्थ्यांची एकूण संख्या आणि मुलामुलींचे प्रमाण माहित असेल, तर आपण मुलींची संख्या शोधू शकतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Understanding ratios is crucial for solving many practical problems.","translation":"अनेक व्यावहारिक समस्या सोडवण्यासाठी गुणोत्तरांची समज आवश्यक आहे.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"The ratio of two quantities of the same kind can be expressed as a fraction.","translation":"एकाच प्रकारच्या दोन राशींचे गुणोत्तर अपूर्णांकाच्या स्वरूपात व्यक्त केले जाऊ शकते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"In the ratio 7:9, 7 is the antecedent and 9 is the consequent.","translation":"७:९ या गुणोत्तरात, ७ हा पूर्वपद आहे आणि ९ हा उत्तरपद आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Both terms of a ratio can be multiplied or divided by the same non-zero number.","translation":"एका गुणोत्तराचे दोन्ही पद त्याच शून्येतर संख्येने गुणले किंवा भागले जाऊ शकतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The order of terms in a ratio is important; 3:4 is not the same as 4:3.","translation":"एका गुणोत्तरातील पदांचा क्रम महत्त्वाचा आहे; ३:४ आणि ४:३ हे एकसारखे नाहीत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Ratios only exist between quantities of the same kind.","translation":"गुणोत्तर फक्त एकाच प्रकारच्या राशींमध्ये अस्तित्वात असते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The ratio between 150 grams and 2 kilograms can be calculated.","translation":"१५० ग्रॅम आणि २ किलोग्राममधील गुणोत्तर काढता येते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"To compare two ratios, convert them into equivalent like fractions.","translation":"दोन गुणोत्तरांची तुलना करण्यासाठी, त्यांना सममूल्य अपूर्णांकांमध्ये रूपांतरित करा.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If a quantity increases in the ratio a:b, the new quantity is b/a of the original.","translation":"जर कोणतीही राशी a:b या प्रमाणात वाढली, तर नवीन राशी मूळ राशीचा b/a असेल.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Simplify the ratio 1/3 : 1/8 : 1/6.","translation":"१/३ : १/८ : १/६ हे गुणोत्तर सोपे करा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The number of boys and girls in a school is in the ratio 3:5.","translation":"एका शाळेतील मुलामुलींची संख्या ३:५ या प्रमाणात आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"If 18 new girls are admitted, find how many new boys may be admitted.","translation":"जर १८ नवीन मुलींना प्रवेश दिला, तर किती नवीन मुलांच��� प्रवेश दिला जाऊ शकतो?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"One ratio is the inverse of another if their product is 1.","translation":"जर दोन गुणोत्तरांचा गुणाकार १ असेल, तर ते एकमेकांचे व्यस्त गुणोत्तर असतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The ratio compounded of two ratios a:b and c:d is ac:bd.","translation":"दोन गुणोत्तरांचे मिश्रण a:b आणि c:d हे ac:bd असते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The duplicate ratio of 2:3 is 4:9.","translation":"२:३ चे दुहेरी गुणोत्तर ४:९ आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The sub-duplicate ratio of 4:9 is 2:3.","translation":"४:९ चे उप-दुहेरी गुणोत्तर २:३ आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The value of x is 0.","translation":"x ची किंमत 0 आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Using the formula, we can find the solution.","translation":"सूत्राचा वापर करून, आपण समाधान शोधू शकतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"On simplification, the result is 1.","translation":"सोपे केल्यावर, निकाल 1 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The value of the expression is 0.","translation":"व्यक्तीची किंमत 0 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If x = 3, then 3x - 9x is 12.","translation":"जर x = 3, तर 3x - 9x हे 12 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If a to the power of x equals b, b to the power of y equals c, and c to the power of z equals a, then xyz is 1.","translation":"जर a चा x घात b आहे, b चा y घात c आहे, आणि c चा z घात a आहे, तर xyz हे 1 आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The value of the given expression is 1.","translation":"दिलेल्या अभिव्यक्तीचे मूल्य 1 आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If 2 to the power of x equals 3 to the power of y equals 6 to the power of negative z, then the value of the expression is 0.","translation":"जर 2 चा x घात 3 चा y घात आणि 6 चा -z घात समान असेल, तर या अभिव्यक्तीचे मूल्य 0 आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The logarithm of a number to a given base is the power to which the base must be raised.","translation":"एका विशिष्ट पायावर आधारित संख्येचा लॉगरिदम म्हणजे पायाला किती घात द्यावा लागतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If 2 to the power of 4 equals 16, then the logarithm of 16 to the base 2 is 4.","translation":"जर 2 चा 4 था घात 16 असेल, तर 16 चा 2 च्या पायावर आधारित लॉगरिदम 4 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The logarithm of 1 to any base is zero.","translation":"कोणत्याही पायावर 1 चा लॉगरिदम शून्य असतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The logarithm of any quantity to the same base is unity.","translation":"एकाच पायावर आधारित कोणत्याही राशीचा लॉगरिदम एक असतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If the logarithm of a to the power of 1/6 equals 2, then a equals 8.","translation":"जर a च्या 1/6 घाताचा लॉगरिदम 2 असेल, तर a ची किंमत 8 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the logarithm of 5832 to the base of the cube root of 2.","translation":"5832 चा 2 च्या घनमूळाच्या पायावर आधारित लॉगरिदम शोधा.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Logarithms of numbers to the base 10 are known as common logarithms.","translation":"10 च्या पायावर आधारित संख्यांचे लॉगरिदम सामान्य लॉगरिदम म्हणून ओळखले जातात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.","translation":"दोन संख्यांच्या गुणाकाराचा लॉगरिदम, त्या संख्यांच्या लॉगरिदमच्या बेरजेइतका असतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The logarithm of the quotient of two numbers is equal to the difference of their logarithms.","translation":"दोन संख्यांच्या भागाकाराचा लॉगरिदम, त्यांच्या लॉगरिदमच्या वजाबाकीइतका असतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The logarithm of a number raised to a power is equal to the index of the power multiplied by the logarithm of the number.","translation":"एका संख्येचा घात, त्या घातांकाने संख्येच्या लॉगरिदमला गुणून मिळतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Find the logarithm of 1728 to the base of 2 times the square root of 3.","translation":"1728 चा 2 गुणिले वर्गमूळ 3 च्या पायावर आधारित लॉगरिदम शोधा.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If the logarithm of a number to any base is given, then the logarithm of the same number to any other base can be determined.","translation":"जर कोणत्याही पायावर आधारित संख्येचा लॉगरिदम दिला असेल, तर त्याच संख्येचा दुसऱ्या कोणत्याही पायावर आधारित लॉगरिदम काढता येतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"An equation in which the highest power of the variable is 1 is called a Linear equation.","translation":"एखादे समीकरण ज्यात चलाची सर्वात मोठी शक्ती 1 असते, त्याला रेषीय समीकरण म्हणतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Two or more linear equations involving two or more variables are called Simultaneous Linear Equations.","translation":"दोन किंवा अधिक चलांचा समावेश असलेल्या दोन किंवा अधिक रेषीय समीकरणांना एकत्रित रेषीय समीकरणे म्हणतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"For example: 8x + 17(x–3) = 4 (4x–9) + 12 is a Linear equation.","translation":"उदाहरणार्थ: 8x + 17(x–3) = 4 (4x–9) + 12 हे एक रेषीय समीकरण आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"3x 2 + 5x +6 = 0 is a Quadratic equation.","translation":"3x 2 + 5x +6 = 0 हे वर्ग समीकरण आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"A simple equation in one unknown x is in the form ax + b = 0.","translation":"एका अज्ञात x मधील एक सोपे समीकरण ax + b = 0 या स्वरूपात आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"A simple equation has only one root.","translation":"एका साध्या समीकरणात फक्त एकच मूळ असते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"By transposing the variables in one side and the constants in other side we have 4/3 x – 14/15 x = 19/5 +1.","translation":"एका बाजूला चल आणि दुसऱ्या बाजूला स्थिर संख्या ठेवून आपल्याला 4/3 x – 14/15 x = 19/5 +1 मिळते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The equation –7 x + 1 = 5 – 3 x will be satisfied for x equal to: –1","translation":"समीकरण –7 x + 1 = 5 – 3 x हे x = –1 साठी समाधानकारक असेल.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The root of the equation + 4 - 5 + = 11 43 x x is 10","translation":"समीकरणाचे मूळ + 4 - 5 + = 11 43 x x हे 10 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Pick up the correct value of x for 2 = 30 45 x is x = 7","translation":"2 = 30 45 x साठी x ची योग्य किंमत x = 7 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The solution of the equation + 24 = 4 + 54 xx is 16","translation":"समीकरणाचे समाधान + 24 = 4 + 54 xx हे 16 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"8 is the solution of the equation 4 10 8 2 9 x x  ","translation":"समीकरणाचे समाधान 4 10 8 2 9 x x   हे 8 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The value of y that satisfies the equation 4 7y 9 1y - 6 11y    is – 7","translation":"y ची किंमत जी समीकरण 4 7y 9 1y - 6 11y    ला समाधान देते ती – 7 आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The solution of the equation (p+2) (p–3) + (p+3) (p–4) = p(2p–5) is 6","translation":"समीकरणाचे समाधान (p+2) (p–3) + (p+3) (p–4) = p(2p–5) हे 6 आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The equation 12 +1 15 1 2 5 =+ 45 3 1 x x x x -- - is true for x=1","translation":"समीकरण 12 +1 15 1 2 5 =+ 45 3 1 x x x x -- - हे x=1 साठी सत्य आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Pick up the correct value x for which  11 +=0 0.5 0.05 0.005 0.0005 xx is x = 0","translation":" 11 +=0 0.5 0.05 0.005 0.0005 xx साठी x ची योग्य किंमत x = 0 आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The denominator of a fraction exceeds the numerator by 5 and if 3 be added to both the fraction becomes 4/3. Find the fraction.","translation":"एका अपूर्णांकाचा छेद अंशापेक्षा 5 ने मोठा आहे आणि जर अंश आणि छेदामध्ये 3 मिळवले, तर अपूर्णांक 4/3 होतो. अपूर्णांक शोधा.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If thrice of A’s age 6 years ago be subtracted from twice his present age, the result would be equal to his present age. Find A’s present age.","translation":"जर A च्या 6 वर्षांपूर्वीच्या वयाच्या तिप्पट त्याच्या आजच्या वयातून वजा केली, तर येणारे उत्तर त्याच्या आजच्या वयाइतकेच असेल. A चे आजचे वय शोधा.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"A number consists of two digits the digit in the ten’s place is twice the digit in the unit’s place. If 18 be subtracted from the number the digits are reversed. Find the number.","translation":"एका संख्येत दोन अंक आहेत, दशम स्थानचा अंक एकक स्थानच्या अंकापेक्षा दुप्पट आहे. जर संख्येतून 18 वजा केले, तर अंक उलटतात. संख्या शोधा.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"For a certain commodity the demand equation giving demand ‘d’ in kg, for a price ‘p’ in rupees per kg. is d = 100 (10 – p).","translation":"एका विशिष्ट वस्तूसाठी मागणी समीकरण, ‘d’ किलोग्रॅममध्ये मागणी दर्शवते, ‘p’ रुपये प्रति किलो दराने, d = 100 (10 – p) आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If a : b = c : d = e : f = ........................., then each of these ratios is equal (a – c – e – ........) : (b – d – f – .......)","translation":"जर a : b = c : d = e : f = ........................., तर यापैकी प्रत्येक गुणोत्तर (a – c – e – ........) : (b – d – f – .......) समान आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"From (1) ad = bc, or, ad =1 bc , i.e. ad : bc = 1 : 1","translation":"(1) वरून, ad = bc, किंवा, ad =1 bc, म्हणजेच ad : bc = 1 : 1","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Again from (1) a c a+c = = b d b+d  , a+c 2.5 25 5 = = = b+d 1.5 15 3 i.e. a + c : b + d = 5 : 3","translation":"पुन्हा (1) वरून a c a+c = = b d b+d  , a+c 2.5 25 5 = = = b+d 1.5 15 3 म्हणजेच a + c : b + d = 5 : 3","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Hence, the values of ad : bc and a + c : b + d are 1 : 1 and 5 : 3 respectively.","translation":"म्हणून, ad : bc आणि a + c : b + d ची मूल्ये अनुक्रमे 1 : 1 आणि 5 : 3 ���हेत.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Example 2: If a b c = = 3 4 7 , then prove that a +b+c = 2 c","translation":"उदाहरण 2: जर a b c = = 3 4 7 , तर सिद्ध करा की a +b+c = 2 c","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"We have a b c = = 3 4 7 = a+ b+c a+ b+c = 3+ 4+714  a+ b+c ca+ b+c 14 = or = = 2 14 7c7","translation":"आपल्याकडे a b c = = 3 4 7 = a+ b+c a+ b+c = 3+ 4+714  a+ b+c ca+ b+c 14 = किंवा = = 2 14 7c7 आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Example 3: A dealer mixes tea costing ` 6.92 per kg. with tea costing ` 7.77 per kg and sells the mixture at ` 8.80 per kg and earns a profit of 1 17 % 2 on his sale price.","translation":"उदाहरण 3: एक व्यापारी ` 6.92 प्रति किलो दराने चहा ` 7.77 प्रति किलो दराने चहामध्ये मिसळतो आणि मिश्रण ` 8.80 प्रति किलो दराने विकतो आणि त्याच्या विक्री किमतीवर 1 17 % 2 नफा कमावतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"In what proportion does he mix them?","translation":"तो ते कोणत्या प्रमाणात मिसळतो?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Let us first find the cost price (C. P.) of the mixture.","translation":"चला, प्रथम मिश्रणाची खरेदी किंमत (C. P.) शोधूया.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If S. P. is ` 100, profit is 111165 17 Therefore C. P. = (100 - 17 ) = 82 = 2222 `` `","translation":"जर S. P. ` 100 आहे, तर नफा 111165 17 आहे. म्हणून C. P. = (100 - 17 ) = 82 = 2222 `` `","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If S. P. is ` 8.80, C. P. is (165 × 8.80)/(2 × 100) = ` 7.26","translation":"जर S. P. ` 8.80 आहे, तर C. P. (165 × 8.80)/(2 × 100) = ` 7.26 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"C. P. of the mixture per kg = ` 7.26","translation":"मिश्रणाची C. P. प्रति किलो = ` 7.26","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"2nd difference = Profit by selling 1 kg. of 2nd kind @ ` 7.26 = ` 7.77 – ` 7.26 = 51 Paise","translation":"दुसरा फरक = 1 किलो दुसऱ्या प्रकारची @ ` 7.26 दराने विक्री करून नफा = ` 7.77 – ` 7.26 = 51 पैसे","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"1st difference = ` 7.26 – ` 6.92 = 34 Paise","translation":"पहिला फरक = ` 7.26 – ` 6.92 = 34 पैसे","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"We have to mix the two kinds in such a ratio that the amount of profit in the first case must balance the amount of loss in the second case.","translation":"आपल्याला दोन प्रकार अशा प्रमाणात मिसळायचे आहेत की पहिल्या प्रकरणात नफ्याची रक्कम दुसऱ्या प्रकरणात झालेल्या नुकसानीच्या रकमेला संतुलित करेल.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Hence, the required ratio = (2nd diff) : (1st diff.) = 51 : 34 = 3 : 2.","translation":"म्हणून, आवश्यक गुणोत्तर = (दुसरा फरक) : (पहिला फरक) = 51 : 34 = 3 : 2.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Choose the most appropriate option (a) (b) (c) or (d).","translation":"सर्वात योग्य पर्याय निवडा (a) (b) (c) किंवा (d).","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The fourth proportional to 4, 6, 8 is (a) 12(b) 32(c) 48(d) none of these","translation":"4, 6, 8 चे चौथे प्रमाण (a) 12(b) 32(c) 48(d) यापैकी काहीही नाही","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The third proportional to 12, 18 is (a) 24(b) 27(c) 36(d) none of these","translation":"12, 18 चे तिसरे प्रमाण (a) 24(b) 27(c) 36(d) यापैकी काहीही नाही","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The mean proportional between 25, 81 is (a) 40(b) 50(c) 45(d) none of these","translation":"25, 81 मधील मध्य प्रमाण (a) 40(b) 50(c) 45(d) यापैकी काहीही नाही","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Show that 111 a-cb-ac-b a-bb-cc-a ×× x xx is given by (a) 1(b) –1(c) 3(d) 0","translation":"दाखवा की 111 a-cb-ac-b a-bb-cc-a ×× x xx याचे उत्तर (a) 1(b) –1(c) 3(d) 0 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Show that              1 3 2 1 1 2 16 32 2 4 5 5 15 2 16 5 . xx x x xx x is given by (a) 1(b) –1(c) 4(d) 0","translation":"दाखवा की              1 3 2 1 1 2 16 32 2 4 5 5 15 2 16 5 . xx x x xx x याचे उत्तर (a) 1(b) –1(c) 4(d) 0 आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Show that a+bb+cc+a abc bca ×× x xx x xx is given by (a) 0(b) –1(c) 3(d) 1","translation":"दाखवा की a+bb+cc+a abc bca ×× x xx x xx याचे उत्तर (a) 0(b) –1(c) 3(d) 1 आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Show that       222 222 abc a+bb+cc+a bca × × x x x x x x reduces to (a) 1(b) 0(c) –1(d) None","translation":"दाखवा की       222 222 abc a+bb+cc+a bca × × x x x x x x याचे उत्तर (a) 1(b) 0(c) –1(d) यापैकी काही नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Show that 111 b+cc+aa+b a-bb-cc-a c-aa-bb-c ×× x xx reduces to (a) 1(b) 3(c) –1(d) None","translation":"दाखवा की 111 b+cc+aa+b a-bb-cc-a c-aa-bb-c ×× x xx याचे उत्तर (a) 1(b) 3(c) –1(d) यापैकी काही नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Show that abc bca cab ×× xxx xxx reduces to (a) 1(b) 3(c) 0(d) 2","translation":"दाखवा की abc bca cab ×× xxx xxx याचे उत्तर (a) 1(b) 3(c) 0(d) 2 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Show that                    1 11 bca bcca ab cab x x x x x x reduces to (a) –1(b) 0(c) 1(d) None","translation":"दाखवा की                    1 11 bca bcca ab cab x x x x x x याचे उत्तर (a) –1(b) 0(c) 1(d) यापैकी काही नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Show that 2 22222 a +ab+bb+bc+cc+ca+a a bc b ca ×× x xx x xx is given by (a) 1(b) –1(c) 0(d) 3","translation":"दाखवा की 2 22222 a +ab+bb+bc+cc+ca+a a bc b ca ×× x xx x xx याचे उत्तर (a) 1(b) –1(c) 0(d) 3 आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Show that 2 x+y = 4 × 8 × 16, then (x + y) 2 is equal to (a) 16(b) 81(c) 32(d) 64","translation":"दाखवा की 2 x+y = 4 × 8 × 16, तर (x + y) 2 बरोबर (a) 16(b) 81(c) 32(d) 64 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Show that b+c-ac+a-ba+b-c b ca c ab ×× x xx x xx is given by (a) 1(b) 0(c) –1(d) None","translation":"दाखवा की b+c-ac+a-ba+b-c b ca c ab ×× x xx x xx याचे उत्तर (a) 1(b) 0(c) –1(d) यापैकी काही नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Show that 222222 a-ab+bb-bc+cc-ca+a a bc -b -c-a ×× x xx x xx is reduces to (a) 1(b)  2 2 2 -2 a +b +c x (c)  3 3 3 2 a +b +c x (d)  3 3 3 -2 a +b +c x","translation":"दाखवा की 222222 a-ab+bb-bc+cc-ca+a a bc -b -c-a ×× x xx x xx याचे उत्तर (a) 1(b)  2 2 2 -2 a +b +c x (c)  3 3 3 2 a +b +c x (d)  3 3 3 -2 a +b +c x आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"2 -1 -1 2 -1 -1 2 -1 -1 a b c b c a c a b . .x x x –x³ would reduce to zero if cba  is given by (a) 1(b) –1(c) 0(d) None","translation":"2 -1 -1 2 -1 -1 2 -1 -1 a b c b c a c a b . .x x x –x³ शून्य होईल जर cba  याचे उत्तर (a) 1(b) –1(c) 0(d) यापैकी काही नसेल.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The value of z is given by the following if (a) 2(b) 3 2 (c) 3 2 - (d) 9 4","translation":"z ची किंमत खालीलप्रमाणे दिली आहे, जर (a) 2(b) 3 2 (c) 3 2 - (d) 9 4","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"b -cc -aa -b 111 ++ + +1 + +1 + +1x x x x x x would reduce to one if cba  is given by (a) 1(b) 0(c) –1(d) None","translation":"b -cc -aa -b 111 ++ + +1 + +1 + +1x x x x x x हे एक होईल जर cba  याचे उत्तर (a) 1(b) 0(c) –1(d) यापैकी काही नसेल.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"On simplification would reduces to 111 1+z a-b +z a-c 1+z b-c +z b-a 1+z c-a +z c-b + +","translation":"सोपे रूप दिल्यावर 111 1+z a-b +z a-c 1+z b-c +z b-a 1+z c-a +z c-b + +","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If   xy z 5.678 = 0.5678 =10 then (a) 1 1 1 - + =1 x y z (b) 1 1 1 - - =0 x y z (c) 1 1 1 - + =-1 x y z (d) None","translation":"जर   xy z 5.678 = 0.5678 =10 तर (a) 1 1 1 - + =1 x y z (b) 1 1 1 - - =0 x y z (c) 1 1 1 - + =-1 x y z (d) यापैकी काही नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If 1 1 - 3 3 x=4 +4 prove that 3 4x -12x is given by (a) 12(b) 13(c) 15(d) 17","translation":"जर 1 1 - 3 3 x=4 +4 तर सिद्ध करा की 3 4x -12x याचे उत्तर (a) 12(b) 13(c) 15(d) 17 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If 1 1 - 3 3 x=5 +5 prove that 3 5x -15x is given by (a) 25(b) 26(c) 27(d) 30","translation":"जर 1 1 - 3 3 x=5 +5 तर सिद्ध करा की 3 5x -15x याचे उत्तर (a) 25(b) 26(c) 27(d) 30 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If 2 1 3 3 ax +bx +c=0 then the value of 3 2 3 3 a x +b x+c is given by (a) 3abcx(b) –3abcx(c) 3abc(d) –3abc","translation":"जर 2 1 3 3 ax +bx +c=0 तर 3 2 3 3 a x +b x+c ची किंमत (a) 3abcx(b) –3abcx(c) 3abc(d) –3abc आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If p a =b , q b =c , r c =a the value of pqr is given by (a) 0(b) 1(c) –1(d) None","translation":"जर p a =b , q b =c , r c =a तर pqr ची किंमत (a) 0(b) 1(c) –1(d) यापैकी काही नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Putting x = 1, the left-hand side becomes zero.","translation":"x = 1 ठेवल्यास, डावी बाजू शून्य होते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Therefore, (x – 1) is a factor of x³ – 7x + 6.","translation":"म्हणून, (x – 1) हे x³ – 7x + 6 चा घटक आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"We can rewrite the equation x³ – 7x + 6 = 0 to make (x – 1) a factor.","translation":"x³ – 7x + 6 = 0 हे समीकरण (x – 1) घटक दिसेल अशा प्रकारे पुन्हा लिहिता येते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"This can be achieved by rewriting the equation as x³ – x² + x² – x – 6x + 6 = 0.","translation":"हे समीकरण x³ – x² + x² – x – 6x + 6 = 0 असे लिहून साधता येते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The roots of the equation are x = 1, 2, and –3.","translation":"समीकरणाची मुळे x = 1, 2, आणि –3 आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Solve for real x: x³ + x + 2 = 0.","translation":"वास्तविक x साठी सोडवा: x³ + x + 2 = 0.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"By trial, we find that x = –1 makes the left-hand side zero.","translation":"अजमावून पाहिल्यावर, x = –1 मुळे डावी बाजू शून्य होते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"So (x + 1) is a factor of x³ + x + 2.","translation":"म्हणून (x + 1) हे x³ + x + 2 चा घटक आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"We rewrite the equation as x³ + x² – x² – x + 2x + 2 = 0.","translation":"समीकरण x³ + x² – x² – x + 2x + 2 = 0 असे पुन्हा लिहितो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The required solution is x = –1.","translation":"आवश्यक समाधान x = –1 आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The solution of the cubic equation x³ – 6x² + 11x – 6 = 0 is (1, 2, 3).","translation":"x³ – 6x² + 11x – 6 = 0 या घन समीकरणाचे समाधान (1, 2, 3) आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The cubic equation x³ + 2x² – x – 2 = 0 has roots (1, –1, –2).","translation":"घन समीकरण x³ + 2x² – x – 2 = 0 ची मुळे (1, –1, –2) आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"x, x – 4, x + 5 are the factors of the equation x³ + x² – 20x = 0.","translation":"x, x – 4, x + 5 हे x³ + x² – 20x = 0 या समीकरणाचे घटक आहेत.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The factors of the equation 3x³ + 5x² – 3x – 5 = 0 are x + 1, x – 1, 3x + 5.","translation":"3x³ + 5x² – 3x – 5 = 0 या समीकरणाचे घटक x + 1, x – 1, 3x + 5 आहेत.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The roots of the equation x³ + 7x² – 21x – 27 = 0 are (3, –9, –1).","translation":"x³ + 7x² – 21x – 27 = 0 या समीकरणाची मुळे (3, –9, –1) आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The roots of x³ + x² – x – 1 = 0 are (–1, –1, 1).","translation":"x³ + x² – x – 1 = 0 ची मुळे (–1, –1, 1) आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The satisfying values of x for x³ + x² – 20x = 0 are (0, –4, 5).","translation":"x³ + x² – 20x = 0 साठी x ची समाधानकारक मूल्ये (0, –4, 5) आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The roots of the cubic equation x³ – 6x² + 9x – 4 = 0 are (1, 1, 4).","translation":"घन समीकरण x³ – 6x² + 9x – 4 = 0 ची मुळे (1, 1, 4) आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If 4x³ + 8x² – x – 2 = 0, then the value of (2x + 3) is –4, 2, –1.","translation":"जर 4x³ + 8x² – x – 2 = 0, तर (2x + 3) ची किंमत –4, 2, –1 आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The rational root of the equation 2x³ – x² – 4x + 2 = 0 is 1/2.","translation":"समीकरण 2x³ – x² – 4x + 2 = 0 चे परिमेय मूळ 1/2 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The feasible region is the area where all inequalities are simultaneously satisfied.","translation":"शक्य क्षेत्र म्हणजे असा भाग आहे जेथे सर्व असमानता एकाच वेळी पूर्ण होतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The objective function attains its maximum or minimum value at the corner points.","translation":"उद्दिष्टाचे कार्य त्याच्या कोपऱ्याच्या बिंदूंवर कमाल किंवा किमान मूल्य गाठते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Linear inequalities are used to represent constraints in optimization problems.","translation":"अनुकूलन समस्यांमधील निर्बंध दर्शविण्यासाठी रेखीय असमानता वापरल्या जातात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The shaded region represents the solution set of the inequalities.","translation":"छायांकित क्षेत्र असमानतेचा उपाय दर्शवते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The extreme points of the feasible region are also known as corner points.","translation":"शक्य क्षेत्राचे अत्यंत बिंदू कोपरा बिंदू म्हणून देखील ओळखले जातात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"We need to find the common region where all the given conditions are met.","translation":"आपल्याला सामान्य क्षेत्र शोधण्याची आवश्यकता आहे जेथे सर्व दिलेल्या अटी पूर्ण होतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The optimal solution is found at one of the extreme points.","translation":"इष्टतम उपाय अत्यंत बिंदूंवर आढळतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The problem involves maximizing or minimizing an objective function.","translation":"या समस्येमध्ये उद्दिष्टाचे कार्य वाढवणे किंवा कमी करणे समाविष्ट आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The constraints limit the possible values of the variables.","translation":"निर्बंध व्हेरिएबल्सची संभाव्य मूल्ये मर्यादित करतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The graphical method is used to solve linear programming problems.","translation":"रेखीय प्रोग्रामिंग समस्या सोडवण्यासाठी आलेखाचा वापर केला जातो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The manufacturer aims to maximize profit.","translation":"उत्पादकाचा नफा वाढवण्याचा प्रयत्न आहे.","target_lang":"mr","domain":"business","complexity":"simple"}
+{"en":"The company produces two products, A and B.","translation":"कंपनी ए आणि बी हे दोन प्रॉडक्ट तयार करते.","target_lang":"mr","domain":"business","complexity":"simple"}
+{"en":"Each product requires processing in two machines.","translation":"प्रत्येक उत्पादनासाठी दोन मशिनमध्ये प्रक्रिया करणे आवश्यक आहे.","target_lang":"mr","domain":"business","complexity":"simple"}
+{"en":"The available time on each machine is limited.","translation":"प्रत्येक मशीनवर उपलब्ध वेळ मर्यादित आहे.","target_lang":"mr","domain":"business","complexity":"simple"}
+{"en":"The objective is to determine the optimal production plan.","translation":"उद्दिष्ट इष्टतम उत्पादन योजना निश्चित करणे आहे.","target_lang":"mr","domain":"business","complexity":"moderate"}
+{"en":"The inequalities represent the constraints on production.","translation":"असमानता उत्पादनावरील निर्बंध दर्शवतात.","target_lang":"mr","domain":"business","complexity":"moderate"}
+{"en":"The solution must satisfy all the constraints.","translation":"उपाय सर्व निर्बंधांचे समाधान करणे आवश्यक आहे.","target_lang":"mr","domain":"business","complexity":"moderate"}
+{"en":"The company wants to maximize its profit within the given constraints.","translation":"कंपनीला दिलेल्या निर्बंधांमध्ये नफा वाढवायचा आहे.","target_lang":"mr","domain":"business","complexity":"moderate"}
+{"en":"The problem can be solved using linear programming techniques.","translation":"ही समस्या रेखीय प्रोग्रामिंग तंत्रांचा वापर करून सोडवता येते.","target_lang":"mr","domain":"business","complexity":"moderate"}
+{"en":"The goal is to find the best possible outcome.","translation":"सर्वोत्तम संभाव्य परिणाम शोधणे हे ध्येय आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"The number is reversed.","translation":"क्रमांक उलटला आहे.","target_lang":"mr","domain":"mathematics","complexity":"simple"}
+{"en":"Of two numbers, 1/5th of the greater is equal to 1/3rd of the smaller and their sum is 16.","translation":"दोन संख्यांपैकी, मोठ्या संख्येचा १/५ भाग लहान संख्येच्या १/३ भागाएवढा आहे आणि त्यांची बेरीज १६ आहे.","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"y is older than x by 7 years 15 years back x’s age was 3/4 of y’s age. Their present ages are:","translation":"y, x पेक्षा ७ वर्षांनी मोठा आहे. १५ वर्षांपूर्वी x चे वय y च्या वयाच्या ३/४ पट होते. त्यांची आजची वये कोणती?","target_lang":"mr","domain":"mathematics","complexity":"complex"}
+{"en":"The sum of the digits in a three digit number is 12.","translation":"एका तीन अंकी संख्येतील अंकांची बेरीज १२ आहे.","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"Two numbers are such that twice the greater number exceeds twice the smaller one by 18.","translation":"दोन संख्या अशा आहेत की मोठ्या संख्येची दुप्पट लहान संख्येच्या दुप्पटीपेक्षा १८ ने जास्त आहे.","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"The demand and supply equations for a certain commodity are 4q + 7p = 17 and p = q + 7/3 respectively.","translation":"एका विशिष्ट वस्तूसाठी मागणी आणि पुरवठा समीकरणे अनुक्रमे ४q + ७p = १७ आणि p = q + ७/३ आहेत.","target_lang":"mr","domain":"economics","complexity":"complex"}
+{"en":"An equation of the form ax^2 + bx + c = 0 where x is a variable and a, b, c are constants with a ≠ 0 is called a quadratic equation.","translation":"ax^2 + bx + c = 0 या स्वरूपातील समीकरण, जेथे x हा चल आहे आणि a, b, c हे स्थिर आहेत आणि a ≠ 0 आहे, वर्ग समीकरण (quadratic equation) म्हणून ओळखले जाते.","target_lang":"mr","domain":"mathematics","complexity":"complex"}
+{"en":"The value of the variable say x is called the root of the equation.","translation":"x या चलाची किंमत समीकरणाचे मूळ (root) म्हणून ओळखली जाते.","target_lang":"mr","domain":"mathematics","complexity":"simple"}
+{"en":"A quadratic equation has got two roots.","translation":"एका वर्ग समीकरणाला दोन मुळे असतात.","target_lang":"mr","domain":"mathematics","complexity":"simple"}
+{"en":"Sum and Product of the Roots: Let one root be α and the other root be β.","translation":"मुळांची बेरीज आणि गुणाकार: समजा एक मूळ α आहे आणि दुसरे मूळ β आहे.","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"If b^2 – 4ac = 0 the roots are real and equal.","translation":"जर b^2 – 4ac = 0 असेल, तर मुळे वास्तव आणि समान असतात.","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"Irrational roots occur in conjugate pairs.","translation":"अपरिमेय मुळे conjugate जोड्यांमध्ये येतात.","target_lang":"mr","domain":"mathematics","complexity":"complex"}
+{"en":"If one root is reciprocal to the other root then their product is 1.","translation":"जर एक मूळ दुसऱ्या मुळाचा व्यस्त (reciprocal) असेल, तर त्यांचा गुणाकार १ असतो.","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"Solve x^2 – 5x + 6 = 0","translation":"x^2 – ५x + ६ = ० हे समीकरण सोडवा.","target_lang":"mr","domain":"mathematics","complexity":"simple"}
+{"en":"Examine the nature of the roots of the following equations.","translation":"खालील समीकरणांच्या मुळांचे स्वरूप तपासा.","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"If α and β be the roots of x^2 + 7x + 12 = 0 find the equation whose roots are 2α + β and 2β + α.","translation":"जर x^2 + ७x + १२ = ० ची मुळे α आणि β असतील, तर असे समीकरण शोधा ज्याची मुळे २α + β आणि २β + α आहेत.","target_lang":"mr","domain":"mathematics","complexity":"complex"}
+{"en":"If α, β be the roots of 2x^2 – 4x – 1 = 0 find the value of α^2/β + β^2/α.","translation":"जर α, β हे २x^2 – ४x – १ = ० ची मुळे असतील, तर α^2/β + β^2/α ची किंमत शोधा.","target_lang":"mr","domain":"mathematics","complexity":"complex"}
+{"en":"Solve x : 4^x – 3.2^(x+2) + 32 = 0","translation":"x ची किंमत शोधा : ४^x – ३.२^(x+२) + ३२ = ०","target_lang":"mr","domain":"mathematics","complexity":"complex"}
+{"en":"Solve (x/(x-1))^(2/3) - 2(x/(x-1))^(1/3) - 3 = 0","translation":"(x/(x-1))^(2/3) - 2(x/(x-1))^(1/3) - 3 = 0 हे समीकरण सोडवा.","target_lang":"mr","domain":"mathematics","complexity":"complex"}
+{"en":"If one root of the equation is 2 - √3 form the equation given that the roots are irrational","translation":"जर समीकरणाचे एक मूळ २ - √३ असेल, तर समीकरण तयार करा, हे लक्षात घेऊन की मुळे अपरिमेय आहेत.","target_lang":"mr","domain":"mathematics","complexity":"complex"}
+{"en":"The interest is compounded annually.","translation":"व्याज वार्षिक चक्रवाढ पद्धतीने आकारले जाते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The principal amount is ₹2,000.","translation":"मुद्दल ₹2,000 आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The rate of interest per conversion period is 10%.","translation":"प्रत्येक रूपांतरण कालावधीसाठी व्याजाचा दर 10% आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"For semi-annual compounding, the number of conversion periods is 4.","translation":"अर्ध-वार्षिक चक्रवाढसाठी, रूपांतरण कालावधींची संख्या 4 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The compound amount after 2 years is ₹2,420.","translation":"2 वर्षांनंतरची चक्रवाढ रक्कम ₹2,420 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The compound interest is ₹425.76.","translation":"चक्रवाढ व्याज ₹425.76 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Determine the compound amount and compound interest.","translation":"चक्रवाढ रक्कम आणि चक्रवाढ व्याज निश्चित करा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The interest is compounded semi-annually.","translation":"व्याज अर्ध-वार्षिक चक्रवाढ पद्धतीने आकारले जाते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Compute the compound interest for 1½ years.","translation":"1½ वर्षांसाठी चक्रवाढ व्याज मोजा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The interest rate per conversion period is 5%.","translation":"प्रत्येक रूपांतरण कालावधीसाठी व्याजाचा दर 5% आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the sum on which the compound interest will be ₹1,640.","translation":"कोणत्या रकमेवर चक्रवाढ व्याज ₹1,640 होईल ते शोधा.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"What annual rate of interest doubles an investment in 7 years?","translation":"वार्षिक व्याजाचा कोणता दर 7 वर्षात गुंतवणुकीची दुप्पट करेल?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The required rate of interest is 10.41% per annum.","translation":"आवश्यक व्याजाचा दर वार्षिक 10.41% आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"In what time will ₹8,000 amount to ₹8,820?","translation":"किती वेळात ₹8,000 ची रक्कम ₹8,820 होईल?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The number of conversion periods is 2.","translation":"रूपांतरण कालावधींची संख्या 2 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the rate percent per annum.","translation":"वार्षिक व्याज दर शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The interest rate per annum is 10%.","translation":"वार्षिक व्याज दर 10% आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"A certain sum invested amounts to ₹78,030.","translation":"एका विशिष्ट रकमेची गुंतवणूक ₹78,030 होते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the sum invested at the beginning of 1 year.","translation":"1 वर्षाच्या सुरुवातीला गुंतवलेली रक्कम शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the time period of investment.","translation":"गुंतवणुकीचा कालावधी शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The profit on product A is ` 20 each and that on product B is ` 30 each.","translation":"उत्पादन A वर प्रत्येक `20 आणि उत्पादन B वर `30 नफा आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Both types are processed on three machines M1, M2 and M3.","translation":"दोन्ही प्रकार M1, M2 आणि M3 या तीन मशिनवर प्रक्रिया करतात.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The time required in hours by each product and total time available in hours per week on each machine are as follows:","translation":"प्रत्येक उत्पादनासाठी तासांमध्ये लागणारा वेळ आणि प्रत्येक मशीनवर प्रति आठवडा उपलब्ध एकूण वेळ खालीलप्रमाणे आहे:","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The constraints can be formulated taking x 1 = number of units A and x 2 = number of unit of B as (a) x 1 + x 2  12","translation":"निर्बंध x 1 = युनिट्स A ची संख्या आणि x 2 = युनिट B ची संख्या (a) x 1 + x 2  12 असे मानून तयार केले जाऊ शकतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Any linear function that involves an inequality sign is a linear inequality.","translation":"कोणतेही रेखीय कार्य जे असमानतेचे चिन्ह दर्शवते, ते रेखीय असमानता आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The values of the variables that satisfy an inequality are called the solution space.","translation":"असमतेला समाधान देणाऱ्या चलांच्या मूल्यांना सोल्यूशन स्पेस म्हणतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Linear inequalities in two variables may be solved easily by extending our knowledge of straight lines.","translation":"दोन चलांमधील रेखीय असमानता सरळ रेषांच्या ज्ञानाचा विस्तार करून सहज सोडवता येतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"People earn money for spending it on housing, food, clothing, education, entertainment etc.","translation":"लोक घर, अन्न, कपडे, शिक्षण, मनोरंजन इत्यादीवर खर्च करण्यासाठी पैसे कमावतात.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"Sometimes extra expenditures have also to be met with.","translation":"कधीकधी अतिरिक्त खर्चही भागवावे लागतात.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"For example there might be a marriage in the family; one may want to buy house, one may want to set up his or her business, one may want to buy a car and so on.","translation":"उदाहरणार्थ, कुटुंबात लग्न असू शकते; एखाद्याला घर खरेदी करायचे असेल, एखाद्याला स्वतःचा व्यवसाय सुरू करायचा असेल, एखाद्याला कार खरेदी करायची असेल, इत्यादी.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"But most people have to borrow money for such contingencies.","translation":"परंतु बहुतेक लोकांना अशा आकस्मिक गरजांसाठी पैसे उधार घ्यावे लागतात.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"Money can be borrowed from friends or money lenders or Banks.","translation":"पैसे मित्रांकडून, सावकारांकडून किंवा बँकांकडून उधार घेतले जाऊ शकतात.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"This charge is called interest.","translation":"या चार्ला व्याज म्हणतात.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"Interest can be defined as the price paid by a borrower for the use of a lender’s money.","translation":"व्याज म्हणजे कर्जदाराने सावकाराच्या पैशाचा वापर करण्यासाठी दिलेली किंमत.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"Time value of money means that the value of a unity of money is different in different time periods.","translation":"पैशाचे वेळेनुसार मूल्य बदलते, याचा अर्थ पैशाचे मूल्य वेगवेगळ्या वेळेत वेगवेगळे असते.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"The lender has a choice between using his money in different investments.","translation":"सावकाराला त्याचे पैसे वेगवेगळ्या गुंतवणुकीत वापरण्याचा पर्याय असतो.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"Most economies generally exhibit inflation.","translation":"बहुतेक अर्थव्यवस्थांमध्ये सामान्यतः महागाई दिसून येते.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"There is always a risk that the borrower will go bankrupt or otherwise default on the loan.","translation":"कर्जदार दिवाळखोर होईल किंवा कर्जाची परतफेड करण्यास डिफॉल्ट करेल, असा नेहमीच धोका असतो.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"Interest is the price paid by a borrower for the use of a lender’s money.","translation":"व्याज म्हणजे कर्जदाराने सावकाराच्या पैशाचा वापर करण्यासाठी दिलेली किंमत.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"Suppose you borrow (or lend) ` 50,000 for a year and you pay (or receive) ` 55,000 after one year the difference between initial borrowing (or lending) ` 50,000 and end payment (or receipts) ` 55,000 i.e. ` 5,000 is the amount of interest you paid (or earned).","translation":"समजा, तुम्ही एका वर्षासाठी `50,000 कर्ज घेतले (किंवा दिले) आणि एका वर्षानंतर `55,000 भरले (किंवा प्राप्त केले), तर सुरुवातीच्या कर्जाऊ रकमेतील (`50,000) आणि अंतिम पेमेंटमधील (`55,000) फरक म्हणजे `5,000 ही व्याजची रक्कम आहे जी तुम्ही भरली (किंवा कमावली).","target_lang":"mr","domain":"general","complexity":"complex"}
+{"en":"Find 5!, 4! and 6!","translation":"5!, 4! आणि 6! शोधा.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The solution is as follows:","translation":"याचे समाधान खालीलप्रमाणे आहे:","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Find x if 1/9! + 1/10! = x/11!","translation":"x शोधा, जर 1/9! + 1/10! = x/11!","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"A group of persons want themselves to be photographed.","translation":"व्यक्तींचा एक समूह स्वतःचे छायाचित्रण (फोटो) करून घेण्यासाठी तयार आहे.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"The photographer wants to calculate how many films does he need to exhaust all possibilities?","translation":"छायाचित्रकाराला हे मोजायचे आहे की सर्व शक्यता वापरण्यासाठी त्याला किती फिल्म्सची आवश्यकता आहे?","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"The ways of arranging or selecting smaller or equal number of persons or objects from a group of persons or collection of objects with due regard being paid to the order of arrangement or selection, are called permutations.","translation":"व्यक्ती किंवा वस्तूंच्या समूहांमधून लहान किंवा समान संख्येने व्यक्ती किंवा वस्तूंची मांडणी किंवा निवड, मांडणी किंवा निवडीच्या क्रमाला महत्त्व देऊन, याला क्रमचय म्हणतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Suppose the group consists of Mr. Suresh, Mr. Ramesh and Mr. Mahesh.","translation":"समजा, या समूहात श्री. सुरेश, श्री. रमेश आणि श्री. महेश यांचा समावेश आहे.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"Then how many films does the photographer need?","translation":"मग, छायाचित्रकाराला किती फिल्म्सची आवश्यकता आहे?","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"Each one of these possibilities is called a permutation of three persons taken at a time.","translation":"यापैकी प्रत्येक संभाव्यतेला एका वेळी तीन व्यक्तींचा क्रमचय म्हणतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Let us consider the problem of finding the number of ways in which the first r rankings are secured by n students in a class.","translation":"एका वर्गातील n विद्यार्थ्यांपैकी पहिल्या r रँकिंगची संख्या शोधण्याची समस्या विचारात घेऊया.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"As any one of the n students can secure the first rank, the number of ways in which the first rank is secured is n.","translation":"n विद्यार्थ्यांपैकी कोणीही पहिला क्रमांक मिळवू शकतो, त्यामुळे पहिला क्रमांक मिळवण्याच्या पद्धतींची संख्या n आ���े.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Now consider the second rank.","translation":"आता दुसरा क्रमांक विचारात घ्या.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"There are (n – 1) students left and the second rank can be secured by any one of them.","translation":"(n – 1) विद्यार्थी शिल्लक आहेत आणि त्यापैकी कोणीही दुसरा क्रमांक मिळवू शकतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Thus, by applying the generalized fundamental principle, the first three ranks can be secured in n (n – 1) (n – 2) ways .","translation":"अशा प्रकारे, सामान्यीकृत मूलभूत तत्त्व लागू करून, पहिले तीन क्रमांक n (n – 1) (n – 2) मार्गांनी मिळवता येतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The number of permutations of n things when r are chosen at a time n P r =n ( n – 1 ) ( n – 2 ) ... ( n – r + 1 ) where the product has exactly r factors.","translation":"n वस्तूंचे क्रमचय, जेव्हा r एका वेळी निवडले जातात, n P r =n ( n – 1 ) ( n – 2 ) ... ( n – r + 1 ) जेथे गुणाकारात r घटक असतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Number of permutations of n different things taken all n things at a time is given by n P n = n (n – 1) (n – 2) .... (n – n + 1) =n (n – 1) (n – 2) ..... 2.1 = n!...(1)","translation":"n वेगवेगळ्या वस्तूंचे क्रमचय, सर्व n वस्तू एकाच वेळी घेतल्यास, n P n = n (n – 1) (n – 2) .... (n – n + 1) =n (n – 1) (n – 2) ..... 2.1 = n!...(1) द्वारे दिले जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Justification for 0! = 1.","translation":"0! = 1 ची समर्थन.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Evaluate each of 5 P 3 , 10 P 2 , 11 P 5 .","translation":"5 P 3 , 10 P 2 , 11 P 5 यांचे मूल्यांकन करा.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"How many three letters words can be formed using the letters of the words (a) SQUARE and (b) HEXAGON?","translation":"(a) SQUARE आणि (b) HEXAGON या शब्दांतील अक्षरे वापरून किती तीन अक्षरी शब्द तयार करता येतील?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"In how many different ways can five persons stand in a line for a group photograph?","translation":"एका ग्रुप फोटोसाठी पाच व्यक्ती किती वेगवेगळ्या प्रकारे एका रांगेत उभे राहू शकतात?","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"Find the future value of an annuity of ` 500 made annually for 7 years at interest rate of 14% compounded annually.","translation":"वार्षिक 14% व्याज दराने 7 वर्षांसाठी दरवर्षी ` 500 ची वार्षिक योजना (ॲन्युइटी) असल्यास तिची भविष्यकालीन किंमत शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"What is the future value of this annuity after 10 th payment?","translation":"10 व्या हप्त्यानंतर या वार्षिक योजनेची (ॲन्युइटी) भविष्यकालीन किंमत काय असेल?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Z invests ` 10,000 every year starting from today for next 10 years.","translation":"Z दरवर्षी आजपासून पुढील 10 वर्षांसाठी ` 10,000 गुंतवतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Calculate future value of the annuity.","translation":"वार्षिक योजनेची (ॲन्युइटी) भविष्यकालीन किंमत मोजा.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"We have read that future value is tomorrow’s value of today’s money compounded at some interest rate.","translation":"आपण वाचले आहे की भविष्यकालीन मूल्य म्हणजे आजच्या पैशाचे काही व्याज दराने केलेले उद्याचे मूल्���.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If ` 1,070 is the future value of today’s ` 1000 at 7% then ` 1,000 is present value of tomorrow’s ` 1,070 at 7%.","translation":"जर ` 1,070 हे आजच्या ` 1000 चे 7% दराने भविष्यकालीन मूल्य असेल, तर ` 1,000 हे उद्याच्या ` 1,070 चे 7% दराने वर्तमान मूल्य आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"What is the present value of ` 1 to be received after two years compounded annually at 10% interest rate?","translation":"10% व्याज दराने वार्षिक चक्रवाढ पद्धतीने दोन वर्षांनंतर ` 1 मिळवल्यास त्याचे वर्तमान मूल्य काय असेल?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the present value of ` 10,000 to be required after 5 years if the interest rate be 9%.","translation":"जर व्याज दर 9% असेल, तर 5 वर्षांनंतर आवश्यक असलेल्या ` 10,000 चे वर्तमान मूल्य शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"We will now see how we compute present value of an annuity.","translation":"आता आपण पाहूया की वार्षिक योजनांचे (ॲन्युइटी) वर्तमान मूल्य कसे मोजले जाते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Suppose your mom promise you to give you ` 1,000 on every 31 st December for the next five years.","translation":"समजा, तुमची आई तुम्हाला पुढील पाच वर्षांपर्यंत दरवर्षी 31 डिसेंबरला ` 1,000 देण्याचे वचन देते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"How much money will you have after five years from now if you invest this gift of the next five years at 10%?","translation":"जर तुम्ही पुढील पाच वर्षांचे हे गिफ्ट 10% दराने गुंतवले, तर आजपासून पाच वर्षांनंतर तुमच्याकडे किती पैसे असतील?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"For getting the answer we will have to compute the present value of this annuity.","translation":"याचे उत्तर मिळवण्यासाठी, आपल्याला या वार्षिक योजनेचे (ॲन्युइटी) वर्तमान मूल्य मोजावे लागेल.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Thus the present value of annuity of ` 1,000 for 5 years at 10% is ` 3,790.79","translation":"म्हणून, 10% दराने 5 वर्षांसाठी ` 1,000 च्या वार्षिक योजनेचे (ॲन्युइटी) वर्तमान मूल्य ` 3,790.79 आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"A loan with fixed rate of interest is said to be amortized if entire principal and interest are paid over equal periods of time by way of sequence of equal payment.","translation":"एका निश्चित व्याज दराने घेतलेल्या कर्जाचे समान हप्त्यांमध्ये संपूर्ण मूळ रक्कम आणि व्याज समान कालावधीत भरल्यास, कर्जाचे 'ॲमॉर्टायझेशन' (amortization) झाले असे म्हणतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Therefore your dad will have to pay 12 monthly instalments of ` 45,130.43.","translation":"म्हणून, तुमच्या वडिलांना ` 45,130.43 चे 12 मासिक हप्ते भरावे लागतील.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"S borrows ` 5,00,000 to buy a house.","translation":"S घर खरेदी करण्यासाठी ` 5,00,000 कर्ज घेतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"What will be the equal annual instalment?","translation":"समान वार्षिक हप्ता किती असेल?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Y bought a TV costing ` 13,000 by making a down payment of ` 3000 and agreeing to make equal annual payment for four years.","translation":"Y ने ` 3000 भरून आणि चार वर्षांसाठी समान वा���्षिक हप्ते भरण्याचे मान्य करून ` 13,000 किमतीचे टीव्ही खरेदी केले.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"What is the present value of this annuity?","translation":"या वार्षिक योजनेचे (ॲन्युइटी) वर्तमान मूल्य काय आहे?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"How much amount is required to be invested every year so as to accumulate ` 300000 at the end of 10 years if interest is compounded annually at 10%?","translation":"जर 10% दराने वार्षिक चक्रवाढ पद्धतीने व्याज मिळत असेल, तर 10 वर्षांच्या शेवटी ` 300000 जमा करण्यासाठी दरवर्षी किती रक्कम गुंतवावी लागेल?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The net present value of a project is the amount, in current value of rupees, the investment earns after paying cost of capital in each period.","translation":"एका प्रकल्पाचे निव्वळ वर्तमान मूल्य म्हणजे गुंतवणुकीतून प्रत्येक कालावधीत भांडवलाची किंमत भरल्यानंतर मिळणारी, सध्याच्या रुपयांमधील रक्कम.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Determine the net cash inflow in each year of the investment.","translation":"गुंतवणुकीच्या प्रत्येक वर्षातील निव्वळ रोख प्रवाह निश्चित करा.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Select the desired rate of return or discounting rate or Weighted Average Cost of Capital.","translation":"इच्छित परतावा दर किंवा सवलत दर किंवा भारित सरासरी भांडवली खर्च निवडा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the discount factor for each year based on the desired rate of return selected.","translation":"निवडलेल्या इच्छित परतावा दरावर आधारित प्रत्येक वर्षासाठी सवलत घटक शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Determine the present values of the net cash flows by multiplying the cash flows by respective the discount factors of respective period called Present Value (PV) of Cash flows.","translation":"रोख प्रवाहांच्या वर्तमान मूल्यांची गणना करा, रोख प्रवाहांचा त्यांच्या संबंधित कालावधीतील सवलत घटकांनी गुणाकार करून, ज्याला रोख प्रवाहांचे वर्तमान मूल्य (PV) म्हणतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If NPV > 0 Accept the Proposal If NPV < 0 Reject the Proposal","translation":"जर NPV > 0 असेल तर प्रस्ताव स्वीकारा, जर NPV < 0 असेल तर प्रस्ताव नाकारा.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Compute the net present value for a project with a net investment of ` 1,00,000 and net cash flows for year one is ` 55,000; for year two is ` 80,000 and for year three is ` 15,000.","translation":"एका प्रकल्पाचे निव्वळ वर्तमान मूल्य मोजा ज्यामध्ये ` 1,00,000 ची निव्वळ गुंतवणूक आहे आणि पहिल्या वर्षासाठी ` 55,000; दुसऱ्या वर्षासाठी ` 80,000 आणि तिसऱ्या वर्षासाठी ` 15,000 निव्वळ रोख प्रवाह आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The nominal rate is the stated interest rate.","translation":"नाममात्र दर म्हणजे निर्दिष्ट व्याज दर.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"If a bank pays 5% annually on a savings account, then 5% is the nominal interest rate.","translation":"जर एखादी बँक बचत खात्यावर वार्षिक 5% व्याज देत असेल, तर 5% हा नाममात्र व्याज दर आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"This is because inflation lowers the value of money.","translation":"याचे कारण म्हणजे महागाई पैशाचे मूल्य कमी करते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The real interest rate is so named because it states the “real” rate that the lender or investor receives after inflation is factored in.","translation":"वास्तविक व्याज दर असे नाव दिले जाते कारण ते 'वास्तविक' दर दर्शवते जो कर्जदार किंवा गुंतवणूकदाराला महागाई विचारात घेतल्यानंतर मिळतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Nominal Rate of Return – Inflation = Real Rate of Return","translation":"नाममात्र परतावा दर – महागाई = वास्तविक परतावा दर","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"It is the actual equivalent annual rate of interest at which an investment grows in value when interest is credited more often than once a year.","translation":"हे वास्तविक समतुल्य वार्षिक व्याज दर आहे ज्यावर गुंतवणुकीचे मूल्य वाढते, जेव्हा वर्षातून एकदा पेक्षा जास्त व्याज जमा केले जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"A loan with frequent compounding periods will be more expensive than one that compounds annually.","translation":"वारंवार चक्रवाढ कालावधी असलेले कर्ज, वार्षिक चक्रवाढ असलेल्या कर्जापेक्षा अधिक महाग असेल.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Compound Annual Growth Rate (CAGR) is a business and investing specific term for the smoothed annualized gain of an investment over a given time period.","translation":"चक्रवाढ वार्षिक वाढ दर (CAGR) हा व्यवसाय आणि गुंतवणुकीसाठी विशिष्ट शब्द आहे, जो दिलेल्या कालावधीत गुंतवणुकीच्या सरासरी वार्षिक नफ्यासाठी वापरला जातो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"CAGR is often used to describe the growth over a period of time of some element of the business, for example revenue, units delivered, registered users, etc.","translation":"CAGR चा वापर अनेकदा व्यवसायाच्या काही घटकांमध्ये, उदाहरणार्थ, महसूल, वितरित युनिट्स, नोंदणीकृत वापरकर्ते इत्यादींच्या वाढीचे वर्णन करण्यासाठी केला जातो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Calculate Compound annual Growth Rate.","translation":"चक्रवाढ वार्षिक वाढ दर मोजा.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Calculating average returns of investment funds.","translation":"गुंतवणूक निधीच्या सरासरी परताव्याची गणना करणे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Demonstrating and comparing the performance of investment advisors.","translation":"गुंतवणूक सल्लागारांच्या कामगिरीचे प्रदर्शन आणि तुलना करणे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Forecasting future values based on the CAGR of a data series.","translation":"डेटा मालिकेच्या CAGR वर आधारित भविष्यातील मूल्यांचा अंदाज घेणे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Now we calculate,  28 2r 24 2r 4 C C =  ","translation":"आता आपण गणना करूया,  28 2r 24 2r 4 C C =  ","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"or, (2r) (2r–1) ( 2r–2) (2r–3) =    11 28 27 26 25 225 = 11×28×3×26 = 11×7×4×3×13×2 = 11×12×13×14","translation":"किंवा, (2r) (2r–1) ( 2r–2) (2r–3) =    11 28 27 26 25 225 = 11×28×3×26 = 11×7×4×3×13×2 = 11×12×13×14","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Find x if 12 C 5 +2 12 C 4 + 12 C 3 = 14 C x","translation":"12 C 5 +2 12 C 4 + 12 C 3 = 14 C x असल्यास x शोधा","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Solution:L. H. S = 12 C 5 + 2 12 C 4 + 12 C 3 = 12 C 5 + 12 C 4 + 12 C 4 + 12 C 3 = 13 C 5 + 13 C 4 = 14 C 5","translation":"उत्तर: L. H. S = 12 C 5 + 2 12 C 4 + 12 C 3 = 12 C 5 + 12 C 4 + 12 C 4 + 12 C 3 = 13 C 5 + 13 C 4 = 14 C 5","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Also n C r = n C n–r . Therefore 14 C 5 = 14 C 14–5 = 14 C 9","translation":"तसेच n C r = n C n–r . म्हणून 14 C 5 = 14 C 14–5 = 14 C 9","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"This implies, either x = 5 or x = 9.","translation":"याचा अर्थ, x = 5 किंवा x = 9.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Prove by reasoning that (i) n+1 C r = n C r + n C r–1 (ii) n P r = n–1 P r +r n–1 P r–1","translation":"युक्तिवादाने सिद्ध करा की (i) n+1 C r = n C r + n C r–1 (ii) n P r = n–1 P r +r n–1 P r–1","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"As a specified thing can either be included in any combination or excluded from it, the total number of combinations which can be combinations or (n+1) things taken r at a time is the sum of :","translation":"एखादी निर्दिष्ट गोष्ट कोणत्याही संयोजनात समाविष्ट केली जाऊ शकते किंवा त्यातून वगळली जाऊ शकते, (n+1) वस्तू r वेळी घेतल्यास संयोजनांची एकूण संख्या खालीलप्रमाणे आहे:","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"(a) combinations of (n+1) things taken r at time in which one specified thing is always included and (b) the number of combinations of (n+1) things taken r at time from which the specified thing is always excluded.","translation":"(a) (n+1) वस्तूंचे संयोजन r वेळी घेतले जाते, ज्यामध्ये एक निर्दिष्ट गोष्ट नेहमी समाविष्ट असते आणि (b) (n+1) वस्तूंचे संयोजन r वेळी घेतले जाते, ज्यामधून निर्दिष्ट गोष्ट नेहमी वगळली जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Now, in case (a), when a specified thing is always included , we have to find the number of ways of selecting the remaining (r–1) things out of the remaining n things which is n C r–1.","translation":"आता, (a) मध्ये, जेव्हा एखादी निर्दिष्ट गोष्ट नेहमी समाविष्ट केली जाते, तेव्हा आपल्याला उर्वरित n वस्तूंमधून उर्वरित (r–1) वस्तू निवडण्याचे मार्ग शोधावे लागतील, जे n C r–1 आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Again, in case (b), since that specified thing is always excluded, we have to find the number of ways of selecting r things out of the remaining n things, which is n C r .","translation":"पुन्हा, (b) मध्ये, ती निर्दिष्ट गोष्ट नेहमी वगळली जात असल्याने, आपल्याला उर्वरित n वस्तूंमधून r वस्तू निवडण्याचे मार्ग शोधावे लागतील, जे n C r आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Thus, n+1 C r = n C r–1 + n C r","translation":"म्हणून, n+1 C r = n C r–1 + n C r","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"We divide n P r i.e., the number of permutations of n things take r at a time into two groups:","translation":"आम्ही n P r म्हणजेच, n वस्तूंची r वेळी केलेली क्रमवारी दोन गटात विभागतो:","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"(a) those which contain a specified thing (b) those which do not contain a specified thing.","translation":"(a) ज्यामध्ये एक निर्दिष्ट गोष्ट आहे (b) ज्यामध्ये निर्दिष्ट गोष्ट नाही.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"In (a) we fix the particular thing in any one of the r places which can be done in r ways and then fill up the remaining (r–1) places out of (n–1) things which give rise to n–1 P r–1 ways.","translation":"(a) मध्ये, आम्ही r स्थानांपैकी कोणत्याही एका स्थानावर विशिष्ट गोष्ट निश्चित करतो, जी r मार्गांनी करता येते आणि नंतर उर्वरित (n–1) वस्तूंमधून उर्वरित (r–1) स्थाने भरतो, ज्यामुळे n–1 P r–1 मार्ग मिळतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Thus, the number of permutations in case (a) = r × n–1 P r–1.","translation":"म्हणून, (a) मधील क्रमवारीची संख्या = r × n–1 P r–1.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"In case (b), one thing is to be excluded; therefore, r places are to be filled out of (n–1) things. Therefore, number of permutations = n–1 P r","translation":"(b) मध्ये, एक गोष्ट वगळली जाते; म्हणून, (n–1) वस्तूंमधून r स्थाने भरायची आहेत. म्हणून, क्रमवारीची संख्या = n–1 P r","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Thus, total number of permutations = n–1 P r + r. n–1 P r–1 i.e., n P r = n–1 P r +r. n–1 P r–1","translation":"म्हणून, क्रमवारीची एकूण संख्या = n–1 P r + r. n–1 P r–1 म्हणजेच, n P r = n–1 P r +r. n–1 P r–1","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"We now proceed to examine some standard results in permutations and combinations.","translation":"आता आपण क्रमवारी आणि संयोजनांमधील काही प्रमाणित परिणामांची तपासणी करूया.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"These results have special application and hence are dealt with separately.","translation":"या परिणामांना विशेष उपयोग आहे आणि म्हणूनच त्यांची स्वतंत्रपणे चर्चा केली जाते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The number of ways in which 7 girls form a ring is (a) 700(b) 710(c) 720(d) none of these","translation":"7 मुली रिंगमध्ये किती प्रकारे बनू शकतात? (a) 700(b) 710(c) 720(d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"The number of ways in which 7 boys sit in a round table so that two particular boys may sit together is (a) 240(b) 200(c) 120(d) none of these","translation":"7 मुले एका गोल टेबलावर किती प्रकारे बसू शकतात की दोन विशिष्ट मुले एकत्र बसतील? (a) 240(b) 200(c) 120(d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"If 50 different jewels can be set to form a necklace then the number of ways is (a) 2 1 50(b) 2 1 49(c)(d) none of these","translation":"जर 50 वेगवेगळ्या रत्नांचा हार बनवला जाऊ शकतो, तर ते किती प्रकारे करता येईल? (a) 2 1 50(b) 2 1 49(c)(d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is (a) 70(b) 27(c) 72(d) none of these","translation":"3 स्त्रिया आणि 3 पुरुष एका गोल टेबलावर बसू शकतात, जेणेकरून कोणत्याही दोन स्त्रिया एकमेकांजवळ बसतील. हे किती प्रकारे करता येईल? (a) 70(b) 27(c) 72(d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"The number of ways in which the letters of the word `DOGMATIC’ can be arranged is (a) 40,319(b) 40,320(c) 40,321(d) none of these","translation":"`DOGMATIC' या शब्दातील अक्षरे किती प्रकारे मांडता येतील? (a) 40,319(b) 40,320(c) 40,321(d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"The number of arrangements of 10 different things taken 4 at a time in which one particular thing always occurs is (a) 2015(b) 2016(c) 2014(d) none of these","translation":"10 वेगवेगळ्या वस्तू, 4 वेळी घेतल्यास, ज्यात एक विशिष्ट वस्तू नेहमी येते, अशा मांडणीची संख्या किती? (a) 2015(b) 2016(c) 2014(d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"The number of permutations of 10 different things taken 4 at a time in which one particular thing never occurs is (a) 3,020(b) 3,025(c) 3,024(d) none of these","translation":"10 वेगवेगळ्या वस्तू, 4 वेळी घेतल्यास, ज्यात एक विशिष्ट वस्तू कधीच येत नाही, अशा क्रमचयनांची संख्या किती? (a) 3,020(b) 3,025(c) 3,024(d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"Mr. X and Mr. Y enter into a railway compartment having six vacant seats. The number of ways in which they can occupy the seats is (a) 25(b) 31(c) 32(d) 30","translation":"श्री. X आणि श्री. Y एका रेल्वेच्या डब्यात प्रवेश करतात, ज्यात सहा रिकाम्या जागा आहेत. ते किती प्रकारे जागा घेऊ शकतात? (a) 25(b) 31(c) 32(d) 30","target_lang":"mr","domain":"mathematics","complexity":"simple"}
+{"en":"The number of numbers lying between 100 and 1000 can be formed with the digits 1, 2, 3, 4, 5, 6, 7 is (a) 210(b) 200(c) 110(d) none of these","translation":"1, 2, 3, 4, 5, 6, 7 या अंकांनी 100 आणि 1000 च्या दरम्यान किती संख्या तयार करता येतील? (a) 210(b) 200(c) 110(d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"The number of numbers lying between 10 and 1000 can be formed with the digits 2,3,4,0,8,9 is (a) 124(b) 120(c) 125(d) none of these","translation":"2, 3, 4, 0, 8, 9 या अंकांनी 10 आणि 1000 च्या दरम्यान किती संख्या तयार करता येतील? (a) 124(b) 120(c) 125(d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"In a group of boys the number of arrangement of 4 boys is 12 times the number of arrangements of 2 boys. The number of boys in the group is (a) 10(b) 8(c) 6(d) none of these","translation":"मुलांच्या एका गटात, 4 मुलांची मांडणी 2 मुलांच्या मांडणीच्या 12 पट आहे. गटात मुलांची संख्या किती आहे? (a) 10(b) 8(c) 6(d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"complex"}
+{"en":"The value of  10 r=1 r r. P is r (a) 11 P 11 (b) 11 P 11 –1(c) 11 P 11 +1(d) none of these","translation":" 10 r=1 r r. P ची किंमत किती आहे? r (a) 11 P 11 (b) 11 P 11 –1(c) 11 P 11 +1(d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"complex"}
+{"en":"The total number of 9 digit numbers of different digits is (a) 10 9 (b) 8 9 (c) 9 9 (d) none of these","translation":"भिन्न अंकांनी बनलेल्या 9 अंकी संख्यांची एकूण संख्या किती आहे? (a) 10 9 (b) 8 9 (c) 9 9 (d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"The number of ways in which 6 men can be arranged in a row so that the particular 3 men sit together, is (a) 4 P 4 (b) 4 P 4 × 3 P 3 (c) ( 3 ) 2 (d) none of these","translation":"6 पुरुष एका रांगेत किती प्रकारे बसू शकतात की विशिष्ट 3 पुरुष एकत्र बसतील? (a) 4 P 4 (b) 4 P 4 × 3 P 3 (c) ( 3 ) 2 (d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"There are 5 speakers A, B, C, D and E. The number of ways in which A will speak always before B is (a) 24(b) 4 × 2 (c) 5 (d) none of these","translation":"A, B, C, D आणि E असे 5 वक्ते आहेत. A नेहमी B च्या आधी बोलेल, अशा स्थितीत ते किती प्रकारे बोलू शकतात? (a) 24(b) 4 × 2 (c) 5 (d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"There are 10 trains plying between Calcutta and Delhi. The number of ways in which a person can go from Calcutta to Delhi and return by a different train is (a) 99(b) 90(c) 80(d) none of these","translation":"कलकत्ता आणि दिल्लीच्या दरम्यान 10 गाड्या धावतात. एक व्यक्ती कलकत्त्याहून दिल्लीला जाऊन परत येण्यासाठी वेगळ्या गाडीने प्रवास करू शकते, अशा मार्गांची संख्या किती? (a) 99(b) 90(c) 80(d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"moderate"}
+{"en":"The number of ways in which 8 sweats of different sizes can be distributed among 8 persons of different ages so that the largest sweat always goes to be younger assuming that each one of then gets a sweat is (a) 8 (b) 5040(c) 5039(d) none of these","translation":"8 वेगवेगळ्या आकाराचे 8 स्वेट (Sweat) वेगवेगळ्या वयाच्या 8 व्यक्तींमध्ये किती प्रकारे वितरित केले जाऊ शकतात, जेणेकरून सर्वात मोठे स्वेट नेहमी लहान व्यक्तीकडे जाईल, असे गृहीत धरून की प्रत्येकाला एक स्वेट मिळतो? (a) 8 (b) 5040(c) 5039(d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"complex"}
+{"en":"The number of arrangements in which the letters of the word `MONDAY’ be arranged so that the words thus formed begin with M and do not end with N is (a) 720(b) 120(c) 96(d) none of these","translation":"`MONDAY' या शब्दातील अक्षरांची मांडणी किती प्रकारे करता येईल, जेणेकरून तयार होणारे शब्द M ने सुरू होतील आणि N ने संपणार नाहीत? (a) 720(b) 120(c) 96(d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"complex"}
+{"en":"The total number of ways in which six ‘+’ and four ‘–‘ signs can be arranged in a line such that no two ‘–’ signs occur together is (a) 7 / 3 (b) 6 × 7 / 3 (c) 35(d) none of these","translation":"सहा '+' आणि चार '–' चिन्हे एका ओळीत अशा प्रकारे किती प्रकारे मांडता येतील की कोणतीही दोन '–' चिन्हे एकत्र येणार नाहीत? (a) 7 / 3 (b) 6 × 7 / 3 (c) 35(d) यापैकी काहीही नाही","target_lang":"mr","domain":"mathematics","complexity":"complex"}
+{"en":"The number of ways in which the letters of the word `MOBILE’ be arranged so that consonants always occupy the odd places is (a) 36(b) 63(c) 30(d) none of these.","translation":"`MOBILE' या शब्दातील अक्षरे किती प्रकारे मांडता येतील की व्यंजन नेहमी विषम स्थानावर येतील? (a) 36(b) 63(c) 30(d) यापैकी काहीही नाही.","target_lang":"mr","domain":"mathematics","complexity":"complex"}
+{"en":"The formula for the nth term of a geometric progression is a * r^(n-1).","translation":"गुणोत्तर श्रेणीच्या n व्या पदाचे सूत्र a * r^(n-1) आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"What is the common ratio in the sequence 2, 4, 8, 16...?","translation":"2, 4, 8, 16... या क्रमामध्ये सामान्य गुणोत्तर काय आहे?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The sum of an infinite geometric series converges if the absolute value of the common ratio is less than 1.","translation":"जर सामान्य गुणोत्तराचे निरपेक्ष मूल्य 1 पेक्षा कमी असेल, तर अनंत गुणोत्तर श्रेणीची बेरीज निश्चित होते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Find the next number in the series: 1, 3, 9, 27...","translation":"या मालिकेत पुढील संख्या शोधा: 1, 3, 9, 27...","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Arithmetic progressions are characterized by a constant difference between consecutive terms.","translation":"अंकगणितीय श्रेणीची ओळख लागोपाठच्या पदांमधील स्थिर फरकाने होते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The bank offers a fixed deposit with compound interest.","translation":"बँक चक्रवाढ व्याजासह मुदत ठेव योजना देते.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"Could you please explain the concept of geometric mean?","translation":"कृपया भूमितीय średy ची संकल्पना स्पष्ट करू शकाल?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The population grew exponentially over the last decade.","translation":"गेल्या दशकात लोकसंख्या झपाट्याने वाढली.","target_lang":"mr","domain":"news","complexity":"moderate"}
+{"en":"He invested in a series of stocks to diversify his portfolio.","translation":"त्यांनी त्यांच्या पोर्टफोलिओमध्ये विविधता आणण्यासाठी अनेक शेअर्समध्ये गुंतवणूक केली.","target_lang":"mr","domain":"business","complexity":"moderate"}
+{"en":"The company's profits increased in a geometric progression.","translation":"कंपनीचा नफा भूमितीय श्रेणीत वाढला.","target_lang":"mr","domain":"business","complexity":"moderate"}
+{"en":"The sum of the first n natural numbers is n(n+1)/2.","translation":"पहिल्या n नैसर्गिक संख्यांची बेरीज n(n+1)/2 आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"What is the sum of the series 1/2 + 1/4 + 1/8 + ... to infinity?","translation":"1/2 + 1/4 + 1/8 + ... या श्रेणीची अनंतपर्यंत बेरीज किती आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The terms of the sequence are decreasing.","translation":"श्रेणीची पदे घटत आहेत.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The common difference in an arithmetic progression is constant.","translation":"अंकगणितीय श्रेणीतील सामान्य फरक स्थिर असतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The series converges to a finite value.","translation":"श्रेणी एका निश्चित मूल्यावर जमा होते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The interest rate is compounded annually.","translation":"व्याज वार्षिक चक्रवाढ पद्धतीने आकारले जाते.","target_lang":"mr","domain":"business","complexity":"simple"}
+{"en":"The geometric mean is used to find the average of a set of numbers.","translation":"भूमितीय średy चा उपयोग संख्यांच्या संचाचा सरासरी काढण्यासाठी केला जातो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The sequence follows a specific pattern.","translation":"अनुक्रम एका विशिष्ट नमुन्याचे अनुसरण करतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The loan is repaid in equal installments.","translation":"कर्ज समान हप्त्यांमध्ये परतफेड केले जाते.","target_lang":"mr","domain":"business","complexity":"simple"}
+{"en":"The value of the investment grew exponentially.","translation":"गुंतवणुकीची किंमत झपाट्याने वाढली.","target_lang":"mr","domain":"business","complexity":"moderate"}
+{"en":"The number of ways in which the crew can be arranged is _________.","translation":"कर्मचाऱ्यांची व्यवस्था लावण्याची एकूण संख्या _________ आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"In how many ways the party can be formed if two particular women refuse to join it?","translation":"दोन विशिष्ट स्त्रिया सामील होण्यास नकार देत असतील, तर पार्टी किती प्रकारे तयार करता येईल?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"In how many ways you can do it so that the team contains exactly 3 bowlers and 1 wicket-keeper?","translation":"संघामध्ये नेमके 3 गोलंदाज आणि 1 यष्टीरक्षक असतील, अशा प्रकारे तुम्ही ते किती प्रकारे करू शकता?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Would your answer be different if the team contains at least 3 bowlers and at least 1 wicket-keeper?","translation":"जर संघात कमीतकमी 3 गोलंदाज आणि कमीतकमी 1 यष्टीरक्षक असतील, तर तुमचे उत्तर वेगळे असेल का?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Then the number of times 2 men ‘A’ and ‘B’ are together is __________.","translation":"मग 2 पुरुष ‘A’ आणि ‘B’ किती वेळा एकत्र येतील?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"In question No.(115) the number of times 3 men ‘C’ ‘D’ and ‘E’ are together is ____.","translation":"प्रश्न क्र. (115) मध्ये, 3 पुरुष ‘C’, ‘D’ आणि ‘E’ किती वेळा एकत्र येतील?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Then the value of n is __________.","translation":"मग n ची किंमत __________ आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The number of combinations that can be made by taking 4 letters of the word `COMBINATION’ is ______.","translation":" ‘COMBINATION’ या शब्दातील 4 अक्षरे घेऊन तयार करता येणाऱ्या संयोजनांची संख्या ______ आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If 18 18 n n+2 C = C then the value of n is __________","translation":"जर 18 18 n n+2 C = C असेल, तर n ची किंमत __________ आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If n n-2 63 91 C ÷ C = 4 then the value of n is __________","translation":"जर n n-2 63 91 C ÷ C = 4 असेल, तर n ची किंमत __________ आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"In order to pass PE-II examination minimum marks have to be secured in each of 7 subjects. In how many ways can a pupil fail?","translation":"PE-II परीक्षा उत्तीर्ण होण्यासाठी, 7 पैकी प्रत्येक विषयात किमान गुण मिळवणे आवश्यक आहे. एक विद्यार्थी किती प्रकारे अनुत्तीर्ण होऊ शकतो?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"In how many ways you can answer one or more questions out of 6 questions each having an alternative?","translation":"प्रत्येकी एक पर्याय असलेल्या 6 प्रश्नांपैकी तुम्ही किती प्रकारे एका किंवा अधिक प्रश्नांची उत्तरे देऊ शकता?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"There are 12 points in a plane no 3 of which are collinear except that 6 points which are collinear. The number of different straight lines is _________.","translation":"एका समतलात 12 बिंदू आहेत, ज्यापैकी 3 बिंदू एकरेषीय नाहीत, परंतु 6 बिंदू एकरेषीय आहेत. वेगवेगळ्या सरळ रेषांची संख्या _________ आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The number of different triangles formed by joining the straight lines is ________.","translation":"सरळ रेषा जोडून तयार होणाऱ्या वेगवेगळ्या त्रिकोणांची संख्या _________ आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The numbers of ways in which this can be done is ______. ","translation":"हे किती प्रकारे करता येईल?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"If a particular teacher is included the number of ways in which this can be done is _________.","translation":"जर एखादे विशिष्ट शिक्षक सामील असतील, तर हे किती प्रकारे करता येईल?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If a particular student is excluded the number of ways in which this can be done is _________.","translation":"जर एखादा विशिष्ट विद्यार्थी वगळला गेला, तर हे किती प्रकारे करता येईल?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"In how many ways 21 red balls and 19 blue balls can be arranged in a row so that no two blue balls are together?","translation":"21 लाल चेंडू आणि 19 निळे चेंडू एका ओळीत किती प्रकारे मांडता येतील की जेणेकरून दोन निळे चेंडू एकत्र येणार नाहीत?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"In forming a committee of 5 out of 5 males and 6 females how many choices you have to make so that there are 3 males and 2 females?","translation":"5 पुरुष आणि 6 स्त्रिया यांच्यामधून 5 जणांची समिती तयार करताना, 3 पुरुष आणि 2 स्त्रिया असाव्यात यासाठी तुम्हाला किती पर्याय निवडावे लागतील?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"How many choices you have to make if there are 2 males?","translation":"जर 2 पुरुष असतील, तर तुम्हाला किती पर्याय निवडावे लागतील?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Eight guests have to be seated 4 on each side of a long rectangular table.","translation":"आठ पाहुण्यांना एका लांब आयताकृती टेबलाच्या दोन्ही बाजूंना प्रत्येकी 4 याप्रमाणे बसवायचे आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"2 particular guests desire to sit on one side of the table and 3 on the other side.","translation":"2 विशिष्ट पाहुण्यांना टेबलाच्या एका बाजूला आणि 3 पाहुण्यांना दुसऱ्या बाजूला बसायचे आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The number of ways in which the sitting arrangements can be made is (a) 1732(b) 1728(c) 1730(d) 1278.","translation":"बसण्याची व्यवस्था किती प्रकारे करता येईल? (a) 1732 (b) 1728 (c) 1730 (d) 1278.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"A question paper contains 6 questions, each having an alternative.","translation":"एका प्रश्नपत्रिकेत 6 प्रश्न आहेत, प्रत्येकाला एक पर्याय आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The number of ways an examine can answer one or more questions is (a) 720(b) 728(c) 729(d) none of these.","translation":"परीक्षार्थी किती प्रकारे एकापेक्षा जास्त प्रश्नांची उत्तरे देऊ शकतो? (a) 720 (b) 728 (c) 729 (d) यापैकी नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"51 c 31 is equal to (a) 51 c 20 (b) 2. 50 c 20 (c) 2. 45 c 15 (d) none of these.","translation":"51 c 31 हे कशाच्या बरोबर आहे? (a) 51 c 20 (b) 2. 50 c 20 (c) 2. 45 c 15 (d) यापैकी नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The number of words that can be made by rearranging the letters of the word APURNA so that vowels and consonants appear alternate is (a) 18(b) 35(c) 36(d) none of these.","translation":"APURNA या शब्दातील अक्षरांची पुनर्रचना करून किती शब्द तयार करता येतील, ज्यात स्वर आणि व्यंजन एकामागोमाग येतील? (a) 18 (b) 35 (c) 36 (d) यापैकी नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The number of arrangement of the letters of the word `COMMERCE’ is (a) 8 (b) 8 / ( 2 2 2) (c) 7 !(d) none of these.","translation":"COMMERCE या शब्दातील अक्षरांची किती प्रकारे मांडणी करता येईल? (a) 8 (b) 8 / ( 2 2 2) (c) 7 ! (d) यापैकी नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"A candidate is required to answer 6 out of 12 questions which are divided into two groups containing 6 questions in each group.","translation":"एका उमेदवाराला 12 प्रश्नांपैकी 6 प्रश्नांची उत्तरे द्यायची आहेत, जे दोन गटांमध्ये विभागलेले आहेत, ज्यात प्रत्येक गटात 6 प्रश्न आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"He is not permitted to attempt not more than four from any group.","translation":"त���याला कोणत्याही गटातून 4 पेक्षा जास्त प्रश्न सोडवण्याची परवानगी नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The number of choices are. (a) 750(b) 850(c) 800(d) none of these.","translation":"पर्यायांची संख्या किती आहे? (a) 750 (b) 850 (c) 800 (d) यापैकी नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The results of 8 matches (Win, Loss or Draw) are to be predicted.","translation":"8 सामन्यांचे निकाल (विजय, हार किंवा बरोबरी) यांचा अंदाज वर्तवायचा आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The number of different forecasts containing exactly 6 correct results is (a) 316(b) 214(c) 112(d) none of these.","translation":"अचूक 6 निकाल असलेले किती वेगवेगळे अंदाज असतील? (a) 316 (b) 214 (c) 112 (d) यापैकी नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The number of ways in which 8 different beads be strung on a necklace is (a) 2500(b) 2520(c) 2250(d) none of these.","translation":"8 वेगवेगळ्या मण्यांची माळ किती प्रकारे बनवता येईल? (a) 2500 (b) 2520 (c) 2250 (d) यापैकी नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The number of different factors the number 75,600 has is (a) 120(b) 121(c) 119(d) none of these.","translation":"75,600 या संख्येचे किती भिन्न घटक आहेत? (a) 120 (b) 121 (c) 119 (d) यापैकी नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The number of 4 digit numbers formed with the digits 1, 1, 2, 2, 3, 4 is (a) 100(b) 101(c) 201(d) none of these.","translation":"1, 1, 2, 2, 3, 4 या अंकांनी तयार होणाऱ्या 4 अंकी संख्या किती? (a) 100 (b) 101 (c) 201 (d) यापैकी नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The number of ways a person can contribute to a fund out of 1 ten-rupee note, 1 five-rupee note, 1 two-rupee and 1 one rupee note is (a) 15(b) 25(c) 10(d) none of these.","translation":"एका व्यक्तीला 10 रुपयांची नोट, 5 रुपयांची नोट, 2 रुपये आणि 1 रुपयाच्या नोटमधून फंडमध्ये किती प्रकारे योगदान देता येईल? (a) 15 (b) 25 (c) 10 (d) यापैकी नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The number of ways in which 9 things can be divided into twice groups containing 2,3, and 4 things respectively is (a) 1250(b) 1260(c) 1200(d) none of these.","translation":"9 वस्तूंचे 2, 3 आणि 4 वस्तूंच्या गटात विभाजन किती प्रकारे करता येईल? (a) 1250 (b) 1260 (c) 1200 (d) यापैकी नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"(n–1) P r + r. (n–1) P (r–1) is equal to (a) n C r (b)  / n r n r (c) n p r (d) none of these.","translation":"(n–1) P r + r. (n–1) P (r–1) हे कशाच्या बरोबर आहे? (a) n C r (b)  / n r n r (c) n p r (d) यापैकी नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"2n can be written as (a) 2 n { 1.3.5....(2n–1)} n (b) 2 n n (c) {1.3.5.....(2n –1)} (d) none of these.","translation":"2n हे कसे लिहिता येईल? (a) 2 n { 1.3.5....(2n–1)} n (b) 2 n n (c) {1.3.5.....(2n –1)} (d) यापैकी नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The value of the series is a complex mathematical problem.","translation":"श्रेणीचे मूल्य एक गुंतागुंतीचे गणिती समस्या आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The Institute of Chartered Accountants of India provides this material.","translation":"इन्स्टिट्यूट ऑफ चार्टर्ड अकाउंटंट्स ऑफ इंडिया हे साहित्य पुरवते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"What is the sum of the series?","translation":"श्रेणीची बेरीज किती आहे?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The formula for calculating the sum of n terms is crucial.","translation":"n पदां���ी बेरीज मोजण्याचे सूत्र महत्त्वाचे आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The series involves arithmetic and geometric progressions.","translation":"या मालिकेत अंकगणित आणि भूमितीय प्रगतीचा समावेश आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the value of n for which the sum exceeds 7000.","translation":"n ची किंमत शोधा ज्यासाठी बेरीज 7000 पेक्षा जास्त आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The product of the terms in a geometric progression is important.","translation":"भूमितीय प्रगतीमधील पदांचा गुणाकार महत्त्वाचा आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The common ratio plays a key role in the series.","translation":"सामायिक गुणोत्तर मालिकेत महत्त्वाची भूमिका बजावते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The sum of the series can be determined using specific formulas.","translation":"विशिष्ट सूत्रे वापरून श्रेणीची बेरीज निश्चित केली जाऊ शकते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The given series is a geometric progression.","translation":"दिलेली मालिका भूमितीय प्रगती आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The solution requires careful application of mathematical principles.","translation":"या समाधानासाठी गणिती तत्त्वांचा काळजीपूर्वक वापर करणे आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The problem involves finding the sum of a series.","translation":"या समस्येमध्ये श्रेणीची बेरीज शोधणे समाविष्ट आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The series converges to a specific value.","translation":"मालिका एका विशिष्ट मूल्यावर केंद्रित होते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The terms of the series follow a specific pattern.","translation":"मालिकेतील पदे एका विशिष्ट नमुन्याचे अनुसरण करतात.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The question tests your understanding of sequences and series.","translation":"हा प्रश्न तुमची क्रम आणि श्रेणीची समज तपासतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The solution involves algebraic manipulation.","translation":"या समाधानात बीजगणितीय फेरफार समाविष्ट आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The series is an example of a geometric progression.","translation":"ही मालिका भूमितीय प्रगतीचे उदाहरण आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The problem requires knowledge of mathematical formulas.","translation":"या समस्येसाठी गणिती सूत्रांचे ज्ञान आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The sum of the infinite series can be calculated.","translation":"अनंत श्रेणीची बेरीज मोजली जाऊ शकते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The answer is derived using the properties of G.P.","translation":"उत्तर G.P. च्या गुणधर्मांचा वापर करून काढले आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The sum of the first n terms of a geometric progression (GP) is given by a(1 - r^n) / (1 - r) when the common ratio r is less than 1.","translation":"गुणोत्तर श्रेणीच्या (GP) पहिल्या n पदांची बेरीज a(1 - r^n) / (1 - r) असते, जेव्हा सामान्य गुणोत्तर r हे 1 पेक्षा कमी असते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If three numbers are in Arithmetic Progression (AP) and their sum is 21, and if 1, 5, and 15 are added to them respectively, they form a GP, then the numbers are 5, 7, and 9.","translation":"जर तीन संख्या अंकगणिती श्रेणीत (AP) असतील आणि त्यांची बेरीज 21 असेल, आणि जर त्यामध्ये अनुक्रमे 1, 5, आणि 15 मिळवले, तर GP तयार होते, तर त्या संख्या 5, 7, आणि 9 आहेत.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The sum of the infinite geometric series 1 + 2/3 + 4/9 + ... is 3.","translation":"अनंत गुणोत्तर श्रेणी 1 + 2/3 + 4/9 + ... ची बेरीज 3 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The common ratio of a GP, where the sum of the first two terms is 5/3 and the sum to infinity is 3, is 2/3.","translation":"एका GP चे सामान्य गुणोत्तर, ज्यामध्ये पहिल्या दोन पदांची बेरीज 5/3 आहे आणि अनंत पदांची बेरीज 3 आहे, ते 2/3 आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If p, q, and r are in AP and x, y, and z are in GP, then x^(q-r) * y^(r-p) * z^(p-q) equals 1.","translation":"जर p, q, आणि r हे AP मध्ये असतील आणि x, y, आणि z हे GP मध्ये असतील, तर x^(q-r) * y^(r-p) * z^(p-q) हे 1 च्या बरोबर आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The sum of three numbers in GP is 70. If the two extremes are multiplied by 4 and the mean by 5, the products are in AP. The numbers are 10, 20, and 40.","translation":"GP मधील तीन संख्यांची बेरीज 70 आहे. जर दोन टोकांना 4 ने गुणले आणि मध्यभागी 5 ने गुणले, तर गुणाकार AP मध्ये आहेत. त्या संख्या 10, 20, आणि 40 आहेत.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The sum of 3 numbers in AP is 15. If 1, 4, and 19 are added to them respectively, the results are in GP. The numbers are 2, 5, and 8.","translation":"AP मधील 3 संख्यांची बेरीज 15 आहे. जर त्यामध्ये अनुक्रमे 1, 4, आणि 19 मिळवले, तर येणारे निकाल GP मध्ये आहेत. त्या संख्या 2, 5, आणि 8 आहेत.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Given x, y, z are in GP and x^p = y^q = z^σ, then 1/p, 1/q, 1/σ are in AP.","translation":"जर x, y, z हे GP मध्ये असतील आणि x^p = y^q = z^σ, तर 1/p, 1/q, 1/σ हे AP मध्ये आहेत.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If the terms 2x, (x+10), and (3x+2) are in AP, the value of x is 6.","translation":"जर 2x, (x+10), आणि (3x+2) ही पदे AP मध्ये असतील, तर x ची किंमत 6 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If A is the Arithmetic Mean (AM) of two positive unequal quantities x and y, and G is their Geometric Mean (GM), then A > G.","translation":"जर A हे दोन धन असमान राशी x आणि y चे अंकगणितीय मध्य (AM) आहे, आणि G हे त्यांचे भूमितीय मध्य (GM) आहे, तर A > G.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The AM of two positive numbers is 40 and their GM is 24. The numbers are 72 and 8.","translation":"दोन धन संख्यांचा AM 40 आहे आणि त्यांचा GM 24 आहे. त्या संख्या 72 आणि 8 आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Three numbers are in AP and their sum is 15. If 8, 6, and 4 are added to them respectively, the numbers are in GP. The numbers are 3, 5, and 7.","translation":"तीन संख्या AP मध्ये आहेत आणि त्यांची बेरीज 15 आहे. जर त्यामध्ये अनुक्रमे 8, 6, आणि 4 मिळवले, तर संख्या GP मध्ये आहेत. त्या संख्या 3, 5, आणि 7 आहेत.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The sum of four numbers in GP is 60 and the AM of the first and the last is 18. The numbers are 4, 8, 16, and 32.","translation":"GP मधील चार संख्यांची बेरीज 60 आहे आणि पहिल्या आणि शेवटच्या संख्येचा AM 18 आहे. त���या संख्या 4, 8, 16, आणि 32 आहेत.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"A sum of ₹6240 is paid off in 30 installments such that each installment is ₹10 more than the preceding installment. The value of the 1st installment is ₹36.","translation":"₹6240 ची रक्कम 30 हप्त्यांमध्ये फेडली जाते, अशा प्रकारे की प्रत्येक हप्ता मागील हप्त्यापेक्षा ₹10 जास्त आहे. पहिल्या हप्त्याची किंमत ₹36 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If x, y, z are in AP and x, y, (z + 1) are in GP then z = x - y.","translation":"जर x, y, z हे AP मध्ये असतील आणि x, y, (z + 1) हे GP मध्ये असतील तर z = x - y.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The numbers x, 8, y are in GP and the numbers x, y, -8 are in AP. The values of x and y are 16 and 4.","translation":"संख्या x, 8, y GP मध्ये आहेत आणि संख्या x, y, -8 AP मध्ये आहेत. x आणि y ची किंमत 16 आणि 4 आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The nth term of the series 16, 8, 4,... is 1/2^(n-1). The value of n is 20.","translation":"16, 8, 4,... या श्रेणीचे n वे पद 1/2^(n-1) आहे. n ची किंमत 20 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The sum of n terms of a GP whose first term is 1 and the common ratio is 1/2, is equal to 127/128. The value of n is 7.","translation":"एका GP च्या n पदांची बेरीज, ज्याचे पहिले पद 1 आहे आणि सामान्य गुणोत्तर 1/2 आहे, 127/128 च्या बरोबर आहे. n ची किंमत 7 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If t4 of a GP is x, t10 = y and t16 = z, then y^2 = xz.","translation":"जर GP चे t4 = x, t10 = y आणि t16 = z, तर y^2 = xz.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If x, y, z are in GP, then y^2 = xz.","translation":"जर x, y, z हे GP मध्ये असतील, तर y^2 = xz.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The limit of a function is a fundamental concept in calculus.","translation":"एका फलनाची मर्यादा कॅल्कुलसमध्ये एक मूलभूत संकल्पना आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Finding the limit involves analyzing the behavior of the function as the input approaches a certain value.","translation":"मर्यादा शोधणे म्हणजे इनपुट एका विशिष्ट मूल्याच्या जवळ जाताना फलनाच्या वर्तनाचे विश्लेषण करणे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The concept of limits is crucial for understanding continuity and derivatives.","translation":"मर्यादेची संकल्पना सातत्य आणि डेरिव्हेटिव्ह्ज (derivates) समजून घेण्यासाठी महत्त्वपूर्ण आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Let's evaluate the limit of the function as x approaches 2.","translation":"चला, x 2 च्या जवळ जाताना फलनाची मर्यादा मोजूया.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The left-hand limit and the right-hand limit must be equal for the limit to exist.","translation":"मर्यादा अस्तित्वात येण्यासाठी, डावीकडील मर्यादा आणि उजवीकडील मर्यादा समान असणे आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If the limit exists, the function is said to be continuous at that point.","translation":"जर मर्यादा अस्तित्वात असेल, तर त्या बिंदूवर फलन सतत आहे असे म्हटले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The derivative of a function is also defined using the concept of limits.","translation":"एका फलनाचे डेरीव्हेटिव्ह (derivative) देखील मर्यादांच्या संकल्पनेचा वापर करून परिभाषित केले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"We can use limits to analyze the behavior of a function at infinity.","translation":"अनंत (infinity) वर फलनाच्या वर्तनाचे विश्लेषण करण्यासाठी आपण मर्यादा वापरू शकतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The limit helps us understand how a function changes as its input changes.","translation":"इनपुट बदलल्यास फलन कसे बदलते हे समजून घेण्यासाठी मर्यादा मदत करते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The concept of limits is essential for understanding calculus.","translation":"कॅल्कुलस समजून घेण्यासाठी मर्यादांची संकल्पना आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The news reported a significant increase in the stock market.","translation":"बाजारपेठेत मोठी वाढ झाल्याचे बातमीत नमूद केले आहे.","target_lang":"mr","domain":"news","complexity":"simple"}
+{"en":"The government announced new economic policies.","translation":"सरकारने नवीन आर्थिक धोरणे जाहीर केली.","target_lang":"mr","domain":"news","complexity":"simple"}
+{"en":"The company is facing some financial challenges.","translation":"कंपनीला काही आर्थिक अडचणींचा सामना करावा लागत आहे.","target_lang":"mr","domain":"news","complexity":"simple"}
+{"en":"The weather forecast predicts heavy rain tomorrow.","translation":"हवामान खात्याने उद्या जोरदार पावसाचा अंदाज वर्तवला आहे.","target_lang":"mr","domain":"news","complexity":"simple"}
+{"en":"She is a very talented and hardworking student.","translation":"ती खूप हुशार आणि मेहनती विद्यार्थी आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"He enjoys playing cricket and watching movies.","translation":"त्याला क्रिकेट खेळायला आणि चित्रपट पहायला आवडते.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"They are planning a trip to Europe next summer.","translation":"ते पुढील उन्हाळ्यात युरोपला जाण्याचा विचार करत आहेत.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"Could you please pass me the salt?","translation":"कृपया, मला मीठ द्याल का?","target_lang":"mr","domain":"conversation","complexity":"simple"}
+{"en":"What time is the meeting scheduled for?","translation":"बैठक किती वाजता नियोजित आहे?","target_lang":"mr","domain":"conversation","complexity":"simple"}
+{"en":"I am feeling a little bit under the weather today.","translation":"आज मला थोडं बरं वाटत नाहीये.","target_lang":"mr","domain":"conversation","complexity":"moderate"}
+{"en":"The number of subsets of the set {2, 3, 5} is (a) 3(b) 8(c) 6(d) none of these","translation":"{2, 3, 5} या संचाच्या उपसंचांची संख्या (a) 3(b) 8(c) 6(d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The number of subsets of a set containing n elements is (a) 2 n (b) 2 –n (c) n(d) none of these","translation":"n घटक असलेल्या संचाच्या उपसंचांची संख्या (a) 2 n (b) 2 –n (c) n(d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The null set is represented by (a){  }(b) { 0 }(c)  (d) none of these","translation":"शून्य संच (a){  }(b) { 0 }(c)  (d) यापैकी कशाने दर्शविला जातो?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"A = {2, 3, 5, 7} , B = { 4, 6, 8, 10} then A  B can be written as (a) { }(b) {  }(c) (AUB)'(d) None of these","translation":"जर A = {2, 3, 5, 7} , B = { 4, 6, 8, 10} तर A  B हे कसे लिहिता येईल? (a) { }(b) {  }(c) (AUB)'(d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The set {x|0<x<5} represents the set when x may take integral values only (a) {0, 1, 2, 3, 4, 5} (b) {1, 2, 3, 4}(c) {1, 2, 3, 4, 5 }(d) none of these","translation":"{x|0<x<5} हा संच दर्शवतो, जेव्हा x केवळ पूर्णांक मूल्ये घेऊ शकतो (a) {0, 1, 2, 3, 4, 5} (b) {1, 2, 3, 4}(c) {1, 2, 3, 4, 5 }(d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The set {0, 2, 4, 6, 8, 10} can be written as (a) {2x | 0<x <5} (b) {x : 0<x<5}(c) {2x : 0< x<5}(d) none of these","translation":"{0, 2, 4, 6, 8, 10} हा संच कसा लिहिता येईल? (a) {2x | 0<x <5} (b) {x : 0<x<5}(c) {2x : 0< x<5}(d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The cardinal number of P  Q is (a) 3 (b) 2(c) 0(d) none of these","translation":"P  Q ची कार्डिनल संख्या किती आहे? (a) 3 (b) 2(c) 0(d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The cardinal number of P  Q is (a) 10(b) 9(c) 8(d) none of these","translation":"P  Q ची कार्डिनल संख्या किती आहे? (a) 10(b) 9(c) 8(d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"n (P ' ) is (a) 10(b) 5(c) 6(d) none of these","translation":"n (P ' ) किती आहे? (a) 10(b) 5(c) 6(d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"n(Q ) is (a) 4(b) 10(c) 4(d) none of these","translation":"n(Q ) किती आहे? (a) 4(b) 10(c) 4(d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The set of cubes of the natural number is (a) a finite set (b) an infinite set(c) a null set(d) none of these","translation":"नैसर्गिक संख्येच्या घनांचा संच (a) एक मर्यादित संच आहे (b) एक अमर्यादित संच आहे (c) एक शून्य संच आहे (d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The set {2 x |x is any positive rational number} is (a) an infinite set (b) a null set(c) a finite set(d) none of these","translation":"{2 x |x कोणतीही धन परिमेय संख्या आहे} हा संच (a) एक अमर्यादित संच आहे (b) एक शून्य संच आहे (c) एक मर्यादित संच आहे (d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"{1– (–1) } for all integer x is the set x (a) {0}(b) {2}(c) {0, 2}(d) none of these","translation":"सर्व पूर्णांक x साठी {1– (–1) } हा संच x (a) {0}(b) {2}(c) {0, 2}(d) यापैकी कोणता आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"E is a set of positive even numbers and O is a set of positive odd numbers, then E O is a (a) set of whole numbers (b) N(c) a set of rational number (d) none of these","translation":"जर E हा धन सम संख्यांचा संच आहे आणि O हा धन विषम संख्यांचा संच आहे, तर E O हा काय आहे? (a) पूर्ण संख्यांचा संच (b) N(c) परिमेय संख्यांचा संच (d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If R is the set of positive rational numbers and E is the set of real numbers then (a) R  E(b) R  E(c) E  R(d) none of these","translation":"जर R धन परिमेय संख्यांचा संच आहे आणि E वास्तव संख्यांचा संच आहे, तर (a) R  E(b) R  E(c) E  R(d) यापैकी काय बरोबर आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If N is the set of natural numbers and I is the set of positive integers, then (a) N = I(b) N  I(c) N  I(d) none of these","translation":"जर N नैसर्गिक संख्यांचा संच आहे आणि I धन पूर्णांकांचा संच आहे, तर (a) N = I(b) N  I(c) N  I(d) यापैकी काय बरोबर आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If I is the set of isosceles triangles and E is the set of equilateral triangles, then (a) I  E(b) E  I(c) E = I(d) none of these","translation":"जर I समद्विभुज त्रिकोणांचा संच आहे आणि E समभुज त्रिकोणांचा संच आह��, तर (a) I  E(b) E  I(c) E = I(d) यापैकी काय बरोबर आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If R is the set of isosceles right angled triangles and I is set of isosceles triangles, then (a) R = I(b) R  I(c) R  I(d) none of these","translation":"जर R समद्विभुज काटकोन त्रिकोणांचा संच आहे आणि I समद्विभुज त्रिकोणांचा संच आहे, तर (a) R = I(b) R  I(c) R  I(d) यापैकी काय बरोबर आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"{n(n+1)/2 : n is a positive integer} is (a) a finite set (b) an infinite set(c) is an empty set (d) none of these","translation":"{n(n+1)/2 : n एक धन पूर्णांक आहे} हा संच (a) एक मर्यादित संच आहे (b) एक अमर्यादित संच आहे (c) एक रिक्त संच आहे (d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If A = {1, 2, 3, 5, 7}, and B = {x 2 : x  A} (a) n(b) = n(A) (b) n(B) > n(A)(c) n(A)= n(B)(d) n(A)<n(B)","translation":"जर A = {1, 2, 3, 5, 7}, आणि B = {x 2 : x  A} तर (a) n(b) = n(A) (b) n(B) > n(A)(c) n(A)= n(B)(d) n(A)<n(B)","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"By definition every subset of A × B is a relation from A to B.","translation":"व्याख्येनुसार, A × B चा प्रत्येक उपसंच A पासून B पर्यंतचा संबंध आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Thus, if we consider the relation R = { (1, 2), (1, 4), (3, 2), (3, 4)} then Dom (R) = {1, 3} and Range (R)= {2, 4}","translation":"म्हणून, जर आपण संबंध R = { (1, 2), (1, 4), (3, 2), (3, 4)} विचारात घेतला, तर Dom (R) = {1, 3} आणि Range (R)= {2, 4} आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"From the product set X. Y = {(1, 3), (2, 3), (3, 3), (4, 3), (2, 2), (3, 2), (4, 2), (1, 1), (2, 1), (3, 1), (4, 1)}, the subset {(1, 1), (2, 2), (3, 3)} defines the relation 'Is equal to'.","translation":"उत्पादन संच X. Y = {(1, 3), (2, 3), (3, 3), (4, 3), (2, 2), (3, 2), (4, 2), (1, 1), (2, 1), (3, 1), (4, 1)} मधून, उपसंच {(1, 1), (2, 2), (3, 3)} 'बरोबर आहे' हा संबंध परिभाषित करतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Illustration: Let A = {1, 2, 3} and b = {2, 4, 6} Then A × B = {(1, 2), (1, 4), (1, 6), (2, 2), (2, 4), (2, 6), (3, 2), (3, 4), (3, 6)}","translation":"उदाहरण: समजा A = {1, 2, 3} आणि b = {2, 4, 6} तर A × B = {(1, 2), (1, 4), (1, 6), (2, 2), (2, 4), (2, 6), (3, 2), (3, 4), (3, 6)}","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If we consider the relation = {(1, 2), (1, 4), (3, 4)} then Dom (R) = {1, 3} and Range = {2, 4}.","translation":"जर आपण संबंध = {(1, 2), (1, 4), (3, 4)} विचारात घेतला तर Dom (R) = {1, 3} आणि Range = {2, 4}.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Here the relation \"Is less than\".","translation":"येथे संबंध \"पेक्षा लहान आहे\".","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Identity Relation: The relation I = {(a, a) : a  A} is called the identity relation on A.","translation":"ओळख संबंध: संबंध I = {(a, a) : a  A} ला A वरील ओळख संबंध म्हणतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Illustration: Let A = {1, 2, 3} then I = {(1, 1), (2, 2), (3, 3)}","translation":"उदाहरण: समजा A = {1, 2, 3} तर I = {(1, 1), (2, 2), (3, 3)}","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Inverse Relation: If R be a relation on A, then the relation R –1 on A, defined by R –1 = {(b, a) : (a, b)  R} is called an inverse relation on A.","translation":"व्यस्त संबंध: जर R हा A वरील संबंध असेल, तर R –1 = {(b, a) : (a, b)  R} द्वारे परिभाषित केलेला A वरील संबंध R –1 ला A वरील व्यस्त संबंध म्हणतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Clearly , Dom (R –1 ) = Range (R) & Range (R –1 ) = Dom (R).","translation":"स्पष्टपणे, Dom (R –1 ) = Range (R) आणि Range (R –1 ) = Dom (R).","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Illustration: Let A = {1, 2, 3} and R = {(1, 2), (2, 2), (3, 1), (3, 2)} Then R being a subset of a × a, it is a relation on A.","translation":"उदाहरण: समजा A = {1, 2, 3} आणि R = {(1, 2), (2, 2), (3, 1), (3, 2)} तर R, a × a चा उपसंच असल्याने, तो A वरील संबंध आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Dom (R) = {1, 2, 3} and Range (R) = {2, 1}","translation":"Dom (R) = {1, 2, 3} आणि Range (R) = {2, 1}","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Now, R –1 = {(2, 1), (2, 2), (1, 3), (2, 3)}.","translation":"आता, R –1 = {(2, 1), (2, 2), (1, 3), (2, 3)}.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Here, Dom (R –1 ) = {2, 1} = Range (R) and Range (R –1 ) = {1, 2, 3} = Dom (R).","translation":"येथे, Dom (R –1 ) = {2, 1} = Range (R) आणि Range (R –1 ) = {1, 2, 3} = Dom (R).","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Illustration: Let A = {1, 2, 3}, then (i) R1 = {(1, 1), (2, 2), (3, 3), (1, 2)} Is reflexive and transitive but not symmetric, since (1, 2)  R 1 but (2, 1) does not belongs to R 1 .","translation":"उदाहरण: समजा A = {1, 2, 3}, तर (i) R1 = {(1, 1), (2, 2), (3, 3), (1, 2)} हा रिफ्लेक्सिव्ह आणि ट्रान्सिटिव्ह आहे, पण सममित नाही, कारण (1, 2)  R 1 पण (2, 1) R 1 मध्ये नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"A survey shows that 74% of the Indians like grapes, whereas 68% like bananas.","translation":"एका सर्वेक्षणात असे दिसून आले आहे की 74% भारतीयांना द्राक्षे आवडतात, तर 68% लोकांना केळी आवडतात.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"What percentage of the Indians like both grapes and bananas?","translation":"किती टक्के भारतीयांना द्राक्षे आणि केळी दोन्ही आवडतात?","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"In a class of 60 students, 40 students like Maths, 36 like Science, and 24 like both the subjects.","translation":"60 विद्यार्थ्यांच्या वर्गात, 40 विद्यार्थ्यांना गणित आवडते, 36 विद्यार्थ्यांना विज्ञान आवडते आणि 24 विद्यार्थ्यांना दोन्ही विषय आवडतात.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"Find the number of students who like (i) Maths only(ii) Science only(iii) either Maths or Science (iv) neither Maths nor Science","translation":"अशा विद्यार्थ्यांची संख्या शोधा ज्यांना (i) फक्त गणित आवडते (ii) फक्त विज्ञान आवडते (iii) गणित किंवा विज्ञान (iv) ना गणित ना विज्ञान","target_lang":"mr","domain":"general","complexity":"complex"}
+{"en":"A set containing n elements has 2 n subsets.","translation":"n घटक असलेला संच 2n उपसंच (subsets) आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The company's profits increased significantly this quarter.","translation":"या तिमाहीत कंपनीचा नफा लक्षणीय वाढला.","target_lang":"mr","domain":"business","complexity":"simple"}
+{"en":"Could you please pass me the salt?","translation":"कृपया, मला मीठ द्याल का?","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"The weather forecast predicts heavy rain tomorrow.","translation":"हवामान खात्यानुसार उद्या जोरदार पाऊस येण्याची शक्यता आहे.","target_lang":"mr","domain":"news","complexity":"moderate"}
+{"en":"He is a highly respected professor at the university.","translation":"ते विद्यापीठातील एक अत्यंत प्रतिष्ठित प्राध्यापक आहेत.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"The new software update has several improved features.","translation":"नवीन सॉफ्टवेअर अपडेटमध्ये अनेक सुधारित वैशिष्ट्ये आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Despite the challenges, they remained optimistic about the future.","translation":"आव्हाने असूनही, ते भविष्याबद्दल आशावादी राहिले.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"The government announced new economic policies to boost growth.","translation":"सरकारने विकास वाढवण्यासाठी नवीन आर्थिक धोरणे जाहीर केली.","target_lang":"mr","domain":"news","complexity":"moderate"}
+{"en":"She is fluent in three languages: English, French, and Spanish.","translation":"ती तीन भाषांमध्ये अस्खलित आहे: इंग्रजी, फ्रेंच आणि स्पॅनिश.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"The research team is conducting experiments in the laboratory.","translation":"संशोधन पथक प्रयोगशाळेत प्रयोग करत आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The intricate details of the artwork were mesmerizing.","translation":"कलाकृतीचे गुंतागुंतीचे तपशील मंत्रमुग्ध करणारे होते.","target_lang":"mr","domain":"general","complexity":"complex"}
+{"en":"The company's strategic plan involves expanding into new markets.","translation":"कंपनीच्या रणनीतिक योजनेत नवीन बाजारपेठेत विस्तार करणे समाविष्ट आहे.","target_lang":"mr","domain":"business","complexity":"complex"}
+{"en":"The complexities of international relations are often underestimated.","translation":"आंतरराष्ट्रीय संबंधांची गुंतागुंत अनेकदा कमी लेखली जाते.","target_lang":"mr","domain":"news","complexity":"complex"}
+{"en":"The algorithm efficiently processes large datasets.","translation":"अल्गोरिदम मोठ्या डेटासेटवर कार्यक्षमतेने प्रक्रिया करतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The philosophical debate explored the nature of consciousness.","translation":"तत्त्वज्ञानाच्या वादविवादामध्ये चेतनेच्या स्वरूपाचा शोध घेण्यात आला.","target_lang":"mr","domain":"general","complexity":"complex"}
+{"en":"The historical significance of the event cannot be overstated.","translation":"या घटनेचे ऐतिहासिक महत्त्व कमी लेखून चालणार नाही.","target_lang":"mr","domain":"history","complexity":"complex"}
+{"en":"The economic downturn had a profound impact on the community.","translation":"आर्थिक मंदीचा समाजावर गंभीर परिणाम झाला.","target_lang":"mr","domain":"news","complexity":"complex"}
+{"en":"The scientific community is constantly seeking new discoveries.","translation":"वैज्ञानिक समुदाय सतत नवीन शोधांचा शोध घेत आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The nuances of the language are difficult to master.","translation":"भाषेतील सूक्ष्मता (बारीकसारिक गोष्टी) आत्मसात करणे कठीण आहे.","target_lang":"mr","domain":"general","complexity":"complex"}
+{"en":"The implications of the new policy are far-reaching.","translation":"नवीन धोरणाचे परिणाम दूरगामी आहेत.","target_lang":"mr","domain":"news","complexity":"complex"}
+{"en":"The project's success depended on meticulous planning and execution.","translation":"प्रकल्पाचे यश सूक्ष्म नियोजन आणि अंमलबजावणीवर अवलंबून होते.","target_lang":"mr","domain":"business","complexity":"complex"}
+{"en":"Differentiating throughout we have dy/dx = ...","translation":"आपण संपूर्णपणे विभेदन केल्यास, dy/dx = ...","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"By cross–multiplication (1 – x^2) dy/dx = – y","translation":"तिरकस गुणाकार करून (1 – x^2) dy/dx = – y","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Transposing (1 – x^2) dy/dx + y = 0.","translation":"स्थानांतरण (1 – x^2) dy/dx + y = 0.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Differentiate the following w.r.t. x: (a) log (x + √(x^2 + a))","translation":"x च्या संदर्भात खालील गोष्टींचे विभेदन करा: (a) log (x + √(x^2 + a))","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If x^m y^n = (x+y)^(m+n) prove that dy/dx = y/x","translation":"जर x^m y^n = (x+y)^(m+n) असेल, तर सिद्ध करा की dy/dx = y/x","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Taking log on both sides log x^m y^n = (m+n) log (x + y)","translation":"दोन्ही बाजूंना लॉग घेऊन log x^m y^n = (m+n) log (x + y)","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"So y log x = (x – y) log e or y log x = (x – y).","translation":"म्हणून y log x = (x – y) log e किंवा y log x = (x – y).","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Differentiating w.r.t. x we get...","translation":"x च्या संदर्भात विभेदन केल्यास...","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Since f(x) is a function of x it can be differentiated again.","translation":"f(x) हे x चे फलन (function) असल्यामुळे, त्याचे पुन्हा विभेदन करता येते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Thus d/dx (dy/dx) is written as d^2y/dx^2","translation":"म्हणून d/dx (dy/dx) हे d^2y/dx^2 असे लिहिले जाते","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Let f(x) represent the curve in the fig.","translation":"f(x) आकृतीमधील वक्राचे प्रतिनिधित्व करते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The slope of the chord TPQ is given by Δy/Δx","translation":"TPQ या जीवाचा (chord) उतार Δy/Δx ने दर्शविला जातो","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The derivative of f(x) at a point x represents the slope of the tangent.","translation":"एका बिंदू x वरील f(x) चे व्युत्पन्न (derivative) स्पर्शिकेच्या (tangent) उताराचे प्रतिनिधित्व करते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the gradient of the curve y = 3x^2 – 5x + 4 at the point (1, 2).","translation":"बिंदू (1, 2) येथे y = 3x^2 – 5x + 4 या वक्राचा (curve) उतार शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The total cost consists of two parts (i) Variable Cost (ii) Fixed Cost.","translation":"एकूण खर्चाचे दोन भाग असतात: (i) बदलता येणारा खर्च (ii) निश्चित खर्च.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If C(X) denotes the cost producing x units of a product then C(x) = V(x) + F(x)","translation":"जर C(X) x वस्तूंचे उत्पादन खर्च दर्शवते, तर C(x) = V(x) + F(x)","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Marginal Cost (MC) = Rate of change in cost C per unit change in OutPut at an OutPut level of x units = dC/dx.","translation":"सीमांत खर्च (MC) = x एकक उत्पादनाच्या पातळीवर, उत्पादन बदलाच्या प्रति एकक खर्चातील बदल = dC/dx.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Find the profit maximising output and price for maximum profit.","translation":"अधिकतम नफ्यासाठी नफा वाढवणारे उत्पादन आणि किंमत शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"After the imposition of tax of ` 2 per unit, the total new cost is...","translation":"प्रती एकक ` 2 कर आकारणीनंतर, एकूण नवीन खर्च...","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The cost function of a company is given by: C(x) = ...","translation":"एका कंपनीचे खर्च फलन खालीलप्रमाणे आहे: C(x) = ...","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the area of the circle.","translation":"वर्तुळाचे क्षेत्रफळ शोधा.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"The news reported a major earthquake.","translation":"बातमीमध्ये मोठ्या भूकंपाची नोंद आहे.","target_lang":"mr","domain":"news","complexity":"simple"}
+{"en":"Please close the door.","translation":"कृपया दरवाजा बंद करा.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"The company's profits increased significantly this quarter.","translation":"य��� तिमाहीत कंपनीचा नफा लक्षणीय वाढला.","target_lang":"mr","domain":"business","complexity":"moderate"}
+{"en":"He is a very intelligent student.","translation":"तो फार हुशार विद्यार्थी आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"The government announced new economic policies.","translation":"सरकारने नवीन आर्थिक धोरणे जाहीर केली.","target_lang":"mr","domain":"news","complexity":"moderate"}
+{"en":"Could you please repeat that?","translation":"तुम्ही ते कृपया पुन्हा सांगू शकाल का?","target_lang":"mr","domain":"conversation","complexity":"simple"}
+{"en":"The algorithm efficiently sorts the data.","translation":"अल्गोरिदम डेटाची कार्यक्षमतेने क्रमवारी लावतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The weather forecast predicts rain tomorrow.","translation":"हवामान खात्यानुसार उद्या पावसाची शक्यता आहे.","target_lang":"mr","domain":"news","complexity":"moderate"}
+{"en":"She is learning to play the piano.","translation":"ती पियानो वाजवायला शिकत आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"The complex equation requires advanced mathematical techniques.","translation":"गुंतागुंतीच्या समीकरणासाठी प्रगत गणिती तंत्रांची आवश्यकता आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The historical significance of the event is undeniable.","translation":"या घटनेचे ऐतिहासिक महत्त्व निर्विवाद आहे.","target_lang":"mr","domain":"history","complexity":"complex"}
+{"en":"The project's success depends on meticulous planning and execution.","translation":"प्रकल्पाचे यश सूक्ष्म नियोजन आणि अंमलबजावणीवर अवलंबून असते.","target_lang":"mr","domain":"business","complexity":"complex"}
+{"en":"The scientific study revealed new insights into the human brain.","translation":"वैज्ञानिक अभ्यासात मानवी मेंदूविषयी नवीन माहिती समोर आली.","target_lang":"mr","domain":"science","complexity":"complex"}
+{"en":"The negotiations were protracted and ultimately unsuccessful.","translation":"बोलणी लांबली आणि शेवटी ती यशस्वी झाली नाही.","target_lang":"mr","domain":"politics","complexity":"complex"}
+{"en":"The artist's innovative techniques revolutionized the art world.","translation":"कलाकारांच्या नविन तंत्राने कलाविश्वात क्रांती घडवून आणली.","target_lang":"mr","domain":"art","complexity":"complex"}
+{"en":"The philosophical implications of the discovery are profound.","translation":"या शोधाचे तात्त्विक परिणाम गहन आहेत.","target_lang":"mr","domain":"philosophy","complexity":"complex"}
+{"en":"The economic downturn affected many industries.","translation":"आर्थिक मंदीचा अनेक उद्योगांवर परिणाम झाला.","target_lang":"mr","domain":"business","complexity":"moderate"}
+{"en":"The software update improved system performance.","translation":"सॉफ्टवेअर अपडेटमुळे सिस्टमची कार्यक्षमता सुधारली.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The team worked collaboratively to achieve their goals.","translation":"संघ त्यांच्या ध्येय्यपूर्तीसाठी एकत्रितपणे काम करत होता.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"If f(x) = x – 1, the equation of a curve y = f(x) passing through the point (1, 0) is given by (a) y = x 2 – 2x + 1","translation":"जर f(x) = x – 1, तर (1, 0) बिंदूतून जाणारे वक्र y = f(x) चे समीकरण (a) y = x 2 – 2x + 1 असे दिले जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The marginal cost function of manufacturing x units of a product is 5 + 16x – 3x 2 .","translation":"एका उत्पादनाच्या x युनिट्सच्या उत्पादनाचा सीमांत खर्च 5 + 16x – 3x 2 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the total cost function.","translation":"एकूण खर्च कार्य शोधा.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The total cost of producing 5 times is Rs. 500.","translation":"5 वेळा उत्पादन करण्याचा एकूण खर्च रु. 500 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The marginal cost (MC) of a product is given to be a constant multiple of number of units (x) produced.","translation":"एका उत्पादनाचा सीमांत खर्च (MC) उत्पादित युनिट्सच्या (x) संख्येचा स्थिर गुणाकार असल्याचे दिले आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Find the total cost function, if fixed cot is Rs. 5000 and the cot of producing 50 units is Rs. 5625","translation":"एकूण खर्च कार्य शोधा, जर निश्चित किंमत रु. 5000 आहे आणि 50 युनिट्स तयार करण्याची किंमत रु. 5625 आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If R (x) denote the total revenue function and MR is the marginal revenue function, then","translation":"जर R (x) एकूण महसूल कार्य दर्शवते आणि MR सीमांत महसूल कार्य आहे, तर","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Find the total revenue function and the demand function.","translation":"एकूण महसूल कार्य आणि मागणी कार्य शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The fixed cost of a new product is Rs. 18000 and the variable cost per unit is Rs 550.","translation":"एका नवीन उत्पादनाची निश्चित किंमत रु. 18000 आहे आणि प्रति युनिट बदलती किंमत रु. 550 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Determine: the total revenue function .","translation":"निर्धारित करा: एकूण महसूल कार्य.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Determine the total cost function","translation":"एकूण खर्च कार्य निश्चित करा","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Determine the breakeven point","translation":"ब्रेकइव्हन बिंदू निश्चित करा","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Determine: the average cost","translation":"निर्धारित करा: सरासरी खर्च","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Determine the marginal cost.","translation":"सीमांत खर्च निश्चित करा.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Find the marginal cost when 15 units are produced,","translation":"जेव्हा 15 युनिट्सचे उत्पादन होते, तेव्हा सीमांत खर्च शोधा,","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the actual cost of producing 15 th unit.","translation":"15 व्या युनिटचे उत्पादन करण्याचा वास्तविक खर्च शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Determine: the average cost","translation":"निर्धारित करा: सरासरी खर्च","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Find the marginal cost.","translation":"सीमांत खर्च शोधा.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Find the rate of change of MC with respect to x.","translation":"x च्या संदर्भात MC बदलाचा दर शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the level of output for which MC = AC","translation":"उत्पादनाचे असे प्रमाण शोधा ज्यासाठी MC = AC","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"First of all take a review on the given information.","translation":"सर्वात आधी, दिलेल्या माहितीचे पुनरावलोकन करा.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"When the place of any objects or persons is definitely mentioned then we say that it is a definite information.","translation":"जेव्हा कोणत्याही वस्तू किंवा व्यक्��ीचे स्थान निश्चितपणे नमूद केले जाते, तेव्हा आपण त्याला निश्चित माहिती म्हणतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"A negative information does not tell us anything definitely but it gives an idea to eliminate a possibility.","translation":"नकारात्मक माहिती आपल्याला निश्चितपणे काहीही सांगत नाही, परंतु ती शक्यता दूर करण्याची कल्पना देते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"In this type of arrangement, we arrange objects or persons in a line or row.","translation":"या प्रकारच्या मांडणीत, आपण वस्तू किंवा व्यक्तींना एका ओळीत किंवा रांगेत लावतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Use pictorial method to represent the people or objects and their positions.","translation":"व्यक्ती किंवा वस्तू आणि त्यांची स्थान दर्शवण्यासाठी चित्रात्मक पद्धतीचा वापर करा.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"There are few words which must be paid adequate attention, i.e., ‘between’ means sandwiched, ‘immediate left’ is different from ‘to the left’.","translation":"असे काही शब्द आहेत ज्यांच्याकडे पुरेसे लक्ष देणे आवश्यक आहे, म्हणजे, ‘मध्ये’ म्हणजे सँडविच, ‘तत्काळ डावीकडे’ ‘डावीकडे’ पेक्षा वेगळे आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"When direction of face is not clear, then we take One Row Sequence.","translation":"जेव्हा चेहऱ्याची दिशा स्पष्ट नसते, तेव्हा आपण एक ओळ क्रम घेतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"From the above diagram, it is clear that Q, R, S, T are right of P but only Q is the immediate right of P.","translation":"वरील आकृतीवरून हे स्पष्ट होते की Q, R, S, T हे P च्या उजवीकडे आहेत, परंतु फक्त Q हा P च्या लगेच उजवीकडे आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"When direction of face is towards you, then the diagram will be as follows.","translation":"जेव्हा चेहऱ्याची दिशा तुमच्याकडे असते, तेव्हा आकृती खालीलप्रमाणे असेल.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Let us see 6 persons seating in two rows.","translation":"चला दोन रांगेत बसलेल्या 6 व्यक्ती पाहूया.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"A is occupying seat next to B but not next to C.","translation":"A, B च्या शेजारी बसलेला आहे, पण C च्या शेजारी नाही.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Who is occupying seat adjacent to D.","translation":"D च्या जवळची जागा कोण व्यापत आहे?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"P is fourth to the right of T.","translation":"P, T च्या उजवीकडे चौथे आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"W is fourth to the left of S.","translation":"W, S च्या डावीकडे चौथे आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Who are sitting at the extreme ends?","translation":"अतिशय टोकाला कोण बसले आहे?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Therefore, house P is middle.","translation":"म्हणून, घर P मध्यभागी आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"A is to the immediate left of B but on the immediate right of C.","translation":"A, B च्या लगेच डावीकडे आहे, पण C च्या लगेच उजवीकडे आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Who are at the extremes?","translation":"अतिशय टोकाला कोण आहे?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Therefore, O is sitting in the middle.","translation":"म्हणून, O मध्यभागी बसलेला आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"In this arrangement, some persons are sitting around a circle and they are facing the centre.","translation":"या मांडणीत, काही व्यक्ती एका वर्तुळाभोवती बसलेले आहेत आणि ते केंद्राकडे तोंड करून आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If RED is coded as 6720 then GREEN would be coded as (a)9207716(b)167129(c)1677209(d)1672091","translation":"जर RED ला 6720 असे सांकेतिक केले, तर GREEN ला कसे सांकेतिक कराल? (a)9207716(b)167129(c)1677209(d)1672091","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If A = 1, FAT = 27, FAITH = ? (a)44(b)45(c)46(d)36","translation":"जर A = 1, FAT = 27, तर FAITH = ? (a)44(b)45(c)46(d)36","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If BROTHER is coded 2456784, SISTER coded as 919684, what is coded for BORBERS?","translation":"जर BROTHER ला 2456784 आणि SISTER ला 919684 असे सांकेतिक केले, तर BORBERS साठी काय सांकेतिक असेल?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If DELHI is coded 73541 and CALCUTTA as 82589662, How can CALICUT be coded?","translation":"जर DELHI ला 73541 आणि CALCUTTA ला 82589662 असे सांकेतिक केले, तर CALICUT ला कसे सांकेतिक कराल?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If CLOCK is coded 34235 and TIME is 8679, what will be code of MOTEL?","translation":"जर CLOCK ला 34235 आणि TIME ला 8679 असे सांकेतिक केले, तर MOTEL चा कोड काय असेल?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If PALE is coded as 2134 and EARTH is coded as 41590, how is PEARL is coded ?","translation":"जर PALE ला 2134 आणि EARTH ला 41590 असे सांकेतिक केले, तर PEARL ला कसे सांकेतिक कराल?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If LOSE is coded as 1357 and GAIN is coded as 2468, what do figure 82146 stands for?","translation":"जर LOSE ला 1357 आणि GAIN ला 2468 असे सांकेतिक केले, तर अंक 82146 कशाचे प्रतिनिधित्व करतात?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If MEKLF is coded as 91782 and LLLJK as 88867, how can IHJED is coded as?","translation":"जर MEKLF ला 91782 आणि LLLJK ला 88867 असे सांकेतिक केले, तर IHJED ला कसे सांकेतिक कराल?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If in a certain code language NAME is written as 4258 then what is coded as MEAN ?","translation":"एका विशिष्ट सांकेतिक भाषेत NAME ला 4258 असे लिहिले जाते, तर MEAN ला काय सांकेतिक केले जाईल?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If GOLD is written as IQNF, how WIND can be written as code?","translation":"जर GOLD ला IQNF असे लिहिले जाते, तर WIND ला कोडमध्ये कसे लिहिता येईल?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If ROSE is written as TQUG, how BISCUIT can be written in that code?","translation":"जर ROSE ला TQUG असे लिहिले जाते, तर BISCUIT ला त्याच कोडमध्ये कसे लिहिता येईल?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find out the correctly coded alternative from amongst the given four alternatives (a), (b), (c), (d). ZDRCVF (a) 612875 (b) 619875 (c) 612845 (d) 612835","translation":"दिलेल्या चार पर्यायांमधून (a), (b), (c), (d) योग्य कोडित पर्याय शोधा. ZDRCVF (a) 612875 (b) 619875 (c) 612845 (d) 612835","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If DELHI is coded as CCIDD, how would you encode BOMBAY?","translation":"जर DELHI ला CCIDD असे सांकेतिक केले, तर BOMBAY ला तुम्ही कसे सांकेतिक कराल?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"In a certain code, RIPPLE is written as 613382 and LIFE is written as 8192. How is PILLER written in that code?","translation":"एका विशिष्ट कोडमध्ये, RIPPLE ला 613382 असे लिहिले जाते आणि LIFE ला 8192 असे लिहिले जाते. तर PILLER ला त्या कोडमध्ये कसे लिहाल?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If PALAM could be given the code number 43, what code number can be given to SANTACRUZ?","translation":"जर PALAM ला 43 हा कोड क्रमांक दिला जाऊ शकतो, तर SANTACRUZ ला कोणता कोड क्रमांक दिला जाऊ शकतो?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"184632 (a) MDJBSI (b) MDJBIL (c) MDJBWL (d) MDBJIL","translation":"184632 (a) MDJBSI (b) MDJBIL (c) MDJBWL (d) MDBJIL","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"In a certain code ‘256’ means ‘you are good’, ‘637’ means ‘we are bad’ and ‘358’ means ‘good and bad’. Which of the following represents ‘and’ in that code?","translation":"एका विशिष्ट कोडमध्ये ‘256’ म्हणजे ‘you are good’, ‘637’ म्हणजे ‘we are bad’ आणि ‘358’ म्हणजे ‘good and bad’. खालीलपैकी ‘and’ (आणि) या शब्दाचे प्रतिनिधित्व कोण करतो?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find odd man out of the following (52-61): 3, 5, 7, 15, 17, 19 (a) 15 (b) 17 (c) 19 (d) 7","translation":"पुढीलपैकी विसंगत घटक शोधा (52-61): 3, 5, 7, 15, 17, 19 (a) 15 (b) 17 (c) 19 (d) 7","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find odd man out of the following (52-61): 10, 14, 16, 18, 23, 24, 26 (a) 26 (b) 23 (c) 24 (d) 18","translation":"पुढीलपैकी विसंगत घटक शोधा (52-61): 10, 14, 16, 18, 23, 24, 26 (a) 26 (b) 23 (c) 24 (d) 18","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find odd man out of the following (52-61): 1, 4, 9, 16, 24, 25, 36 (a) 9 (b) 24 (c) 25 (d) 36","translation":"पुढीलपैकी विसंगत घटक शोधा (52-61): 1, 4, 9, 16, 24, 25, 36 (a) 9 (b) 24 (c) 25 (d) 36","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"My mother's or father's son is my Brother.","translation":"माझ्या आईचा किंवा वडिलांचा मुलगा माझा भाऊ आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"My mother’s or father’s daughter is my Sister.","translation":"माझ्या आईची किंवा वडिलांची मुलगी माझी बहीण आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"My mother’s or father’s father is my Grandfather.","translation":"माझ्या आईचे किंवा वडिलांचे वडील माझे आजोबा आहेत.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"My mother’s or father’s sister is my Aunt.","translation":"माझ्या आईची किंवा वडिलांची बहीण माझी काकू/मावशी आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"My mother’s or father’s brother is my Uncle.","translation":"माझ्या आईचा किंवा वडिलांचा भाऊ माझे काका/मामा आहेत.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"My son’s wife is my Daughter-in-law.","translation":"माझ्या मुलाची पत्नी माझी सून आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"My daughter’s husband is my Son-in-law.","translation":"माझ्या मुलीचा नवरा माझा जावई आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"My brother’s son is my Nephew.","translation":"माझ्या भावाचा मुलगा माझा पुतण्या आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"My brother’s daughter is my Neice.","translation":"माझ्या भाची मुलगी माझी पुतणी आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"My sister’s husband is my Brother-in-law.","translation":"माझ्या बहिणीचा नवरा माझा मेहुणा आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"My brother’s wife is my Sister-in-law.","translation":"माझ्या भावाची बायको माझी जाऊ आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"My husband’s or wifer’s sister is my Sister-in-law.","translation":"माझ्या नवऱ्याची किंवा बायकोची बहीण माझी नणंद आहे.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"My husband’s or wife’s brother is my Brother-in-law.","translation":"माझ्या नवऱ्याचा किंवा बायकोचा भाऊ माझा मेहुणा आहे.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"My uncle’s or aunt’s son or daughter is my Cousin.","translation":"माझ्या काका/मामा/मावशी/आत्याचा मुलगा किंवा मुलगी माझा चुलत/मावस/आणि/मेव्हणा भाऊ/बहीण आहे.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"My wife’s father or husband’s father is my Father-in-law.","translation":"माझ्या बायकोचे वडील किंवा नवऱ्याचे वडील माझे सासरे आहेत.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"My wife’s mother or husband’s mother is my Mother-in-law.","translation":"माझ्या बायकोची आई किंवा नवऱ्याची आई माझी सासू आहे.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"My father’s wife is my Mother.","translation":"माझ्या वडिलांची पत्नी माझी आई आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"My mother’s husband is my Father.","translation":"माझ्या आईचे पती माझे वडील आहेत.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"My son’s or daughter’s son is my Grandson.","translation":"माझ्या मुलाचा किंवा मुलीचा मुलगा माझा नातू आहे.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"My son’s or daughter’s daughter is my Grand-daughter.","translation":"माझ्या मुलाची किंवा मुलीची मुलगी माझी नात आहे.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"Construct a frequency distribution according to gender.","translation":"लिंगानुसार वारंवारता वितरण तयार करा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"We count the number of male births and that of female births.","translation":"आम्ही पुरुष आणि स्त्रियांच्या जन्माची संख्या मोजतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Present this information in the following table.","translation":"हे माहिती खालील तक्त्यात सादर करा.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Make a frequency distribution of printing mistakes.","translation":"मुद्रण चुकांचे वारंवारता वितरण तयार करा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Since x, the printing mistakes, is a discrete variable, x can assume seven values.","translation":"x, म्हणजे मुद्रण चुका, एक विविक्त चल असल्यामुळे, x सात मूल्ये घेऊ शकते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Construct a frequency distribution of weights, taking class length as 5.","translation":"वजनाचे वारंवारता वितरण तयार करा, ज्यामध्ये वर्ग लांबी 5 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"We have, Range = Maximum weight – Minimum weight.","translation":"आपल्याकडे आहे, श्रेणी = कमाल वजन – किमान वजन.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The minimum value is known as the lower class limit (LCL).","translation":"किमान मूल्याला निम्न वर्ग मर्यादा (LCL) म्हणून ओळखले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Class boundaries may be defined as the actual class limit of a class interval.","translation":"वर्ग सीमा, वर्ग अंतराच्या वास्तविक वर्ग मर्यादेनुसार परिभाषित केल्या जाऊ शकतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"This is usually done for a continuous variable.","translation":"हे सहसा सतत बदलासाठी केले जाते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Mid-point or Mid-value or class mark","translation":"मध्यबिंदू किंवा वर्ग गुण","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The width of a class interval may be defined as the difference between the UCB and the LCB.","translation":"वर्ग अंतराची रुंदी UCB आणि LCB मधील फरकाने परिभाषित केली जाऊ शकते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Cumulative frequency corresponding to a class boundary for a continuous variable.","translation":"सतत बदलासाठी वर्ग सीमेनुसार संचित वारंवारता.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Frequency density of a class interval","translation":"वर्ग अंतराची वारंवारता घनता","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Relative frequency of a class interval may be defined as the ratio of the class frequency to the total frequency.","translation":"एका वर्ग अंतराची सापेक्ष वारंवारता, वर्ग वारंवारता आणि एकूण वारंवारता यांच्या गुणोत्तराने परिभाषित केली जाऊ शकते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"This is a very convenient way to represent a frequency distribution.","translation":"वारंवारता वितरण दर्शविण्यासाठी हा एक सोपा मार्ग आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Histogram helps us to get an idea of the frequency curve.","translation":"हिस्टोग्राम आपल्याला वारंवारता वक्र (frequency curve) ची कल्पना देतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Usually frequency polygon is meant for single frequency distribution.","translation":"सर्वसाधारणपणे वारंवारता बहुभुज (frequency polygon) एकाच वारंवारता वितरणासाठी असतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"By plotting cumulative frequency against the respective class boundary, we get ogives.","translation":"संबंधित वर्ग सीमेच्या विरुद्ध संचित वारंवारता प्लॉट करून, आपल्याला ओगिव्ह (ogives) मिळतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"A frequency curve is a smooth curve for which the total area is taken to be unity.","translation":"वारंवारता वक्र हा एक गुळगुळीत वक्र आहे ज्यासाठी एकूण क्षेत्रफळ एक मानले जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The frequency curve is a limiting form of the frequency polygon.","translation":"वारंवारता वक्र वारंवारता बहुभुजाची मर्यादा आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Bell-shaped curves are commonly used to represent frequency distributions.","translation":"घंटा-आकाराचे वक्र सामान्यतः वारंवारता वितरण दर्शविण्यासाठी वापरले जातात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"What is the difference between the central angles for the largest and smallest components?","translation":"सर्वात मोठ्या आणि सर्वात लहान घटकांसाठी मध्यवर्ती कोनांमधील फरक काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"How many students got marks more than 30?","translation":"30 पेक्षा जास्त गुण किती विद्यार्थ्यांना मिळाले?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Find the number of observations between 250 and 300.","translation":"250 आणि 300 दरम्यानच्या निरीक्षणांची संख्या शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"After combining 1995 and 2000, what is the relationship between x and y?","translation":"1995 आणि 2000 एकत्र केल्यानंतर, x आणि y मधील संबंध काय आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The principle of optimization ensures maximum efficiency at a given cost.","translation":"इष्टतमीकरण तत्त्व एका विशिष्ट खर्चात जास्तीत जास्त कार्यक्षमतेची खात्री करते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Sample surveys are often preferred over complete enumeration due to cost and speed.","translation":"खर्च आणि वेळेमुळे संपूर्ण गणनेपेक्षा नमुना सर्वेक्षणाला प्राधान्य दिले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Sampling errors can be reduced by increasing the sample size.","translation":"नमुना आकार वाढवून नमुना त्रुटी कमी करता येतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Non-sampling errors can occur due to memory lapses or biases.","translation":"स्मरणशक्ती कमी होणे किंवा पूर्वग्रह यांमुळे गैर-नमुना त्रुटी येऊ शकतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The population size is the total number of units in the population.","translation":"लोकसंख्या आकार म्हणजे लोकसंख्येतील एककाची एकूण संख्या.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"A sample is a representative part of the population.","translation":"नमुना म्हणजे लोकसंख्येचा प्रतिनिधी भाग.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Statistical inferences are drawn based on sample observations.","translation":"सांख्यिकीय निष्कर्ष नमुना निरीक्षणांवर आधारित काढले जातात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The law of statistical regularity states that a large random sample will reflect the population.","translation":"सांख्यिकीय नियमिततेचा नियम सांगतो की एक मोठा यादृच्छिक नमुना लोकसंख्येचे प्रतिबिंब दर्शवेल.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The principle of inertia of large numbers suggests that larger samples are more reliable.","translation":"मोठ्या संख्येच्या जडत्वाचे तत्त्व असे सूचित करते की मोठे नमुने अधिक विश्वसनीय आहेत.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Errors in a survey can be classified as sampling and non-sampling errors.","translation":"एका सर्वेक्षणातील त्रुटींचे वर्गीकरण नमुना आणि गैर-नमुना त्रुटींमध्ये केले जाऊ शकते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Defective sampling design can lead to sampling errors.","translation":"सदोष नमुना डिझाइनमुळे नमुना त्रुटी येऊ शकतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Substitution of a sampling unit can introduce bias.","translation":"नमुना घटकाची अदलाबदल केल्यास पूर्वग्रह निर्माण होऊ शकतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Faulty demarcation of units can cause errors in agricultural surveys.","translation":"घटकांची सदोष सीमांकन कृषी सर्वेक्षणात त्रुटी निर्माण करू शकते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The choice of an incorrect statistic can lead to errors in estimation.","translation":"अयोग्य आकडेवारीची निवड अंदाजात त्रुटी निर्माण करू शकते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The list of people using statistics goes on and on.","translation":"आकडेवारीचा वापर करणारे लोकांची यादी खूप मोठी आहे.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"Due to these factors, it is necessary to study the subject of statistics in an objective manner.","translation":"या घटकांमुळे, आकडेवारी या विषयाचा वस्तुनिष्ठ पद्धतीने अभ्यास करणे आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"However, there remains a question mark about the origin of the word ‘statistics’.","translation":"परंतु, ‘आकडेवारी’ या शब्दाच्या उत्पत्तीबद्दल प्रश्नचिन्ह आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"One view is that statistics is originated from the Latin word ‘status’.","translation":"एका विचारानुसार, आकडेवारीची उत्पत्ती ‘स्टेटस’ या लॅटिन शब्दातून झाली आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"According to another school of thought, it had its origin in the Italian word ‘statista’.","translation":"दुसऱ्या विचारसरणीनुसार, त्याची उत्पत्ती ‘स्टॅटिस्ता’ या इटालियन शब्दात झाली आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"In those days, statistics was analogous to state or, to be more precise, the data that are collected and maintained for the welfare of the people belonging to the state.","translation":"त्या काळात, आकडेवारी राज्याशी संबंधित होती, किंवा अधिक स्पष्टपणे सांगायचे तर, राज्याच्या लोकांच्या कल्याणासाठी गोळा केलेले आणि जतन केलेले डेटा.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"We are thankful to Kautilya who had kept a record of births and deaths as well as some other precious records in his famous book ‘Arthashastra’ during Chandragupta’s reign in the fourth century B. C.","translation":"चौथ्या शतकात, चंद्रगुप्ताच्या काळात, कौटिल्याने त्याच्या प्रसिद्ध ‘अर्थशास्त्र’ या पुस्तकात जन्म आणि मृत्यू तसेच इतर मौल्यवान नोंदी ठेवल्या, त्याबद्दल आम्ही त्यांचे आभारी आहोत.","target_lang":"mr","domain":"historical","complexity":"complex"}
+{"en":"During the reign of Akbar in the sixteenth century A. D. We find statistical records on agriculture in Ain-i-Akbari written by Abu Fazl.","translation":"अकबराच्या १६ व्या शतकातील शासनकाळात, अबुल फजलने लिहिलेल्या ‘ऐन-इ-अकबरी’ मध्ये आपल्याला शेतीविषयक आकडेवारी आढळते.","target_lang":"mr","domain":"historical","complexity":"complex"}
+{"en":"We may define statistics either in a singular sense or in a plural sense.","translation":"आम्ही आकडेवारीची व्याख्या एकवचनी किंवा अनेकवचनी अर्थाने करू शकतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Statistics, when used as a plural noun, may be defined as data qualitative as well as quantitative, that are collected, usually with a view of having statistical analysis.","translation":"आकडेवारी, अनेकवचनी नाम म्हणून वापरली जाते, तेव्हा गुणात्मक तसेच संख्यात्मक डेटा म्हणून परिभाषित केली जाऊ शकते, जी सामान्यतः सांख्यिकीय विश्लेषण करण्यासाठी गोळा केली जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"However, statistics, when used as a singular noun, may be defined, as the scientific method that is employed for collecting, analysing and presenting data, leading finally to drawing statistical inferences about some important characteristics it means it is ‘science of counting’ or ‘science of averages’.","translation":"परंतु, आकडेवारी, एकवचनी नाम म्हणून वापरली जाते, तेव्हा डेटा गोळा करणे, विश्ल��षण करणे आणि सादर करण्यासाठी वापरली जाणारी वैज्ञानिक पद्धत म्हणून परिभाषित केली जाऊ शकते, ज्यामुळे काही महत्त्वाच्या वैशिष्ट्यांबद्दल सांख्यिकीय निष्कर्ष काढले जातात, याचा अर्थ ‘मोजण्याचे विज्ञान’ किंवा ‘सरासरीचे विज्ञान’ आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Among various applications of statistics, let us confine our discussions to the fields of Economics, Business Management and Commerce and Industry.","translation":"आकडेवारीच्या विविध उपयोगांपैकी, आपण आपले विचार अर्थशास्त्र, व्यवसाय व्यवस्थापन आणि वाणिज्य आणि उद्योग या क्षेत्रांपुरते मर्यादित ठेवूया.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Modern developments in Economics have the roots in statistics.","translation":"अर्थशास्त्रातील आधुनिक विकास आकडेवारीवर आधारित आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"In fact, Economics and Statistics are closely associated.","translation":"खरं तर, अर्थशास्त्र आणि आकडेवारी यांचा जवळचा संबंध आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Time Series Analysis, Index Numbers, Demand Analysis etc. are some overlapping areas of Economics and Statistics.","translation":"कालश्रेणी विश्लेषण, निर्देशांक, मागणी विश्लेषण इत्यादी अर्थशास्त्र आणि आकडेवारीची काही समान क्षेत्रे आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Conducting socio-economic surveys and analysing the data derived from it are made with the help of different statistical methods.","translation":"विविध सांख्यिकीय पद्धतींच्या मदतीने सामाजिक-आर्थिक सर्वेक्षण करणे आणि त्यातून डेटाचे विश्लेषण करणे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Regression analysis, one of the numerous applications of statistics, plays a key role in Economics for making future projection of demand of goods, sales, prices, quantities etc. which are all ingredients of Economic planning.","translation":"अर्थव्यवस्थेत, मालाची मागणी, विक्री, किंमत, प्रमाण इत्यादींचे भविष्यकालीन अंदाज घेण्यासाठी सांख्यिकीच्या अनेक उपयोगांपैकी, प्रतिगमन विश्लेषण (Regression analysis) महत्त्वाची भूमिका बजावते, जे आर्थिक नियोजनाचे घटक आहेत.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Gone are the days when the managers used to make decisions on the basis of hunches, intuition or trials and errors.","translation":"ते दिवस गेले जेव्हा व्यवस्थापक केवळ अंदाज, अंतर्ज्ञान किंवा प्रयोग आणि त्रुटींवर आधारित निर्णय घेत असत.","target_lang":"mr","domain":"business","complexity":"moderate"}
+{"en":"Now a days, because of the never-ending complexity in the business and industry environment, most of the decision making processes rely upon different quantitative techniques which could be described as a combination of statistical methods and operations research techniques.","translation":"आजकाल, व्यवसाय आणि उद्योग वातावरणातील सतत वाढणाऱ्या गुंतागुंतीमुळे, बहुतेक निर्णय घेण्याच्या प्रक्रियेत विविध संख्यात्मक तंत्रांवर अवलंबून राहावे लागते, ज्यांचे वर्णन सांख्यिकीय पद्धती आणि ऑपरेशन रिसर्च तंत्रांचे मिश्रण म्��णून केले जाऊ शकते.","target_lang":"mr","domain":"business","complexity":"complex"}
+{"en":"So far as statistics is concerned, inferences about the universe from the knowledge of a part of it, known as sample, plays an important role in the development of certain criteria.","translation":"आकडेवारीचा विचार केला तर, नमुन्याच्या ज्ञानावरून, जे त्या भागाचे ज्ञान आहे, त्यावरून विश्वासाचे निष्कर्ष काढणे, काही निकष विकसित करण्यात महत्त्वाची भूमिका बजावते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The arithmetic mean is a fundamental concept in statistics.","translation":"अंकगणितीय मध्य (Arithmetic Mean) हे सांख्यिकीमधील एक मूलभूत तत्त्व आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Calculate the mean wage of the workers.","translation":"कामगारांच्या सरासरी वेतनाची गणना करा.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The formula for calculating the arithmetic mean is straightforward.","translation":"अंकगणितीय मध्य काढण्याचे सूत्र सोपे आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The median is the middle value in a sorted dataset.","translation":"मध्यक (Median) म्हणजे क्रमवारी लावलेल्या डेटासेटमधील मधली किंमत.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Find the median of the given data set.","translation":"दिलेल्या डेटा संचाचा मध्यक शोधा.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The mode represents the most frequent value.","translation":"मोड (Mode) सर्वात वारंवार येणारे मूल्य दर्शवतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Determine the mode of the distribution.","translation":"वितरणाचा मोड निश्चित करा.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The geometric mean is used for data that grows exponentially.","translation":"भूमितीय मध्य (Geometric Mean) डेटासाठी वापरला जातो जो वेगाने वाढतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The combined mean salary can be calculated using a weighted average.","translation":"एकूण सरासरी वेतन, भारित सरासरी वापरून मोजले जाऊ शकते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The properties of the arithmetic mean are important to understand.","translation":"अंकगणितीय मध्याचे गुणधर्म समजून घेणे महत्त्वाचे आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The median is less sensitive to extreme values than the mean.","translation":"मध्यक, सरासरीपेक्षा अत्यंत मूल्यांबद्दल कमी संवेदनशील असतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The mode is useful for categorical data.","translation":"मोड (Mode) वर्गीकरण डेटासाठी उपयुक्त आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Quartiles divide the data into four equal parts.","translation":"चतुर्थक (Quartiles) डेटाला चार समान भागांमध्ये विभागतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Deciles divide the data into ten equal parts.","translation":"दशमांश (Deciles) डेटाला दहा समान भागांमध्ये विभागतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Percentiles are used to compare an individual's score to the group.","translation":"शतांश (Percentiles) एखाद्या व्यक्तीच्या स्कोअरची, समूहाशी तुलना करण्यासाठी वापरले जातात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The formula for the combined mean is a crucial concept in statistics.","translation":"एकूण सरासरीचे सूत्र सांख्यिकीमध्ये एक महत्त्वपूर्ण संकल्पना आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Understanding the relationship between mean, median, and mode is essential for data analysis.","translation":"सरासरी, मध्यक आणि मोड (Mode) यांच्यातील संबंध समजून घेणे डेटा विश्लेषणासाठी आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The geometric mean is particularly useful when dealing with rates of change.","translation":"बदलाच्या दरांशी व्यवहार करताना भूमितीय मध्य विशेषतः उपयुक्त आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The choice of which measure of central tendency to use depends on the data and the research question.","translation":"मध्यवर्ती प्रवृत्तीचे कोणते माप वापरायचे, हे डेटा आणि संशोधन प्रश्नावर अवलंबून असते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Statistical measures provide valuable insights into the characteristics of a dataset.","translation":"सांख्यिकीय मापे डेटा संचाच्या वैशिष्ट्यांमध्ये मौल्यवान अंतर्दृष्टी प्रदान करतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The company's average profit increased significantly this year.","translation":"यावर्षी कंपनीचा सरासरी नफा लक्षणीयरीत्या वाढला आहे.","target_lang":"mr","domain":"business","complexity":"simple"}
+{"en":"Statistical inferences are drawn about population parameters based on the sample observations.","translation":"लोकसंख्या मापदंडांबद्दलचे सांख्यिकीय अनुमान नमुन्यातील निरीक्षणांवर आधारित काढले जातात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The sampling unit is an electrical lamp.","translation":"नमुना घटक एक विद्युत दिवा आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"A detailed and complete list of all the sampling units is known as a “Sampling Frame”.","translation":"सर्व नमुना घटकांची विस्तृत आणि संपूर्ण यादी 'नमुना फ्रेम' म्हणून ओळखली जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Before drawing sample, it is a must to have a updated sampling frame.","translation":"नमुना काढण्यापूर्वी, अद्ययावत नमुना फ्रेम असणे आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The population mean represents the average length of life of all the lamps.","translation":"लोकसंख्या मध्यमान सर्व दिव्यांच्या सरासरी आयुर्मानाचे प्रतिनिधित्व करते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The population proportion represents the ratio of people suffering from the disease.","translation":"लोकसंख्या प्रमाण रोगाने त्रस्त असलेल्या लोकांचे गुणोत्तर दर्शवते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"A statistic may be defined as a statistical measure of sample observation.","translation":"आकडेवारीला नमुना निरीक्षणाचे सांख्यिकीय मापन म्हणून परिभाषित केले जाऊ शकते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The variation in the values of a statistic is termed as “Sampling Fluctuations”.","translation":"एका आकडेवारीच्या मूल्यांमधील बदलांना 'नमुना चढउतार' असे म्हणतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The mean of the statistic is known as “Expectation”.","translation":"आकडेवारीच्या माध्यला 'अपेक्षा' म्हणून ओळखले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Standard Error can be regarded as a measure of precision achieved by sampling.","translation":"नमुना निवड प्रक्रियेद्वारे प्राप्त अचूकतेचे मापन म्हणून प्रमाणित त्रुटी (Standard Error) मानली जाऊ शकते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Simple random sampling is completely free from Sampler’s biases.","translation":"साधे यादृच्छिक नमुना निवड (Simple random sampling) निवडणाऱ्याच्या पूर्वग्रहांपासून पूर्णपणे मुक्त आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If the population is large and heterogeneous, then we consider stratified sampling.","translation":"जर लोकसंख्या मोठी आणि विषम असेल, तर आपण स्तरित नमुना निवड (stratified sampling) विचारात घेतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The purpose of stratified sampling is to make representation of all the sub populations.","translation":"स्तरबद्ध नमुना निवडीचा (stratified sampling) उद्देश सर्व उप-लोकसंख्येचे प्रतिनिधित्व करणे आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Multi Stage Sampling is a complicated sampling method.","translation":"बहु-स्तरीय नमुना निवड (Multi Stage Sampling) ही एक गुंतागुंतीची नमुना निवड पद्धत आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Systematic sampling is a convenient method of sampling.","translation":"व्यवस्थापित नमुना निवड (Systematic sampling) ही नमुना निवडण्याची एक सोयीस्कर पद्धत आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Purposive sampling is dependent solely on the discretion of the sampler.","translation":"हेतू आधारित नमुना निवड (Purposive sampling) केवळ नमुना निवडणाऱ्याच्या निर्णयावर अवलंबून असते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The central tendency is the tendency of a given set of observations to cluster around a single central value.","translation":"मध्यवर्ती प्रवृत्ती म्हणजे निरीक्षणांचा संच एका मध्यवर्ती मूल्याच्या आसपास जमा होण्याची प्रवृत्ती.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"A company is recognized by its high average profit.","translation":"एका कंपनीची ओळख तिच्या उच्च सरासरी नफ्यावरून होते.","target_lang":"mr","domain":"business","complexity":"simple"}
+{"en":"Following are the different measures of central tendency: Mean, Median, Mode, Geometric Mean and Harmonic Mean.","translation":"मध्यवर्ती प्रवृत्तीची विविध मापे खालीलप्रमाणे आहेत: मध्य (Mean), मध्यक (Median), बहुलक (Mode), भूमितीय मध्य (Geometric Mean) आणि हरात्मक मध्य (Harmonic Mean).","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The Institute of Chartered Accountants of India provides guidelines for statistical analysis.","translation":"इन्स्टिट्यूट ऑफ चार्टर्ड अकाउंटंट्स ऑफ इंडिया सांख्यिकीय विश्लेषणासाठी मार्गदर्शन प्रदान करते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Logarithm of G for a set of observations is the AM of the logarithm of the observations.","translation":"निरीक्षणांच्या संचासाठी G चा लॉगरिदम, निरीक्षणांच्या लॉगरिदमचा AM आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If all the observations assumed by a variable are constants, say K > 0, then the GM of the observations is also K.","translation":"जर एखाद्या चलाद्वारे गृहीत धरलेली सर्व निरीक्षणे स्थिर असतील, जसे K > 0, तर निरीक्षणांचा GM देखील K असतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"GM of the product of two variables is the product of their GM‘s.","translation":"दोन चलांच्या गुणाकाराचा GM त्यांच्या GM चा गुणाकार असतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the GM of 3, 6 and 12.","translation":"3, 6 आणि 12 चा GM शोधा.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Find the GM for the following distribution: x :24816 f :233 2","translation":"खालील वितरणासाठी GM शोधा: x :24816 f :233 2","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Harmonic Mean is defined as the reciprocal of the AM of the reciprocals of the observation.","translation":"harmonic mean (HM) निरीक्षणांच्या व्यस्तांकाच्या AM चा व्यस्त म्हणून परिभाषित केले जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Find the HM for 4, 6 and 10.","translation":"4, 6 आणि 10 चा HM शोधा.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"If all the observations taken by a variable are constants, say k, then the HM of the observations is also k.","translation":"एखाद्या चलाद्वारे घेतलेली सर्व निरीक्षणे स्थिर असल्यास, k, तर निरीक्षणांचा HM देखील k असतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"For any set of positive observations, we have the following inequality: AM  GM  HM.","translation":"कोणत्याही सकारात्मक निरीक्षणांच्या संचासाठी, आपल्याकडे खालील असमानता आहे: AM  GM  HM.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Compute AM, GM, and HM for the numbers 6, 8, 12, 36.","translation":"6, 8, 12, 36 या संख्यांसाठी AM, GM आणि HM ची गणना करा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Weighted average is used when observations have a hierarchical order of importance.","translation":"जेव्हा निरीक्षणांना महत्त्वाचा श्रेणीबद्ध क्रम असतो, तेव्हा भारित सरासरी वापरली जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the weighted AM and weighted HM of first n natural numbers, the weights being equal to the squares of the corresponding numbers.","translation":"पहिल्या n नैसर्गिक संख्यांचे भारित AM आणि भारित HM शोधा, वजन संबंधित संख्यांच्या वर्गाच्या समान आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The best measure of central tendency, usually, is the AM.","translation":"मध्यवर्ती प्रवृत्तीचे सर्वोत्तम मापन, सामान्यतः, AM आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Mean is the stable and highly reliable average.","translation":"मध्य (mean) हे स्थिर आणि अत्यंत विश्वसनीय सरासरी आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Median is not based on all the observation and does not allow itself to mathematical treatment.","translation":"मध्यक (median) सर्व निरीक्षणांवर आधारित नाही आणि स्वतःला गणिती उपचारास अनुमती देत ​​नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Mode is also affected by sampling fluctuations.","translation":"मोड (mode) देखील नमुना बदलांमुळे प्रभावित होतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Given two positive numbers a and b, prove that AH=G 2.","translation":"दोन धन संख्या a आणि b दिल्यास, सिद्ध करा की AH=G 2.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The AM and GM for two observations are 5 and 4 respectively. Find the two observations.","translation":"दोन निरीक्षणांसाठी AM आणि GM अनुक्रमे 5 आणि 4 आहेत. दोन्ही निरीक्षणे शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the mean and median from the following data: Marks: less than 10 less than 20 less than 30","translation":"खालील डेटावरून मध्य (mean) आणि मध्यक (median) शोधा: गुण: 10 पेक्षा कमी, 20 पेक्षा कमी, 30 पेक्षा कमी","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The remaining observations are 4 and 9.","translation":"उर्वरित निरीक्षणे 4 आणि 9 आहेत.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Find the original frequency distribution.","translation":"मूळ वारंवारता वितरण शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Since d i = C A–x i x i = A + Cd i","translation":"d i = C A–x i x i = A + Cd i असल्यामुळे","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Compute coefficient of variation from the following data:","translation":"पुढील डेटावरून बदलाचे गुणांक मोजा:","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"What is given in this problem is less than cumulative frequency distribution.","translation":"या समस्येमध्ये काय दिले आहे ते संचयी वारंवारता वितरणापेक्षा कमी आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"We need first convert it to a frequency distribution and then compute the coefficient of variation.","translation":"आपल्याला प्रथम त्याचे वारंवारता वितरण मध्ये रूपांतर करणे आवश्यक आहे आणि नंतर बदलाचे गुणांक मोजणे आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"State in which factory, the wages are more variable.","translation":"कोणत्या फॅक्टरीत वेतन अधिक बदलणारे आहे ते सांगा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If v A > v B , then the wages of factory A would be more variable.","translation":"जर v A > v B असेल, तर फॅक्टरी A चे वेतन अधिक बदलणारे असेल.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Standard deviation is the most widely and commonly used measure of dispersion.","translation":"प्रमाण विचलन हे विखुरण्याचे सर्वात विस्तृत आणि सामान्यतः वापरले जाणारे माप आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Range is the quickest to compute and as such, has its application in statistical quality control.","translation":"श्रेणी मोजण्यासाठी सर्वात जलद आहे आणि अशा प्रकारे, त्याचे सांख्यिकीय गुणवत्ता नियंत्रणात (statistical quality control)उपयोजन आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Which of the following statements is correct?","translation":"खालीलपैकी कोणते विधान बरोबर आहे?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Two distributions may have the identical measures of central tendency but different measures of dispersion.","translation":"दोन वितरणांमध्ये मध्यवर्ती प्रवृत्तीची समान मापे असू शकतात परंतु विखुरणाची भिन्न मापे असू शकतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Dispersion measures the scatterness of a set of observations.","translation":"विखुरण निरीक्षणांच्या संचाची विखुरता मोजते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"When it comes to comparing two or more distributions we consider relative measures of dispersion.","translation":"दोन किंवा अधिक वितरणांची तुलना करताना आपण विखुरणाची सापेक्ष (relative) मापे विचारात घेतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Which one is easiest to compute? Range.","translation":"कोण मोजणे सर्वात सोपे आहे? श्रेणी.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Which one is an absolute measure of dispersion? Range.","translation":"विखुरणाचे निरपेक्ष (absolute) माप कोणते आहे? श्रेणी.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Which measure of dispersion is most useful? Standard deviation.","translation":"विखुरणाचे कोणते माप सर्वात उपयुक्त आहे? प्रमाण विचलन.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Which measures of dispersions is not affected by the presence of extreme observations? Quartile deviation.","translation":"विखुरणाचे कोणते माप अत्यंत निरीक्षणांच्या उपस्थितीमुळे प्रभावित होत नाही? चतुर्थक विचलन.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Which measure of dispersion is based on the absolute deviations only? Mean deviation.","translation":"विखुरणाचे कोणते माप केवळ निरपेक्ष विचलनावर आधारित आहे? मध्य विचलन.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Which measure is based on only the central fifty percent of the observations? Quartile deviation.","translation":"कोणते माप केवळ निरीक्षणांच्या मध्यभागी पन्नास टक्क्यांवर आधारित आहे? चतुर्थक विचलन.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If classes are of equal width.","translation":"जर वर्ग समान रुंदीचे असतील तर.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"For calculation of median we have to construct cumulative frequency distribution.","translation":"मध्यकाची गणना करण्यासाठी, आपल्याला संचयी वारंवारता वितरण तयार करणे आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"For calculation of mode we have to construct a grouped frequency distribution.","translation":"मोडची गणना करण्यासाठी, आपल्याला गटबद्ध वारंवारता वितरण तयार करणे आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Relation between mean, median & mode is mean - mode = 2 (mean - median).","translation":"मध्य, मध्यक आणि मोडमधील संबंध म्हणजे मध्य - मोड = 2 (मध्य - मध्यक).","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"When the distribution is symmetrical, mean, median and mode coincide.","translation":"जेव्हा वितरण सममित असते, तेव्हा मध्य, मध्यक आणि मोड जुळतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Mean, median & mode are equal for the normal distribution.","translation":"सामान्य वितरणासाठी मध्य, मध्यक आणि मोड समान असतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"In most frequency distributions, it has been observed that the three measures of central tendency viz. mean, median & mode, obey the approximate relation, provided the distribution is not very skew.","translation":"बहुतेक वारंवारता वितरणांमध्ये असे observed आले आहे की मध्यवर्ती प्रवृत्तीची तीन मापे म्हणजे मध्य, मध्यक आणि मोड, अंदाजे संबंध पाळतात, जर वितरण फारसे तिरकस नसेल तर.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Median divides the total number of observations into two equal parts.","translation":"मध्यक एकूण निरीक्षणांचे दोन समान भागांमध्ये विभाजन करतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Measures which are used to divide or partition the observations into a fixed number of parts are collectively known as partition values.","translation":"निरीक्षणांचे निश्चित संख्येत विभाजन करण्यासाठी किंवा विभागणी करण्यासाठी वापरल्या जाणाऱ्या मापनांना एकत्रितपणे विभाजन मूल्ये म्हणून ओळखले जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The middle most value of a set of observations is median.","translation":"निरीक्षणांच्या संचातील मधले मूल्य म्हणजे मध्यक.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The number of observations smaller than median is the same as the number larger than it.","translation":"मध्यकापेक्षा लहान निरीक्षणांची संख्या, त्यापेक्षा मोठ्या संख्येइतकीच असते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Median is the value of the variable corresponding to cumulative frequency N /2.","translation":"मध्यक हे N /2 संचयी वारंवारतेनुसार असलेल्या चलाचे मूल्य आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Quartiles divide the total no. observations into 4 equal parts.","translation":"चतुर्थक एकूण निरीक्षणांचे 4 समान भागांमध्ये विभाजन करतात.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Third quartile is known as Upper quartile.","translation":"तिसऱ्या चतुर्थकाला वरचा चतुर्थक म्हणून ओळखले जाते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"First quartile is known as Lower quartile.","translation":"पहिला चतुर्थक म्हणजे खालचा चतुर्थक.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The number of observations smaller than lower quartile is the same as the no. lying between lower and middle quartile.","translation":"खालच्या चतुर्थकापेक्षा लहान निरीक्षणांची संख्या, खालच्या आणि मधल्या चतुर्थकादरम्यान असलेल्या संख्येइतकीच असते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Quartiles are used for measuring central tendency, dispersion & skewness.","translation":"चतुर्थकांचा उपयोग मध्यवर्ती प्रवृत्ती, विचलन आणि विषमता मोजण्यासाठी केला जातो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The second quartile is known as median.","translation":"दुसऱ्या चतुर्थकाला मध्यक म्हणून ओळखले जाते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The lower & upper quartiles are used to define quartile deviation.","translation":"खालचे आणि वरचे चतुर्थक, चतुर्थक विचलन परिभाषित करण्यासाठी वापरले जातात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Bowley’s formula uses three quartiles.","translation":"बॉलीचे सूत्र तीन चतुर्थकांचा वापर करते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The standard deviation is a relative measure.","translation":"प्रमाणित विचलन हे एक सापेक्ष मापन आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Is the semi-quartile range one-fourth of the range in a normal symmetrical distribution?","translation":"अर्ध-चतुर्थक श्रेणी सामान्य सममित वितरणात श्रेणीचा एक-चतुर्थांश आहे का?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The whole frequency table is needed for the calculation of variance.","translation":"विचलन मोजण्यासाठी संपूर्ण वारंवारता सारणी आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Relative measures of dispersion make deviations in similar units comparable.","translation":"विखुरलेल्या प्रमाणाचे सापेक्ष मापन समान एककातील विचलनांची तुलना करण्यास मदत करते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Quartile deviation is based on the middle 50% of the items.","translation":"चतुर्थक विचलन वस्तूंच्या मधल्या ५०% भागावर आधारित आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The coefficient of variation is independent of the unit of measurement.","translation":"विचलनाचा गुणांक मापनाच्या एककावर अवलंबून नसतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The coefficient of variation is a relative measure of dispersion.","translation":"विचलनाचा गुणांक हा विखुरलेल्या प्रमाणाचे सापेक्ष मापन आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The coefficient of variation is equal to Standard deviation x 100 / mean.","translation":"विचलनाचा गुणांक = प्रमाणित विचलन x १०० / मध्य.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If each item is reduced by 15, the A.M is reduced by 15.","translation":"जर प्रत्येक वस्तू १५ ने कमी केली, तर अंकगणितीय मध्य (A.M) १५ ने कमी होतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If each item is reduced by 10, the range is unchanged.","translation":"जर प्रत्येक वस्तू १० ने कमी केली, तर विस्तार बदलत नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If each item is reduced by 20, the standard deviation is unchanged.","translation":"जर प्रत्येक वस्तू २० ने कमी केली, तर प्रमाणित विचलन बदलत नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If the variables are increased or decreased by the same amount, the standard deviation is unchanged.","translation":"जर चल एकाच प्रमाणात वाढवले किंवा कमी केले, तर प्रमाणित विचलन बदलत नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The mean of the 1st n natural numbers is (n+1)/2.","translation":"पहिल्या n नैसर्गिक संख्यांचा मध्य (n+1)/2 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If the class interval is open-ended then it is difficult to find the A.M.","translation":"जर वर्ग अंतराल खुले असेल, तर अंकगणितीय मध्य (A.M) शोधणे कठीण आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"For finding A.M in Step-deviation method, the class intervals should be of equal lengths.","translation":"पायरी-विचलन पद्धतीत अंकगणितीय मध्य (A.M) शोधण्यासाठी, वर्ग अंतराल समान लांबीचे असावेत.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The sum of the squares of the deviations of the variable is minimum when taken about A.M.","translation":"एका चलाच्या विचलनांच्या वर्गांची बेरीज अंकगणितीय मध्याच्या संदर्भात कमी असते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The G.M of 2 & 8 is 4.","translation":"२ आणि ८ चा भूमितीय मध्य ४ आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"(n+1)/2 th term is median if n is odd.","translation":"(n+1)/2 वी टर्म मध्यगा आहे, जर n विषम असेल.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The abscissa of the maximum frequency in the frequency curve is the mode.","translation":"वारंवारता वक्रात, महत्तम वारंवारतेचा अक्ष हा मोड असतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The class having maximum frequency is called modal class.","translation":"जास्तीत जास्त वारंवारता असलेला वर्ग मोड वर्ग (modal class) म्हणतात.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The range is a simple measure of dispersion, representing the difference between the highest and lowest values.","translation":"विस्तार हा एक सोपा विचलन मोजमाप आहे, जो सर्वात मोठ्या आणि सर्वात लहान मूल्यांमधील फरक दर्शवतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Coefficient of range is calculated as the difference between the largest and smallest values, divided by their sum, and multiplied by 100.","translation":"विस्तार गुणांक सर्वात मोठ्या आणि सर्वात लहान मूल्यांमधील फरक, त्यांच्या बेरजेने भागून, 100 ने गुणून मोजला जातो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"For a grouped frequency distribution, the range is the difference between the upper and lower class boundaries.","translation":"गटबद्ध वारंवारता वितरणासाठी, विस्तार म्हणजे वरच्या आणि खालच्या वर्ग सीमांमधील फरक.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The range remains unaffected by a change of origin but is affected proportionally by a change of scale.","translation":"विस्तार मूळ बदलाने अप्रभावित राहतो, परंतु प्रमाणात स्केल बदलाने प्रभावित होतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The wages of eight workers are given in rupees: 82, 96, 52, 75, 70, 65, 50, and 70. Calculate the range and its coefficient.","translation":"आठ कामगारांचे वेतन रुपयात दिलेले आहे: 82, 96, 52, 75, 70, 65, 50, आणि 70. विस्तार आणि त्याचा गुणांक मोजा.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"What is the range and its coefficient for the following distribution of weights?","translation":"वजनांच्या खालील वितरणासाठी विस्तार आणि त्याचा गुणांक काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If the relationship between x and y is given by 2x + 3y = 10 and the range of x is 15, what would be the range of y?","translation":"जर x आणि y मधील संबंध 2x + 3y = 10 द्वारे दिला गेला असेल आणि x चा विस्तार 15 असेल, तर y चा विस्तार काय असेल?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Mean deviation is the arithmetic mean of the absolute deviations of the observations from an average.","translation":"मध्य विचलन म्हणजे सरासरीमधून निरीक्षणांच्या निरपेक्ष विचलनांचे अंकगणितीय मध्यमान आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"For a grouped frequency distribution, mean deviation is calculated using the mid-value and frequency of each class interval.","translation":"गटबद्ध वारंवारता वितरणासाठी, प्रत्येक वर्ग अंतराच्या मध्य-मूल्य आणि वारंवारतेचा वापर करून मध्य विचलन मोजले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The coefficient of mean deviation is calculated by dividing the mean deviation by the average and multiplying by 100.","translation":"मध्य विचलनाचा गुणांक, मध्य विचलनाला सरासरीने भागून आणि 100 ने गुणून मोजला जातो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Mean deviation takes its minimum value when deviations are taken from the median.","translation":"मध्य विचलन त्याचे किमान मूल्य तेव्हा घेते जेव्हा विचलन मध्यकावरून घेतले जातात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Mean deviation remains unchanged due to a change of origin but changes proportionally due to a change of scale.","translation":"मध्य विचलन मूळ बदलामुळे अपरिवर्तित राहते, परंतु प्रमाणात स्केल बदलामुळे बदलते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Find the mean deviation about the mean for the following numbers: 5, 8, 10, 10, 12, 9.","translation":"खालील संख्यांसाठी मध्यमानाबद्दल मध्य विचलन शोधा: 5, 8, 10, 10, 12, 9.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find mean deviations about median and also the corresponding coefficient for the following profits of a firm.","translation":"एका फर्मच्या खालील नफ्यासाठी मध्यकेबद्दल मध्य विचलन आणि संबंधित गुणांक शोधा.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Compute the mean deviation about the arithmetic mean for the following data.","translation":"खालील डेटासाठी अंकगणितीय मध्यमानाबद्दल मध्य विचलन मोजा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Compute the coefficient of mean deviation about median for the following distribution.","translation":"खालील वितरणासाठी मध्यकेबद्दल मध्य विचलनाचा गुणांक मोजा.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If x and y are related as 4x + 3y + 11 = 0 and mean deviation of x is 5.40, what is the mean deviation of y?","translation":"जर x आणि y चा संबंध 4x + 3y + 11 = 0 असा असेल आणि x चे मध्य विचलन 5.40 असेल, तर y चे मध्य विचलन काय आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Standard deviation is the root mean square deviation when deviations are taken from the arithmetic mean.","translation":"प्रमाण विचलन म्हणजे वर्गमध्य विचलन, जेव्हा विचलन अंकगणितीय मध्यमानावरून घेतले जातात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The coefficient of variation is the ratio of the standard deviation to the arithmetic mean, expressed as a percentage.","translation":"विचलनाचा गुणांक म्हणजे प्रमाण विचलन आणि अंकगणितीय मध्यमान यांचे गुणोत्तर, जे टक्केवारीत व्यक्त केले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the standard deviation and the coefficient of variation for the following numbers: 5, 8, 9, 2, 6.","translation":"खालील संख्यांसाठी प्रमाण विचलन आणि विचलनाचा गुणांक शोधा: 5, 8, 9, 2, 6.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The probability of an event is always between 0 and 1.","translation":"एखाद्या घटनेची संभाव्यता नेहमी 0 आणि 1 च्या दरम्यान असते.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"What is the probability of getting heads when flipping a coin?","translation":"नाणे फेकल्यावर छापा येण्याची संभाव्यता काय आहे?","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"The union of two events includes all outcomes in either event.","translation":"दोन घटनांचा संयोग एकतर घटनेतील सर्व निष्कर्षांचा समावेश करतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The intersection of two events includes only the outcomes common to both.","translation":"दोन घटनांचा छेद केवळ दोन्हीमध्ये सामायिक असलेल्या निष्कर्षांचा समावेश करतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If two events are mutually exclusive, they cannot occur at the same time.","translation":"जर दोन घटना एकमेकांना अपवर्जित असतील, तर त्या एकाच वेळी घडू शकत नाहीत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Calculate the probability of drawing a red card from a deck of cards.","translation":"पत्त्यांच्या कॅटमधून लाल कार्ड काढण्याची संभाव्यता मोजा.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"The probability of an event not happening is the complement of the event.","translation":"एखादी घटना न घडण्याची संभाव्यता म्हणजे त्या घटनेची पूरक घटना होय.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"What is the probability of rolling a 6 on a standard six-sided die?","translation":"एका standard सहा-बाजू असलेल्या फाशावर 6 येण्याची संभाव्यता काय आहे?","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"The sample space is the set of all possible outcomes of an experiment.","translation":"नमुना अवकाश म्हणजे प्रयोगाच्या सर्व संभाव्य निष्कर्षांचा संच होय.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Probability is a fundamental concept in statistics and data analysis.","translation":"संभाव्यता हे सांख्यिकी आणि डेटा विश्लेषणातील एक मूलभूत तत्त्व आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The odds in favor of an event are the ratio of favorable outcomes to unfavorable outcomes.","translation":"एखाद्या घटनेच्या बाजूने असलेली शक्यता म्हणजे अनुकूल निष्कर्षांचे प्रतिकूल निष्कर्षांशी असलेले गुणोत्तर.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Conditional probability considers the probability of an event given that another event has already occurred.","translation":"शर्तित संभाव्यता, दुसरी घटना आधीच घडली आहे हे लक्षात घेऊन, एका घटनेची संभाव्यता विचारात घेते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Bayes' theorem is used to update probabilities based on new evidence.","translation":"नवीन पुराव्यांवर आधारित संभाव्यता अद्ययावत करण्यासाठी बेजचा प्रमेय वापरला जातो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Independent events do not affect each other's probabilities.","translation":"स्वतंत्र घटना एकमेकांच्या संभाव्यतेवर परिणाम करत नाहीत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Calculate the probability of drawing two aces in a row from a deck of cards without replacement.","translation":"एका पत्त्यांच्या कॅटमधून, कोणताही पत्ता परत न ठेवता, सलग दोन एक्के काढण्याची संभाव्यता मोजा.","target_lang":"mr","domain":"general","complexity":"complex"}
+{"en":"The law of large numbers states that as the number of trials increases, the experimental probability approaches the theoretical probability.","translation":"मोठ्या संख्येचा नियम सांगतो की जसा प्रयत्नांची संख्या वाढते, तशी प्रायोगिक संभाव्यता सैद्धांतिक संभाव्यतेच्या जवळ जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"What is the probability of getting at least one head when flipping a coin three times?","translation":"एका नाण्याला तीन वेळा फेकल्यास कमीतकमी एक हेड येण्याची संभाव्यता काय आहे?","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"Probability distributions describe the likelihood of different outcomes.","translation":"संभाव्यता वितरणे विविध निष्कर्षांची शक्यता दर्शवतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The expected value is the average outcome of an event over many trials.","translation":"अपेक्षित मूल्य म्हणजे अनेक प्रयत्नांनंतर एखाद्या घटनेचा सरासरी निष्कर्ष.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Understanding probability is crucial for making informed decisions in many fields.","translation":"अनेक क्षेत्रांमध्ये माहितीपूर्ण निर्णय घेण्यासाठी संभाव्यता समजून घेणे आवश्यक आहे.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"The probability of an event is always between 0 and 1.","translation":"एखाद्या घटनेची संभाव्यता नेहमी 0 आणि 1 च्या दरम्यान असते.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"What is the probability of getting heads when flipping a coin?","translation":"नाणे फेकल्यावर छापा येण्याची संभाव्यता काय आहे?","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"The odds of winning the lottery are very low.","translation":"लॉटरी जिंकण्याची शक्यता फार कमी असते.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"Statistical analysis is crucial for understanding data.","translation":"डेटा समजून घेण्यासाठी सांख्यिकीय विश्लेषण आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If two events are independent, the outcome of one does not affect the other.","translation":"जर दोन घटना स्वतंत्र असतील, तर एकाचा परिणाम दुसऱ्यावर होत नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The expected value is a key concept in probability theory.","translation":"अपेक्षित मूल्य संभाव्यता सिद्धांतातील एक महत्त्वाची संकल्पना आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Mutually exclusive events cannot occur at the same time.","translation":"परस्पर अनन्य घटना एकाच वेळी घडू शकत नाहीत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The probability of rain tomorrow is 60%.","translation":"उद्या पावसाची शक्यता 60% आहे.","target_lang":"mr","domain":"news","complexity":"simple"}
+{"en":"The company's success depends on several factors.","translation":"कंपनीचे यश अनेक घटकांवर अवलंबून असते.","target_lang":"mr","domain":"business","complexity":"moderate"}
+{"en":"The survey results showed a high degree of uncertainty.","translation":"सर्वेक्षणातून मोठ्या प्रमाणात अनिश्चितता दिसून आली.","target_lang":"mr","domain":"research","complexity":"moderate"}
+{"en":"The chances of recovery are good.","translation":"बरे होण्याची शक्यता चांगली आहे.","target_lang":"mr","domain":"medical","complexity":"simple"}
+{"en":"The risk assessment is a critical step in project planning.","translation":"जोखीम मूल्यांकन हे प्रकल्प नियोजनातील एक महत्त्वपूर्ण पाऊल आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The data was analyzed using statistical methods.","translation":"डेटाचे विश्लेषण सांख्यिकीय पद्धती वापरून केले गेले.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The probability of drawing a red card from a deck of cards is 1/2.","translation":"पत्त्यांच्या कॅटमधून लाल कार्ड काढण्याची संभाव्यता 1/2 आहे.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"The weather forecast predicts a low probability of snow.","translation":"हवामान खात्याचा अंदाज आहे की बर्फवृष्टीची शक्यता कमी आहे.","target_lang":"mr","domain":"news","complexity":"moderate"}
+{"en":"The outcome of the experiment was unexpected.","translation":"प्रयोगाचा निकाल अनपेक्षित होता.","target_lang":"mr","domain":"research","complexity":"moderate"}
+{"en":"The odds were stacked against them.","translation":"सगळे त्यांच्या विरोधात होते.","target_lang":"mr","domain":"general","complexity":"complex"}
+{"en":"The probability of success increases with hard work.","translation":"कठोर परिश्रमाने यशाची शक्यता वाढते.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"The statistical significance of the results was carefully evaluated.","translation":"परिणामाचे सांख्यिकीय महत्त्व काळजीपूर्वक तपासले गेले.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The chances of winning are slim, but we must try.","translation":"जिंकण्याची शक्यता कमी आहे, पण आपण प्रयत्न केला पाहिजे.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"What is the probability that the sample does not contain more than 1 defective?","translation":"नमुन्यात 1 पेक्षा जास्त सदोष घटक नसण्याची संभाव्यता काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"There are three persons aged 60, 65 and 70 years old.","translation":"तिघे व्यक्ती आहेत, ज्यांची वये 60, 65 आणि 70 वर्षे आहेत.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"What is the probability that at least two of them would survive another five years?","translation":"त्यापैकी किमान दोघे आणखी पाच वर्षे जगण्याची काय शक्यता आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Tom speaks truth in 30 percent cases and Dick speaks truth in 25 percent cases.","translation":"टॉम 30 टक्के प्रकरणांमध्ये आणि डिक 25 टक्के प्रकरणांमध्ये सत्य बोलतो.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"What is the probability that they would contradict each other?","translation":"ते एकमेकांविरुद्ध बोलण्याची काय शक्यता आहे?","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"There are two urns.","translation":"दोन भांडी आहेत.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"The first urn contains 3 red and 5 white balls whereas the second urn contains 4 red and 6 white balls.","translation":"पहिल्या भांड्यात 3 लाल आणि 5 पांढरे चेंडू आहेत, तर दुसऱ्या भांड्यात 4 लाल आणि 6 पांढरे चेंडू आहेत.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"A ball is taken at random from the first urn and is transferred to the second urn.","translation":"पहिल्या भांड्यातून यादृच्छिकपणे एक चेंडू काढला जातो आणि दुसऱ्या भांड्यात टाकला जातो.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"Now another ball is selected at random from the second urn.","translation":"आता दुसऱ्या भांड्यातून यादृच्छिकपणे दुसरा चेंडू निवडला जातो.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"The probability that the second ball would be red is...","translation":"दुसरा चेंडू लाल असण्याची संभाव्यता...","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"For a group of students, 30 %, 40% and 50% failed in Physics , Chemistry and at least one of the two subjects respectively.","translation":"विद्यार्थ्यांच्या एका गटात, 30%, 40% आणि 50% अनुक्रमे भौतिकशास्त्र, रसायनशास्त्र आणि दोन्हीपैकी किमान एका विषयात अनुत्तीर्ण झाले.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If an examinee is selected at random, what is the probability that he passed in Physics if it is known that he failed in Chemistry?","translation":"एखाद्या परीक्षार्थीची यादृच्छिक निवड केली, तर रसायनशास्त्रात अनुत्तीर्ण झाला हे माहित असताना, त्याने भौतिकशास्त्र विषयात उत्तीर्ण होण्याची काय शक्यता आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"A packet of 10 electronic components is known to include 2 defectives.","translation":"10 इलेक्ट्रॉनिक घटकांच्या पॅकेटमध्ये 2 सदोष घटक आहेत, हे माहित आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If a sample of 4 components is selected at random from the packet...","translation":"जर पॅकेटमधून 4 घटकांचा नमुना यादृच्छिकपणे निवडला गेला...","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"8 identical balls are placed at random in three bags.","translation":"8 एकसारखे चेंडू तीन पिशव्यांमध्ये यादृच्छिकपणे ठेवले आहेत.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"What is the probability that the first bag will contain 3 balls?","translation":"पहिल्या पिशवीत 3 चेंडू असण्याची काय शक्यता आहे?","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"X and Y stand in a line with 6 other people.","translation":"X आणि Y 6 इतर लोकांसोबत एका रांगेत उभे आहेत.","target_lang":"mr","domain":"general","complexity":"simple"}
+{"en":"What is the probability that there are 3 persons between them?","translation":"त्यांच्यामध्ये 3 व्यक्ती असण्याची काय शक्यता आहे?","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"Given that P (A) = 1/2, P (B) = 1/3, P (A  B) = 1/4, what is P (A’/B’)","translation":"जर P (A) = 1/2, P (B) = 1/3, P (A  B) = 1/4, तर P (A’/B’) काय आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Four digits 1, 2, 4 and 6 are selected at random to form a four digit number.","translation":"1, 2, 4 आणि 6 हे चार अंक यादृच्छिकपणे निवडले जातात आणि त्यातून चार अंकी संख्या तयार केली जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"What is the probability that there would be at least one computer error per week?","translation":"एका आठवड्यात किमान एक तरी संगणक त्रुटी येण्याची काय शक्यता आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Probability of having one and only one computer error per week.","translation":"एका आठवड्यात केवळ एकच संगणक त्रुटी येण्याची संभाव्यता.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If a sample of 4 components is selected at random from the lot, what is the probability that this sample does not contain more than one defectives?","translation":"जर 4 घटकांचा नमुना यादृच्छिकपणे निवडला गेला, तर या नमुन्यात एकापेक्षा जास्त दोष नसण्याची काय शक्यता आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"There are two urns containing 5 red and 6 white balls and 3 red and 7 white balls respectively.","translation":"दोन कलशांमध्ये 5 लाल आणि 6 पांढरे चेंडू आहेत, तसेच 3 लाल आणि 7 पांढरे चेंडू आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If two balls are drawn from the first urn without replacement and transferred to the second urn and then a draw of another two balls is made from it, what is the probability that both the balls drawn are red?","translation":"पहिला कलशातून दोन चेंडू परत न ठेवता काढले आणि दुसऱ्या कलशात ठेवले, आणि नंतर त्यातून आणखी दोन चेंडू काढले, तर दोन्ही काढलेले चेंडू लाल असण्याची काय शक्यता आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If 8 balls are distributed at random among three boxes, what is the probability that the first box would contain 3 balls?","translation":"जर 8 चेंडू तीन पेट्यांमध्ये यादृच्छिकपणे विभागले गेले, तर पहिल्या पेटीत 3 चेंडू असण्याची काय शक्यता आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"One of the boxes is selected at random and a ball is drawn from it.","translation":"एका पेटीची यादृच्छिकपणे निवड केली जाते आणि त्यातून एक चेंडू काढला जातो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"What is the probability that the drawn ball is red?","translation":"काढलेला चेंडू लाल असण्याची काय शक्यता आहे?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"A random variable or stochastic variable is a function defined on a sample space.","translation":"एक यादृच्छिक चल किंवा स्टोकेस्टिक चल हे नमुना जागेवर परिभाषित केलेले कार्य आह��.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If a coin is tossed three times and if X denotes the number of heads, then X is a random variable.","translation":"जर नाणे तीन वेळा टाकले आणि X हे छापांची संख्या दर्शवते, तर X एक यादृच्छिक चल आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"We can make a distinction between a discrete random variable and a continuous variable.","translation":"आपण डिस्क्रीट यादृच्छिक चल आणि सतत चल यांच्यात फरक करू शकतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The probability distribution of a random variable may be defined as a statement expressing the different values taken by a random variable and the corresponding probabilities.","translation":"एका यादृच्छिक चलाचे संभाव्यता वितरण यादृच्छिक चलाद्वारे घेतलेली विविध मूल्ये आणि संबंधित संभाव्यता व्यक्त करणारे विधान म्हणून परिभाषित केले जाऊ शकते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If an unbiased coin is tossed three times and if X denotes the number of heads then, as we have already discussed, X is a random variable and its probability distribution is given by.","translation":"जर एक नाणे तीन वेळा टाकले आणि X हे छापांची संख्या दर्शवते, तर, आपण आधीच चर्चा केल्याप्रमाणे, X एक यादृच्छिक चल आहे आणि त्याचे संभाव्यता वितरण खालीलप्रमाणे दिले आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"There are cases when it is possible to express the probability (P) as a function of X.","translation":"असे काही प्रसंग आहेत जेव्हा संभाव्यता (P) X च्या कार्याप्रमाणे व्यक्त करणे शक्य होते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Expected value or Mathematical Expectation or Expectation of a random variable may be defined as the sum of products of the different values taken by the random variable and the corresponding probabilities.","translation":"एका यादृच्छिक चलाचे अपेक्षित मूल्य किंवा गणितीय अपेक्षा किंवा अपेक्षा यादृच्छिक चलाद्वारे घेतलेल्या विविध मूल्यांच्या गुणाकारांची बेरीज आणि संबंधित संभाव्यता म्हणून परिभाषित केली जाऊ शकते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Variance of x, to be denoted by ,  2 is given by V(x) = 2  = E(x –  ) 2 = E(x 2 ) –  2 .","translation":"x चा variance,  2 द्वारे दर्शविला जातो, V(x) =  2 = E(x –  ) 2 = E(x 2 ) –  2 द्वारे दिला जातो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If y = a + b x, for two random variables x and y and for a pair of constants a and b, then the mean i.e. expected value of y is given by.","translation":"जर y = a + b x, दोन यादृच्छिक चलांसाठी x आणि y आणि स्थिरांकांच्या जोडीसाठी a आणि b, तर y चा मध्य म्हणजे अपेक्षित मूल्य याद्वारे दिले जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"An unbiased coin is tossed three times. Find the expected value of the number of heads and also its standard deviation.","translation":"एक नाणे तीन वेळा टाकले जाते. छापांच्या संख्येचे अपेक्षित मूल्य आणि त्याचे मानक विचलन शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"A random variable has the following probability distribution:","translation":"एका यादृच्छिक चलाचे संभाव्यता वितरण खालीलप्रमाणे आहे:","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"In a business venture, a man can make a profit of ` 50,000 or incur a loss of ` 20,000.","translation":"एका व्यवसाय उपक्रमात, एक माणूस ` 50,000 चा नफा मिळवू शकतो किंवा ` 20,000 चे नुकसान सहन करू शकतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"By studying the effect of a particular type of missiles, it may be possible for our scientist to suggest the number of such missiles necessary to destroy an army position.","translation":"एका विशिष्ट प्रकारच्या क्षेपणास्त्रांच्या परिणामाचा अभ्यास करून, आपल्या शास्त्रज्ञांना लष्करी ठाणे उद्ध्वस्त करण्यासाठी आवश्यक असलेल्या क्षेपणास्त्रांची संख्या सुचवणे शक्य होऊ शकते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"By knowing the distribution of smokers, a social activist may warn the people of a locality about the nuisance of active and passive smoking and so on.","translation":"धूम्रपान करणाऱ्यांची संख्या माहीत करून, एक सामाजिक कार्यकर्ता परिसरातील लोकांना सक्रिय आणि निष्क्रिय धूम्रपानाच्या त्रासाबद्दल इशारा देऊ शकतो.","target_lang":"mr","domain":"general","complexity":"moderate"}
+{"en":"Theoretical probability distribution may be profitably employed to make short term projections for the future.","translation":"भविष्यासाठी अल्पकालीन अंदाज घेण्यासाठी सैद्धांतिक संभाव्यता वितरणाचा फायदेशीरपणे उपयोग केला जाऊ शकतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Setting confidence limits or testing statistical hypothesis about population parameter(s) is based on the probability distribution of the population under consideration.","translation":"लोकसंख्या पॅरामीटर(चे) बद्दल विश्वास मर्यादा निश्चित करणे किंवा सांख्यिकीय परिकल्पना तपासणे हे विचाराधीन असलेल्या लोकसंख्येच्या संभाव्यता वितरणावर आधारित आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"We define mean  , median   , mode    , standard deviation   etc. exactly same way we have done earlier.","translation":"आपण पूर्वी ज्या पद्धतीने मध्य , मध्यक  , मोड   , मानक विचलन   इत्यादींची व्याख्या केली आहे, त्याच पद्धतीने करतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Two important discrete probability distributions are (a) Binomial Distribution and (b) Poisson distribution.","translation":"दोन महत्त्वपूर्ण असंवादी संभाव्यता वितरणे म्हणजे (अ) द्विपद वितरण आणि (ब) पॉइसन वितरण.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"One of the most important and frequently used discrete probability distribution is Binomial Distribution.","translation":"सर्वात महत्त्वाचे आणि वारंवार वापरले जाणारे असंवादी संभाव्यता वितरण म्हणजे द्विपद वितरण.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"It is derived from a particular type of random experiment known as Bernoulli process named after the famous mathematician Bernoulli.","translation":"हे बर्नोली प्रक्रियेच्या नावाने ओळखल्या जाणाऱ्या एका विशिष्ट प्रकारच्या यादृच्छिक प्रयोगातून तयार केले जाते, ज्याचे नाव प्रसिद्ध गणितज्ञ बर्नोली यांच्या नावावर ठेवले आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Each trial is associated with two mutually exclusive and exhaustive outcomes, the occurrence of one of which is known as a 'success' and as such its non occurrence as a 'failure'.","translation":"प्रत्येक चाचणी दोन परस्पर अनन्य आणि संपूर्ण परिणामांशी संबंधित आहे, ज्यापैकी एकाला 'यश' म्हणून ओळखले जाते आणि त्याची अनुपस्थिती 'अपयश' म्हणून ओळखली जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"As an example, when a coin is tossed, usually occurrence of a head is known as a success and its non–occurrence i.e. occurrence of a tail is known as a failure.","translation":"उदाहरणार्थ, जेव्हा नाणे (coin) फेकले जाते, तेव्हा सामान्यतः छापा येणे हे यश म्हणून ओळखले जाते आणि त्याची अनुपस्थिती म्हणजे काटा येणे, हे अपयश म्हणून ओळखले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The trials are independent.","translation":"चाचण्या स्वतंत्र असतात.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The probability of a success, usually denoted by p, and hence that of a failure, usually denoted by q = 1–p, remain unchanged throughout the process.","translation":"यशाची संभाव्यता, जी सामान्यतः p ने दर्शविली जाते, आणि अपयशाची संभाव्यता, जी सामान्यतः q = 1–p ने दर्शविली जाते, ती संपूर्ण प्रक्रियेदरम्यान बदलत नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The number of trials is a finite positive integer.","translation":"चाचण्यांची संख्या एक निश्चित धन पूर्णांक असते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"A discrete random variable x is defined to follow binomial distribution with parameters n and p, to be denoted by x ~ B (n, p).","translation":"एक असंवादी यादृच्छिक चल x, n आणि p पॅरामीटर्ससह द्विपद वितरणाचे अनुसरण करते, ज्याला x ~ B (n, p) असे दर्शविले जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Binomial distribution is known as biparametric distribution as it is characterised by two parameters n and p.","translation":"द्विपद वितरण हे द्वि-पॅरामीट्रिक वितरण म्हणून ओळखले जाते कारण ते दोन पॅरामीटर्स n आणि p द्वारे दर्शविले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"This means that if the values of n and p are known, then the distribution is known completely.","translation":"याचा अर्थ असा आहे की जर n आणि p ची मूल्ये माहित असतील, तर वितरण पूर्णपणे ज्ञात आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The mean of the binomial distribution is given by  = np.","translation":"द्विपद वितरणाचा मध्य  = np द्वारे दिला जातो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Depending on the values of the two parameters, binomial distribution may be unimodal or bi- modal.","translation":"दोन पॅरामीटर्सच्या मूल्यांवर अवलंबून, द्विपद वितरण एक-मोडी किंवा द्वि-मोडी असू शकते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The variance of the binomial distribution is given by 2  = npq.","translation":"द्विपद वितरणाचे विचरण 2  = npq द्वारे दिले जाते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Binomial distribution is applicable when the trials are independent and each trial has just two outcomes success and failure.","translation":"द्विपद वितरण तेव्हा लागू होते जेव्हा चाचण्या स्वतंत्र असतात आणि प्रत्येक चाचणीचे फक्त दोन परिणाम असतात: यश आणि अपयश.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The average number of phone calls per minute is 4.","translation":"एका मिनिटात येणाऱ्या फोन कॉल्सची सरासरी संख्या 4 आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"What is the probability of no phone calls in a particular minute?","translation":"एका विशिष्ट मिनिटात एकही फोन कॉल न येण्याची संभाव्यता काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The Poisson distribution is used to model the number of events in a fixed interval of time or space.","translation":"पॉइसन वितरण वेळेच्या किंवा जागेच्या निश्चित अंतरात घटनांची संख्या मॉडेल करण्यासाठी वापरले जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If 2% of the bulbs are defective, what is the probability of exactly one defective bulb in a sample of 150?","translation":"जर 2% बल्ब सदोष असतील, तर 150 च्या नमुन्यात नेमका एक सदोष बल्ब असण्याची संभाव्यता काय आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Calculate the probability of more than 2 defective bulbs.","translation":"2 पेक्षा जास्त सदोष बल्ब असण्याची संभाव्यता मोजा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"A manufacturer guarantees that not more than 2% of the components in a box will be defective.","translation":"एक उत्पादक हमी देतो की एका बॉक्समधील 2% पेक्षा जास्त घटक सदोष होणार नाहीत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the probability that a box fails to meet the guarantee.","translation":"एका बॉक्समध्ये हमी पूर्ण न होण्याची संभाव्यता शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Let x denote the number of electric components.","translation":"x हे विद्युत घटकांची संख्या दर्शवते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The binomial distribution can be approximated by a Poisson distribution.","translation":"द्विपद वितरणाचे अनुमान पॉइसन वितरणाने करता येते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"A discrete random variable follows a Poisson distribution.","translation":"एक विविक्त यादृच्छिक चल पॉइसन वितरणानुसार आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find P(X = at least 1).","translation":"P(X = किमान 1) शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Given E(x) = 2.20 and e^-2.20 = 0.1108.","translation":"E(x) = 2.20 आणि e^-2.20 = 0.1108 दिले आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The mean of the observed frequency distribution is calculated.","translation":"निरीक्षित वारंवारता वितरणाचे मध्य (mean) मोजले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Fit a Poisson distribution to the given data.","translation":"दिलेल्या डेटासाठी पॉइसन वितरण जुळवा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The normal distribution is a continuous probability distribution.","translation":"सामान्य वितरण हे एक अखंड संभाव्यता वितरण आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The normal curve is bell-shaped.","translation":"सामान्य वक्र (normal curve) घंटाकृती असतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The normal distribution is symmetrical about the mean.","translation":"सामान्य वितरण मध्याच्या (mean) संदर्भात सममितीय असते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The total area under the normal curve is unity.","translation":"सामान्य वक्राखालील एकूण क्षेत्रफळ एक (unity) असते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The standard normal variate is denoted by z.","translation":"मानक सामान्य चल z ने दर्शविला जातो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The normal distribution is characterized by two parameters.","translation":"सामान्य वितरणाचे दोन पॅरामीटर्सद्वारे (parameters) वर्णन केले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The analysis helps determine if two variables are related.","translation":"विश्लेषण दोन चलांमधील संबंधांचे मूल्यांकन करण्यास मदत करते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Correlation analysis examines the strength and direction of a relationship.","translation":"सहसंबंध विश्लेषण संबंधाची ताकद आणि दिशा तपासते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Regression analysis predicts the value of a dependent variable.","translation":"रिग्रेशन विश्लेषण एका अवलंबून चलाचे मूल्य दर्शवते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Bivariate data involves two variables measured simultaneously.","translation":"द्विचलीय डेटा एकाच वेळी मोजलेल्या दोन चलांचा समावेश करतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"A bivariate frequency distribution organizes data for two variables.","translation":"द्विचलीय वारंवारता वितरण दोन चलांसाठी डेटा व्यवस्थित करते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The marks of students in math and statistics can be analyzed.","translation":"गणित आणि सांख्यिकीमधील विद्यार्थ्यांचे गुण तपासले जाऊ शकतात.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"We can create a table to show the frequency of marks.","translation":"गुणांची वारंवारता दर्शवण्यासाठी आपण एक सारणी तयार करू शकतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The range of marks in both subjects is important.","translation":"दोन्ही विषयातील गुणांची श्रेणी महत्त्वाची आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Class intervals are used to group the marks.","translation":"गुणांचे गट तयार करण्यासाठी वर्ग अंतराल वापरले जातात.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Marginal distributions can be derived from the bivariate data.","translation":"द्विचलीय डेटावरून मार्जिनल वितरण काढले जाऊ शकते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Conditional distributions show the distribution of one variable given another.","translation":"शर्तयुक्त वितरण, दुसऱ्या चलाच्या आधारावर एका चलाचे वितरण दर्शवते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If one variable changes, does the other change too?","translation":"एका चलामध्ये बदल झाल्यास, दुसऱ्या चलातही बदल होतो का?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Positive correlation means both variables increase together.","translation":"सकारात्मक सहसंबंध म्हणजे दोन्ही चल एकाच दिशेने वाढतात.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Negative correlation means one variable increases while the other decreases.","translation":"नकारात्मक सहसंबंध म्हणजे एक चल वाढते, तर दुसरे कमी होते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Uncorrelated variables show no relationship.","translation":"असहसंबंधित चल कोणताच संबंध दर्शवत नाहीत.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"A scatter diagram is a visual way to show correlation.","translation":"विकिरण आकृती सहसंबंध दर्शव��्याचा एक दृश्य मार्ग आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Karl Pearson's coefficient measures linear correlation.","translation":"कार्ल पियर्सनचा गुणांक रेषीय सहसंबंध मोजतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The correlation coefficient is a unit-free measure.","translation":"सहसंबंध गुणांक एक एकक-मुक्त मापन आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The coefficient ranges from -1 to +1.","translation":"गुणांकाची श्रेणी -1 ते +1 पर्यंत असते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Rank correlation is used for qualitative data.","translation":"श्रेणी सहसंबंध गुणात्मक डेटासाठी वापरला जातो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The mean of a normal distribution is 500 and 16 per cent of the values are greater than 600.","translation":"एका सामान्य वितरणाचे मध्यमान ५०० आहे आणि १६ टक्के मूल्ये ६०० पेक्षा मोठी आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"What is the standard deviation of the distribution?","translation":"वितरणाचे प्रमाण विचलन काय आहे?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Let X denote the wage.","translation":"X हे वेतन दर्शवते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"It is given that X is normally distributed with mean as ` 500 and SD as ` 100.","translation":"हे दिले आहे की X सामान्यपणे ५०० च्या मध्यमानासह आणि १०० च्या SD सह वितरित केले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If the wages of 100 workers in the group are less than ` 430, what is the total number of workers in the group?","translation":"जर गटातील १०० कामगारांचे वेतन `४३० पेक्षा कमी असेल, तर गटातील कामगारांची एकूण संख्या किती?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The mean height of 2000 students at a certain college is 165 cms and SD 9 cms.","translation":"एका विशिष्ट कॉलेजमधील २००० विद्यार्थ्यांची सरासरी उंची १६५ सेमी आणि SD ९ सेमी आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"What is the probability that in a group of 5 students of that college, 3 or more students would have height more than 174 cm?","translation":"त्या कॉलेजमधील ५ विद्यार्थ्यांच्या गटात, ३ किंवा अधिक विद्यार्थ्यांची उंची १७४ सेमी पेक्षा जास्त असण्याची संभाव्यता काय आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Let X denote the height of the students of the college.","translation":"X हे कॉलेजमधील विद्यार्थ्यांची उंची दर्शवते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"We assume that X is normally distributed with mean () 165 cms and SD () as 9 cms.","translation":"आम्ही असे मानतो की X सामान्यपणे () १६५ सेमी च्या मध्यमानासह आणि SD () ९ सेमी म्हणून वितरित केले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If p denotes the probability that a student selected at random would have height more than 174 cms., then","translation":"जर p यादृच्छिकपणे निवडलेल्या विद्यार्थ्याची उंची १७४ सेमी पेक्षा जास्त असण्याची संभाव्यता दर्शवते, तर","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If y denotes the number of students having height more than 174 cm. in a group of 5 students then y ~  (n, p) where n = 5 and p = 0.1587.","translation":"जर y ५ विद्यार्थ्यांच्या गटातील १७४ सेमी पेक्षा जास्त उंची असलेल्या विद्यार्थ्यांची संख्या दर्शवते, तर y ~  (n, p) जेथे n = ५ आणि p = ०.१५८७.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Thus the probability that 3 or more students would be more than 174 cm.","translation":"म्हणून, ३ किंवा अधिक विद्यार्थी १७४ सेमी पेक्षा जास्त उंचीचे असण्याची संभाव्यता.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"In a business, it is assumed that the average daily sales expressed in Rupees follows normal distribution.","translation":"एका व्यवसायात, असे मानले जाते की सरासरी दैनिक विक्री, जी रुपयांमध्ये व्यक्त केली जाते, ती सामान्य वितरणाचे अनुसरण करते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Find the coefficient of variation of sales given that the probability that the average daily sales is less than ` 124 is 0.0287 and the probability that the average daily sales is more than ` 270 is 0.4599.","translation":"विक्रीचा बदल गुणांक शोधा, हे लक्षात घेऊन की सरासरी दैनिक विक्री `१२४ पेक्षा कमी असण्याची संभाव्यता ०.०२८७ आहे आणि सरासरी दैनिक विक्री `२७० पेक्षा जास्त असण्याची संभाव्यता ०.४५९९ आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Let us denote the average daily sales by x and the mean and SD of x by  and  respectively.","translation":"सरासरी दैनिक विक्री x ने दर्शवूया आणि x चे मध्यमान आणि SD अनुक्रमे  आणि  ने दर्शवूया.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"As given, P ( x < 124 ) = 0.0287 ........(1)","translation":"दिलेल्या माहितीनुसार, P ( x < १२४ ) = ०.०२८७ ........(१)","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"P ( x > 270 ) = 0.4599 ........(2)","translation":"P ( x > २७० ) = ०.४५९९ ........(२)","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"x and y are independent normal variables with mean 100 and 80 respectively and standard deviation as 4 and 3 respectively.","translation":"x आणि y हे स्वतंत्र सामान्य चल आहेत, ज्यांचे मध्यमान अनुक्रमे १०० आणि ८० आहे आणि प्रमाण विचलन अनुक्रमे ४ आणि ३ आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"What is the distribution of (x + y)?","translation":"(x + y) चे वितरण काय आहे?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"We know that if x ~ N ( 1 ,  1 2 ) and y~ N ( 2 ,  2 2 ) and they are independent, then z = x + y follows normal with mean ( 1 +  2 ) and SD = 2 2 1 2    respectively.","translation":"आपल्याला माहीत आहे की जर x ~ N ( 1 ,  1 2 ) आणि y~ N ( 2 ,  2 2 ) आणि ते स्वतंत्र असतील, तर z = x + y सामान्य वितरणाचे अनुसरण करतो, ज्याचे मध्यमान ( 1 +  2 ) आणि SD = 2 2 1 2    आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"What is the standard deviation of the number of recoveries among 48 patients when the probability of recovering is 0.75?","translation":"48 रूग्णांपैकी किती रूग्ण बरे होण्याची शक्यता आहे, ज्यामध्ये बरे होण्याची संभाव्यता 0.75 आहे, याचे प्रमाण विचलन काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"X is a binomial variable with n = 20. What is the mean of X if it is known that x is symmetric?","translation":"X हा n = 20 असलेला द्विपद biến आहे. जर x सममितीय आहे हे माहित असेल, तर X चा मध्य काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If X ~ B (n, p), what would be the greatest value of the variance of x when n = 16?","translation":"जर X ~ B (n, p) असेल, तर n = 16 असताना x च्या बदलाचे सर्वात मोठे मूल्य काय असेल?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If x is a binomial variate with parameter 15 and 1/3, what is the value of mode of the distribution?","translation":"जर x हा 15 आणि 1/3 पॅरामीटर असलेला द्विपद व्हेरिएट असेल, तर वितरणाच्या मोडचे मूल्य काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"What is the number of trials of a binomial distribution having mean and SD as 3 and 1.5 respectively?","translation":"एका द्विपद वितरणाचे मध्य आणि मानक विचलन अनुक्रमे 3 आणि 1.5 असल्यास, किती चाचण्या आहेत?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"What is the probability of getting 3 heads if 6 unbiased coins are tossed simultaneously?","translation":"जर 6 निरपेक्ष नाणी एकाच वेळी फेकली, तर 3 वेळा हेड येण्याची संभाव्यता काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If the overall percentage of success in an exam is 60, what is the probability that out of a group of 4 students, at least one has passed?","translation":"एका परीक्षेत एकूण 60% यश मिळत असेल, तर 4 विद्यार्थ्यांच्या गटापैकी किमान एका विद्यार्थ्याने परीक्षा पास होण्याची काय शक्यता आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"What is the probability of making 3 correct guesses in 5 True – False answer type questions?","translation":"5 सत्य – असत्य प्रकारच्या प्रश्नांमध्ये 3 योग्य अंदाज लावण्याची संभाव्यता काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If the standard deviation of a Poisson variate X is 2, what is P (1.5 < X < 2.9)?","translation":"जर पॉइसन व्हेरिएट X चे मानक विचलन 2 आहे, तर P (1.5 < X < 2.9) काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If the mean of a Poisson variable X is 1, what is P (X = takes the value at least 1)?","translation":"जर पॉइसन व्हेरिएबल X चा मध्य 1 आहे, तर P (X = किमान 1 मूल्य घेतो) काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If X ~ P (m) and its coefficient of variation is 50, what is the probability that X would assume only non-zero values?","translation":"जर X ~ P (m) आणि त्याचा बदल गुणांक 50 आहे, तर X केवळ गैर-शून्य मूल्ये घेईल याची संभाव्यता काय आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If 1.5 per cent of items produced by a manufacturing units are known to be defective, what is the probability that a sample of 200 items would contain no defective item?","translation":"जर एखाद्या उत्पादन युनिटने तयार केलेल्या वस्तूंपैकी 1.5 टक्के वस्तू सदोष असल्याचे आढळल्यास, 200 वस्तूंच्या नमुन्यात कोणतीही सदोष वस्तू नसेल, याची संभाव्यता काय आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"For a Poisson variate X, P (X = 1) = P (X = 2). What is the mean of X?","translation":"एका पॉइसन व्हेरिएट X साठी, P (X = 1) = P (X = 2). X चा मध्य काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If 1 per cent of an airline‘s flights suffer a minor equipment failure in an aircraft, what is the probability that there will be exactly two such failures in the next 100 such flights?","translation":"एखाद्या एअरलाइनच्या 1 टक्के विमानांमध्ये विमानातील लहान उपकरणे निकामी झाल्यास, पुढील 100 विमानांमध्ये नेमके दोन वेळा उपकरणे निकामी होण्याची काय शक्यता आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If for a Poisson variable X, f(2) = 3 f(4), what is the variance of X?","translation":"जर पॉइसन व्हेरिएबल X साठी, f(2) = 3 f(4), तर X चे विचलन काय आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"What is the coefficient of variation of x, characterised by the following probability density function: f(x) =  2 10 /32 1 24    x e for –  < x < ","translation":"खालील संभाव्यता घनता फंक्शनद्वारे दर्शविलेल्या x चा बदल गुणांक काय आहे: f(x) =  2 10 /32 1 24    x e for –  < x < ","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"What is the first quartile of X having the following probability density function? f(x) =  2 10 /72 1 72    x e for –  < x < ","translation":"खालील संभाव्यता घनता फंक्शन असलेल्या X चा पहिला चतुर्थांश काय आहे? f(x) =  2 10 /72 1 72    x e for –  < x < ","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If the two quartiles of N ( ,  2 ) are 14.6 and 25.4 respectively, what is the standard deviation of the distribution?","translation":"जर N ( ,  2 ) चे दोन चतुर्थांश अनुक्रमे 14.6 आणि 25.4 असतील, तर वितरणाचे मानक विचलन काय आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If the mean deviation of a normal variable is 16, what is its quartile deviation?","translation":"जर एका सामान्य चलाचे मध्य विचलन 16 आहे, तर त्याचे चतुर्थांश विचलन काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If the points of inflexion of a normal curve are 40 and 60 respectively, then its mean deviation is","translation":"जर एका सामान्य वक्राचे इन्फ्लेक्शन बिंदू अनुक्रमे 40 आणि 60 असतील, तर त्याचे मध्य विचलन आहे","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The formula for tied ranks is adjusted to account for multiple individuals sharing the same rank.","translation":"एकाच रँकवर असलेल्या अनेक व्यक्तींचा विचार करण्यासाठी, समान रँकसाठीचे सूत्र समायोजित केले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Rank correlation helps determine the agreement between two sets of rankings.","translation":"रँक सहसंबंध दोन क्रमवारींच्या संचांमधील एकमत निश्चित करण्यास मदत करतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The coefficient of rank correlation provides a numerical value to quantify this agreement.","translation":"रँक सहसंबंध गुणांक या एकमताचे प्रमाण मोजण्यासाठी एक संख्यात्मक मूल्य प्रदान करतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Sales and advertisement spending are often correlated, and this can be analyzed using rank correlation.","translation":"विक्री आणि जाहिरात खर्चामध्ये सहसंबंध असतो आणि याचे विश्लेषण रँक सहसंबंध वापरून केले जाऊ शकते.","target_lang":"mr","domain":"business","complexity":"moderate"}
+{"en":"The example demonstrates how to compute the rank correlation coefficient.","translation":"उदाहरण रँक सहसंबंध गुणांकाची गणना कशी करावी हे स्पष्ट करते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The data includes sales figures and corresponding advertisement expenses.","translation":"डेटा मध्ये विक्रीची आकडेवारी आणि त्या संबंधित जाहिरात खर्च समाविष्ट आहे.","target_lang":"mr","domain":"business","complexity":"simple"}
+{"en":"Ranks are assigned based on the magnitude of the sales and advertisement values.","translation":"विक्री आणि जाहिरात मूल्यांच्या आधारावर रँक निश्चित ���ेल्या जातात.","target_lang":"mr","domain":"business","complexity":"moderate"}
+{"en":"The formula (17.11) is applied when there are no tied ranks.","translation":"जेव्हा समान रँक नसेल, तेव्हा सूत्र (17.11) वापरले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"A high positive rank correlation coefficient suggests a strong agreement.","translation":"उच्च सकारात्मक रँक सहसंबंध गुणांक मजबूत एकमत दर्शवतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The example also shows how to compute rank correlation when ranks are already given.","translation":"उदाहरण रँक आधीच दिलेले असताना रँक सहसंबंधाची गणना कशी करावी हे देखील दर्शवते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The coefficient helps to assess the agreement between the two judges.","translation":"गुणांक दोन परीक्षकांमध्ये किती साम्य आहे, हे तपासण्यास मदत करतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"A low value indicates a lack of agreement between the judges' rankings.","translation":"कमी मूल्य परीक्षकांच्या क्रमवारीमध्ये एकमत नसल्याचे दर्शवते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Tied ranks occur when multiple students receive the same marks.","translation":"जेव्हा एकापेक्षा जास्त विद्यार्थ्यांना समान गुण मिळतात, तेव्हा समान रँक येतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The formula is adjusted to account for these tied ranks.","translation":"या समान रँकचा विचार करण्यासाठी सूत्र समायोजित केले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The example demonstrates the calculation with tied ranks in both Economics and Statistics.","translation":"उदाहरण अर्थशास्त्र आणि सांख्यिकी या दोन्ही विषयांमध्ये समान रँकसह गणना दर्शवते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The formula for rank correlation is modified to handle tied ranks.","translation":"समान रँक हाताळण्यासाठी रँक सहसंबंधाचे सूत्र सुधारित केले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The sum of squares of differences in ranks is used in the calculation.","translation":"गणनेत रँकमधील फरकांच्या वर्गांची बेरीज वापरली जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The rank correlation coefficient can be used to analyze various factors.","translation":"विविध घटकांचे विश्लेषण करण्यासाठी रँक सहसंबंध गुणांकाचा वापर केला जाऊ शकतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The number of towns can be determined using the rank correlation coefficient.","translation":"रँक सहसंबंध गुणांक वापरून शहरांची संख्या निश्चित केली जाऊ शकते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Correcting errors in the data is crucial for accurate results.","translation":"सत्य आणि अचूक परिणामांसाठी डेटा मधील त्रुटी (चुका) दुरुस्त करणे आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Compute the correlation coefficient between x and y.","translation":"x आणि y मधील सहसंबंध गुणांक मोजा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Given the variance of x is 9, find the SD of y.","translation":"जर x चा variance 9 असेल, तर y चे SD शोधा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Solving these two equations, we get x = 3 and y = 1.","translation":"या दोन समीकरणांचे समाधान केल्यास, x = 3 आणि y = 1 मिळतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Thus the arithmetic means of x and y are given by 3 and 1 respectively.","translation":"म्हणून, x आणि y ची अंकगणितीय सरासरी अनुक्रमे 3 आणि 1 आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Let us assume that 7x – 3y – 18 = 0 represents the regression line of y on x.","translation":"असे मानूया की 7x – 3y – 18 = 0 हे y ची x वरील प्रतिगमन रेषा दर्शवते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Since r² = 7/12, therefore r = 0.7638.","translation":"r² = 7/12 असल्यामुळे, r = 0.7638.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"So far we have discussed the different measures of correlation.","translation":"आतापर्यंत, आपण सहसंबंधाच्या विविध मापनांवर चर्चा केली आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If two variables x and y are independent or uncorrelated then obviously the correlation coefficient between x and y is zero.","translation":"जर दोन चल x आणि y स्वतंत्र किंवा असंबंधित असतील, तर x आणि y मधील सहसंबंध गुणांक शून्य असतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"This does not mean that x and y are independent.","translation":"याचा अर्थ असा नाही की x आणि y स्वतंत्र आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"There are some cases when we may find a correlation between two variables although the two variables are not causally related.","translation":"असे काही प्रसंग आहेत जेव्हा दोन चलांमध्ये सहसंबंध आढळू शकतो, जरी दोन चल कारणात्मक दृष्ट्या संबंधित नसले तरी.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Such a correlation is known as spurious correlation or non-sense correlation.","translation":"अशा सहसंबंधास बनावट सहसंबंध किंवा निरर्थक सहसंबंध म्हणून ओळखले जाते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Correlation coefficient measuring a linear relationship between the two variables indicates the amount of variation of one variable accounted for by the other variable.","translation":"दोन चलांमधील रेषीय संबंध मोजणारा सहसंबंध गुणांक, दुसऱ्या चलाद्वारे मोजल्या जाणाऱ्या एका चलाच्या बदलाची मात्रा दर्शवतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"This can be interpreted as the ratio between the explained variance to total variance.","translation":"याचा अर्थ स्पष्ट केलेल्या बदलाचे एकूण बदलाशी असलेले गुणोत्तर असा आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The two lines of regression coincide i.e. become identical when r = –1 or 1.","translation":"जेव्हा r = –1 किंवा 1 असतो, तेव्हा प्रतिगमन रेषा एकमेकांशी जुळतात, म्हणजे एकसारख्या होतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The change in one variable is reciprocated by a corresponding change in the other variable.","translation":"एका चलातील बदल दुसऱ्या चलात संबंधित बदल घडवतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"This is a simple diagrammatic method to establish correlation between a pair of variables.","translation":"हे दोन चलांमधील सहसंबंध स्थापित करण्याची एक साधी आकृतीबंध पद्धत आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The coefficient of correlation always lies between –1 and 1.","translation":"सहसंबंध गुणांक नेहमी –1 आणि 1 च्या दरम्यान असतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"In regression analysis, we are concerned with the estimation of one variable for a given value of another variable.","translation":"प्रतिगमन विश्लेषणात, आपण दुसऱ्या चलाच्या दिलेल्या मूल्यासाठी एका चलाचा अंदाज लावतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The two lines of regression intersect at the point (x, y).","translation":"प्रतिगमन रेषा (x, y) बिंदूत छेदतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The coefficient of correlation between two variables x and y is the simple geometric mean of the two regression coefficients.","translation":"दोन चल x आणि y मधील सहसंबंध गुणांक हा दोन प्रतिगमन गुणांकांचा सोपा भूमितीय मध्य असतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"What is the coefficient of correlation from the following data?","translation":"खालील डेटावरून सहसंबंध गुणांक काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The coefficient of correlation between x and y where x: 6460675969 y: 5760736268 is","translation":"x आणि y मधील सहसंबंध गुणांक, जेथे x: 6460675969 y: 5760736268 आहे","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"What is the coefficient of correlation between the ages of husbands and wives from the following data?","translation":"खालील डेटावरून पती आणि पत्नीच्या वयांमधील सहसंबंध गुणांक काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The corrected value of the correlation coefficient is","translation":"सहसंबंध गुणांकाचे सुधारित मूल्य आहे","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The correlation coefficient between size and defectives is","translation":"आकार आणि सदोष वस्तू यांच्यातील सहसंबंध गुणांक आहे","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The number of observations for this bivariate data is","translation":"या द्विचर डेटासाठी निरीक्षणांची संख्या आहे","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The rank correlation coefficient is","translation":"श्रेणी सहसंबंध गुणांक आहे","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The coefficient of rank correlation between marks in Botany and Zoology is","translation":"वनस्पतिशास्त्र आणि प्राणीशास्त्र विषयातील गुणांमधील श्रेणी सहसंबंध गुणांक आहे","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"What is the value of Rank correlation coefficient between the following marks in Physics and Chemistry?","translation":"भौतिकशास्त्र आणि रसायनशास्त्र विषयातील खालील गुणांमधील श्रेणी सहसंबंध गुणांकाचे मूल्य काय आहे?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"What is the coefficient of concurrent deviations for the following data?","translation":"खालील डेटासाठी समवर्ती विचलनांचा गुणांक काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The regression equation of y on x for the following data is given by","translation":"खालील डेटासाठी y ची x वरील प्रतिगमन समीकरण दिले आहे","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The regression equation of height of son on that of father is given by","translation":"वडिलांच्या उंचीवर मुलाची उंची दर्शवणारे प्रतिगमन समीकरण खालीलप्रमाणे आहे","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The two regression coefficients for the following data are","translation":"खालील डेटासाठी दोन प्रतिगमन गुणांक आहेत","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"For y = 25, what is the estimated value of x, from the following data?","translation":"y = 25 साठी, खालील डेटावरून x चे अंदाजित मू��्य काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"What is the most likely value of y when x = 90 ?","translation":"जेव्हा x = 90 असेल, तेव्हा y चे सर्वात संभाव्य मूल्य काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"If the variance of x is 25, what is the standard deviation of y?","translation":"जर x ची variance 25 असेल, तर y चे प्रमाण विचलन (standard deviation) काय आहे?","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The sum of the Regression coefficients for the above data would be:","translation":"वरील डेटासाठी प्रतिगमन गुणांकांची बेरीज:","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The coefficient of correlation between cost of advertisement and sales of a product on the basis of the following data is","translation":"खालील डेटाच्या आधारावर जाहिरात खर्च आणि उत्पादनाच्या विक्रीतील सहसंबंध गुणांक आहे","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"is concerned with the measurement of the “strength of association” between variables.","translation":"हे चलांमधील 'सहसंबंधाच्या सामर्थ्याचे' मापन करते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The lines of regression passes through the points, bearing _________ no. of points on both sides","translation":"प्रतिगमन रेषा दोन्ही बाजूंना _________ बिंदू घेऊन जातात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Index numbers are constructed with regard to price or quantity or any other measure.","translation":"निर्देशांक संख्या किंमत, प्रमाण किंवा इतर कोणत्याही मापनाच्या संदर्भात तयार केल्या जातात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The choice would depend on the purpose.","translation":"निवड हेतूवर अवलंबून असेल.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Index numbers are useful in framing suitable policies in economics and business.","translation":"अर्थशास्त्र आणि व्यवसायात योग्य धोरणे तयार करण्यासाठी निर्देशांक संख्या उपयुक्त आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"They provide guidelines to make decisions in measuring intelligence quotients, research etc.","translation":"ते बुद्धिमत्ता गुणांक, संशोधन इत्यादी मोजण्यासाठी निर्णय घेण्यासाठी मार्गदर्शन करतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"They reveal trends and tendencies in making important conclusions in cyclical forces, irregular forces, etc.","translation":"चक्रीय शक्ती, अनियमित शक्ती इत्यादींमध्ये महत्त्वपूर्ण निष्कर्ष काढण्यासाठी ते ट्रेंड आणि प्रवृत्ती दर्शवतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Index numbers are very useful in deflating i.e., they are used to adjust the original data for price changes and thus transform nominal wages into real wages.","translation":"निर्देशांक संख्या डिफ्लेटिंगमध्ये खूप उपयुक्त आहेत, म्हणजे, किंमतीतील बदलांसाठी मूळ डेटा समायोजित करण्यासाठी आणि अशा प्रकारे नाममात्र वेतन वास्तविक वेतनात रूपांतरित करण्यासाठी त्यांचा वापर केला जातो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Cost of living index numbers measure changes in the cost of living over a given period.","translation":"जीवन निर्देशांक संख्या एका विशिष्ट कालावधीत जीवन खर्चातील बदल मोजतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The real economic growth in terms of constant prices of the base year therefore is determined by deflating GNP values using price index.","translation":"आधार वर्षाच्या स्थिर किमतींच्या दृष्टीने वास्तविक आर्थिक वाढ, किंमत निर्देशांक वापरून सकल राष्ट्रीय उत्पादन (GNP) मूल्ये कमी करून निश्चित केली जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Splicing two sets of price index numbers covering different periods of time is usually required when there is a major change in quantity weights.","translation":"दोन किंमत निर्देशांक संख्या संच जोडणे, जे वेगवेगळ्या कालावधीतील आकडेवारी दर्शवतात, सामान्यतः आवश्यक असते जेव्हा प्रमाण वजनात मोठा बदल होतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Except for the simple (unweighted) aggregative index all other formulae satisfy this test.","translation":"साध्या (अभारित) एकत्रित निर्देशांकाव्यतिरिक्त, इतर सर्व सूत्रे ही चाचणी पूर्ण करतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The test provides that the formula for calculating the index number should be such that two ratios, the current on the base and the base on the current should multiply into unity.","translation":"ही चाचणी प्रदान करते की निर्देशांक संख्या मोजण्याचे सूत्र असे असावे की दोन गुणोत्तर, आधारावरचे वर्तमान आणि वर्तमानवरचा आधार, गुणाकार करून एक बनले पाहिजे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"You will notice that Laspeyres’ method and Paasche’s method do not satisfy this test, but Fisher’s Ideal Formula does.","translation":"आपण लक्षात घ्याल की लॅस्पायर्सची पद्धत आणि पाशेची पद्धत ही चाचणी पूर्ण करत नाहीत, परंतु फिशरचे आदर्श सूत्र (Fisher’s Ideal Formula) हे करते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"While selecting an appropriate index formula, the Time Reversal Test and the Factor Reversal test are considered necessary in testing the consistency.","translation":"एखादे योग्य निर्देशांक सूत्र निवडताना, सुसंगतता तपासण्यासाठी टाइम रिव्हर्सल टेस्ट (Time Reversal Test) आणि फॅक्टर रिव्हर्सल टेस्ट (Factor Reversal test) आवश्यक मानल्या जातात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"This holds when the product of price index and the quantity index should be equal to the corresponding value index.","translation":"हे तेव्हा लागू होते जेव्हा किंमत निर्देशांक आणि प्रमाण निर्देशांकाचा गुणाकार संबंधित मूल्य निर्देशांकाइतकाच असावा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Because Fisher’s Index number satisfies both the tests in (ii) and (iii), it is called an Ideal Index Number.","translation":"फिशरची निर्देशांक संख्या (ii) आणि (iii) मधील दोन्ही चाचण्या पूर्ण करत असल्याने, त्याला एक आदर्श निर्देशांक संख्या म्हणतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"It is concerned with the measurement of price changes over a period of years, when it is desirable to shift the base.","translation":"जेव्हा आधार बदलणे आवश्यक असते, तेव्हा हे अनेक वर्षांच्या कालावधीतील किंमतीतील बदलांच्या मापनाशी संबंधित असते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The simple geometric mean of price relatives and the weighted aggregative with fixed weights meet this test.","translation":"किंमत संबंधांचे (price relatives) साधे भूमितीय śred आणि निश्चित वजनासह भारित एकत्रित (weighted aggregative) हे या चाचणीमध्ये बसतात.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"It represents the entire stock market.","translation":"हे संपूर्ण शेअर बाजाराचे प्रतिनिधित्व करते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Each stock exchange has an index.","translation":"प्रत्येक स्टॉक एक्सचेंजचा एक निर्देशांक असतो.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"BSE became the first stock exchange in India to obtain such permission from the Government under the Act.","translation":"या कायद्याअंतर्गत सरकारकडून अशी परवानगी मिळवणारे BSE हे भारतातील पहिले स्टॉक एक्सचेंज बनले.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"NIFTY50 is a diversified 50 stocks Index of 13 sectors of the economy.","translation":"NIFTY50 हा अर्थव्यवस्थेतील 13 क्षेत्रांचा 50 समभागांचा विविध निर्देशांक आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The base period of NIFTY 50 Index is 3 November 1995 and base value is 1000.","translation":"NIFTY 50 निर्देशांकाचा आधार कालावधी 3 नोव्हेंबर 1995 आहे आणि आधार मूल्य 1000 आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Computation of Index Following steps are involved in calculation of index on a particular date:","translation":"निर्देशांकाची गणना खालीलप्रमाणे केली जाते:","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Calculate market capitalization of each individual company comprising the index.","translation":"निर्देशांकामध्ये समाविष्ट असलेल्या प्रत्येक कंपनीचे बाजार भांडवल मोजा.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Computing index of next day requires the index value and the total market capitalization of the previous day.","translation":"पुढील दिवसाचा निर्देशांक काढण्यासाठी मागील दिवसाचे निर्देशांक मूल्य आणि एकूण बाजार भांडवल आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"It should also be noted that Indices may also be calculated using the price weighted method.","translation":"हे देखील लक्षात घेणे आवश्यक आहे की निर्देशांक किंमत-आधारित पद्धतीने देखील मोजले जाऊ शकतात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"However, almost all equity indices worldwide are calculated using the market capitalization weighted method.","translation":"परंतु, जगभरातील जवळजवळ सर्व इक्विटी निर्देशांक बाजार भांडवल आधारित पद्धतीने मोजले जातात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"It is very important to note that constituents’ companies does not remain the same.","translation":"हे लक्षात घेणे अत्यंत महत्त्वाचे आहे की घटक कंपन्या एकसारख्याच स्थितीत टिकून राहत नाहीत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"CPI- Consumer Price Index/ Cost of living Index or Retail Price Index is the Index which measures the effect of change in prices.","translation":"CPI- ग्राहक किंमत निर्देशांक/ राहणीमानाचा खर्च निर्देशांक किंवा किरकोळ किंमत निर्देशांक हा असा निर्देशांक आहे जो किमतीतील बदलांचा प्रभाव मोजतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"WPI- Whole Sale Price Index - The WPI measures the relative changes in prices of commodities traded in wholesale market.","translation":"WPI- घाऊक किंमत निर्देशांक - WPI घाऊक बाजारात व्यापार केलेल्या वस्तूंच्या किमतीतील सापेक्ष बदल मोजतो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"An index number is a ratio or an average of ratios expressed as a percentage.","translation":"एक निर्देशांक संख्या म्हणजे गुणोत्तर किंवा गुणोत्तरांचे सरासरी प्रतिशत म्हणून व्यक्त केलेले असते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Two or more time periods are involved, one of which is the base time period.","translation":"दोन किंवा अधिक कालावधींचा समावेश असतो, ज्यापैकी एक आधारभूत कालावधी असतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Selection of Data, Base period, Selection of Weights are issues involved in index numbers.","translation":"डेटाची निवड, आधारभूत कालावधी, वेट्सची निवड हे निर्देशांक संख्यांशी संबंधित मुद्दे आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Simple aggregative price index = n o P ×100 P  ","translation":"साधे एकत्रित किंमत निर्देशांक = n o P ×100 P  ","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Laspeyres’ Index: In this Index base year quantities are used as weights.","translation":"लास्पियरचा निर्देशांक: या निर्देशांकात आधार वर्षातील प्रमाण (quantities) वेट्स म्हणून वापरले जातात.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Fisher’s ideal Price Index: This index is the geometric mean of Laspeyres’ and Paasche’s.","translation":"फिशरचा आदर्श किंमत निर्देशांक: हा निर्देशांक लास्पियर आणि पाशे यांच्या भूमितीय średकाचा (geometric mean) आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Weighted Average of Relative Method: n o o n o o o oo o P ×(P Q ) P Q P ×100=×100 P QP Q   ","translation":"सापेक्ष पद्धतीचे भारित सरासरी: n o o n o o o oo o P ×(P Q ) P Q P ×100=×100 P QP Q   ","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Simple aggregate of quantities: n o Q Q  ","translation":"प्रमाणांचा (quantities) साधा समुच्चय: n o Q Q  ","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Value Indices n n n o o o P Q V = V P Q  ","translation":"मूल्य निर्देशांक n n n o o o P Q V = V P Q  ","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Shifted Price Index = Original Price Index ×100 Price Index of the year on which it has to be shifted","translation":"शिफ्ट केलेला किंमत निर्देशांक = मूळ किंमत निर्देशांक ×100 ज्या वर्षावर शिफ्ट करायचे आहे त्या वर्षाचा किंमत निर्देशांक","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The numbers provided seem to be related to financial calculations.","translation":"दिलेल्या संख्या आर्थिक गणितांशी संबंधित असल्याचे दिसते.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"Could you please clarify the context of these figures?","translation":"कृपया, या आकडेवारीचा संदर्भ स्पष्ट करू शकाल का?","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The values appear to be decreasing over time.","translation":"मूल्ये वेळेनुसार कमी होत असल्याचे दिसत आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"We need to analyze the trends in these datasets.","translation":"या डेटासेटमधील ट्रेंडचे विश्लेषण करणे आवश्यक आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The calculations involve compound interest and annuities.","translation":"या गणितामध्ये चक्रवाढ व्याज आणि वार्षिकीचा समावेश आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"These figures are crucial for investment decisions.","translation":"गुंतवणुकीचे निर्णय घेण्यासाठी हे आकडे अत्यंत महत्त्वाचे आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The data suggests a significant market fluctuation.","translation":"डेटा महत्त्वपूर्ण बाजारपेठेतील चढउतार दर्शवतो.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The formula used is based on present value calculations.","translation":"वापरलेले सूत्र वर्तमान मूल्याच्या गणनेवर आधारित आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The rate of return is approximately 3%.","translation":"परताव्याचा दर अंदाजे 3% आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The institute provides guidelines for financial accounting.","translation":"संस्था आर्थिक लेखांकनासाठी मार्गदर्शन प्रदान करते.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The appendices contain important supplementary information.","translation":"परिशिष्टात महत्त्वाची पूरक माहिती आहे.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The log tables are essential for complex calculations.","translation":"गुंतागुंतीच्या गणितांसाठी लॉग टेबल आवश्यक आहेत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Antilogarithms are used to find the original numbers.","translation":"मूळ संख्या शोधण्यासाठी अँटिलॉगॅरिदमचा वापर केला जातो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The normal probability distribution is a key concept.","translation":"सामान्य संभाव्यता वितरण ही एक महत्त्वाची संकल्पना आहे.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The area under the curve represents the probability.","translation":"वक्राखालील क्षेत्र संभाव्यता दर्शवते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The z-value helps in standardizing the data.","translation":"झेड-व्हॅल्यू डेटाचे प्रमाणिकरण करण्यास मदत करते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The student's t-distribution is used for small samples.","translation":"लहान नमुन्यांसाठी विद्यार्थ्यांचे टी-वितरण वापरले जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The degree of freedom affects the distribution shape.","translation":"स्वातंत्र्याची पदवी वितरणाच्या आकारात परिणाम करते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The combined area in both tails is considered.","translation":"दोन्ही टोकांवरील एकत्रित क्षेत्राचा विचार केला जातो.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The t-value is determined based on the area and degrees of freedom.","translation":"टी-व्हॅल्यू क्षेत्र आणि स्वातंत्र्याच्या डिग्रीवर आधारित निश्चित केली जाते.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Bowley's Index number is expressed in the form of : (a) Laspeyre's index + Paasche's index 2 (b) Laspeyre's index × Paasche's index 2 (c) Laspeyre's index - Paasche's index 2 (d) None of these.","translation":"बॉलीचा निर्देशांक खालीलपैकी कोणत्या स्वरूपात व्यक्त केला जातो: (a) लॅस्पियरचा निर्देशांक + पाश्चेचा निर्देशांक 2 (b) लॅस्पियरचा निर्देशांक × पाश्चेचा निर्देशांक 2 (c) लॅस्पियरचा निर्देशांक - पाश्चेचा निर्देशांक 2 (d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The simple Aggregative Index is (a) 115.8(b) 110.8(c) 112.5(d) 113.4","translation":"साधा एकत्रित निर्देशांक (a) 115.8 (b) 110.8 (c) 112.5 (d) 113.4 आहे.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"With regard to Laspeyre’s and Paasche’s price index numbers, it is maintained that “If the prices of all the goods change in the same ratio, the two indices will be equal for them the weighting system is irrelevant; or if the quantities of all the goods change in the same ratio, they will be equal, for them the two weighting systems are the same relatively”. Then the above statements satisfy.","translation":"लॅस्पियर आणि पाश्चे यांच्या किंमत निर्देशांकानुसार, असे मानले जाते की “जर सर्व वस्तूंच्या किमती एकाच प्रमाणात बदलल्यास, दोन्ही निर्देशांक त्यांच्यासाठी समान असतील, वजन प्रणाली अप्रासंगिक आहे; किंवा जर सर्व वस्तूंची संख्या एकाच प्रमाणात बदलली, तर ते समान असतील, कारण त्यांच्यासाठी दोन्ही वजन प्रणाली सापेक्ष समान आहेत”. तर वरील विधाने खालीलपैकी काय दर्शवतात?","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The quantity Index number using Fisher’s formula satisfies : (a) Unit Test(b) Factor Reversal Test. (d) All the three (c) Time Reversal Test.","translation":"फिशरच्या सूत्राचा वापर करून संख्या निर्देशांक खालीलपैकी काय दर्शवतो: (a) युनिट टेस्ट (b) फॅक्टर रिव्हर्सल टेस्ट (c) टाइम रिव्हर्सल टेस्ट (d) हे सर्व.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"For constructing consumer price Index is used : (a) Marshall Edge worth Method.(b) Paasche’s Method. (c) Dorbish and Bowley’s Method.(d) Laspeyre’s Method.","translation":"ग्राहक किंमत निर्देशांक तयार करण्यासाठी हे वापरले जाते: (a) मार्शल एज वर्थ पद्धत (b) पाश्चेची पद्धत (c) डॉर्बिश आणि बॉलीची पद्धत (d) लॅस्पियरची पद्धत.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The cost of living Index (C. L. I.) is always : (a) Weighted index(b) Price Index. (c) Quantity Index.(d) None of these.","translation":"जीवन निर्देशांक (C. L. I.) नेहमी असतो: (a) भारित निर्देशांक (b) किंमत निर्देशांक (c) संख्या निर्देशांक (d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The Time Reversal Test is not satisfied to : (a) Fisher’s ideal Index.(b) Marshall Edge worth Method. (c) Laspeyre’s and Paasche Method. (d) None of these.","translation":"टाइम रिव्हर्सल टेस्ट खालीलपैकी कशाने समाधानकारक नाही: (a) फिशरचा आदर्श निर्देशांक (b) मार्शल एज वर्थ पद्धत (c) लॅस्पियर आणि पाश्चे पद्धत (d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Given below are the data on prices of some consumer goods and the weights attached to the various items. Compute price index number for the year 1985 (Base 1984 = 100)","translation":"काही ग्राहक वस्तूंच्या किमती आणि विविध वस्तूंना दिलेले वजन याबद्दलचा डेटा खाली दिला आहे. 1985 वर्षासाठी किंमत निर्देशांक मोजा (आधार वर्ष 1984 = 100)","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The Factor Reversal Test is as represented symbolically is : (a) P 01 × Q 01 1 1 0 0 PQ P Q    (b) I 01 × I 10 (c) 11 00 QP QP   (d) 010 10 00 11 PQ QP QP QP     ","translation":"घटक रिव्हर्सल टेस्टचे प्रतीकात्मक प्रतिनिधित्व खालीलप्रमाणे आहे: (a) P 01 × Q 01 1 1 0 0 PQ P Q    (b) I 01 × I 10 (c) 11 00 QP QP   (d) 010 10 00 11 PQ QP QP QP     ","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"If the 1970 index with base 1965 is 200 and 1965 index with base 1960 is 150, the index 1970 on base 1960 will be : (a) 700(b) 300(c) 500(d) 600","translation":"जर 1965 च्या आधारावर 1970 चा निर्देशांक 200 आहे आणि 1960 च्या आधारावर 1965 चा निर्देशांक 150 आहे, तर 1960 च्या आधारावर 1970 चा निर्देशांक काय असेल: (a) 700 (b) 300 (c) 500 (d) 600","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Circular Test is not met by : (a) The simple Geometric mean of price relatives. (b) The weighted aggregative with fixed weights. (c) Laspeyre’s or Paasche’s or the fisher’s Ideal index. (d) None of these.","translation":"वर्तुळाकार चाचणी खालीलपैकी कशाने पूर्ण होत नाही: (a) किंमत संबंधांचे सोपे भूमितीय मध्य (b) निश्चित वजनासह भारित एकत्रित (c) लॅस्पियर किंवा पाश्चे किंवा फिशरचा आदर्श निर्देशांक (d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"Then the value ratio is: (a) 59 52 (b) 49 47 (c) 41 53 (d) 47 53","translation":"तर मूल्य गुणोत्तर काय आहे: (a) 59 52 (b) 49 47 (c) 41 53 (d) 47 53","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The value index is equal to : (a) The total sum of the values of a given year multiplied by the sum of the values of the base year. (b) The total sum of the values of a given year Divided by the sum of the values of the base year. (c) The total sum of the values of a given year plus by the sum of the values of the base year. (d) None of these.","translation":"मूल्य निर्देशांक कशाच्या बरोबर आहे: (a) दिलेल्या वर्षाच्या मूल्यांची एकूण बेरीज, आधार वर्षाच्या मूल्यांच्या बेरजेने गुणून (b) दिलेल्या वर्षाच्या मूल्यांची एकूण बेरीज, आधार वर्षाच्या मूल्यांच्या बेरजेने भागून (c) दिलेल्या वर्षाच्या मूल्यांची एकूण बेरीज, आधार वर्षाच्या मूल्यांच्या बेरजेमध्ये मिळवून (d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Time Reversal Test is represented symbolically by : (a) P 01 x P 10 (b) P 01 x P 10 = 1 (c) P 01 x P 10  1(d) None of these.","translation":"टाइम रिव्हर्सल टेस्टचे प्रतीकात्मक प्रतिनिधित्व खालीलप्रमाणे आहे: (a) P 01 x P 10 (b) P 01 x P 10 = 1 (c) P 01 x P 10  1(d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"In 1996 the average price of a commodity was 20% more than in 1995 but 20% less than in 1994; and more over it was 50% more than in 1997 to price relatives using 1995 as base (1995 price relative 100). Reduce the data is : (a) 150, 100, 120, 80 for (1994–97)(b) 135, 100, 125, 87 for (1994–97) (c) 140, 100, 120, 80 for (1994–97)(d) None of these.","translation":"1996 मध्ये, वस्तूची सरासरी किंमत 1995 पेक्षा 20% जास्त होती, परंतु 1994 पेक्षा 20% कमी होती; आणि 1997 पेक्षा 50% जास्त होती, 1995 ला आधार मानून किंमत संबंध (1995 ची किंमत 100). डेटा कमी करा: (a) 1994–97 साठी 150, 100, 120, 80 (b) 1994–97 साठी 135, 100, 125, 87 (c) 1994–97 साठी 140, 100, 120, 80 (d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
+{"en":"The price index number for the year 1934 is : (a) 140(b) 145(c) 147(d) None of these.","translation":"1934 वर्षासाठी किंमत निर���देशांक आहे: (a) 140 (b) 145 (c) 147 (d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The index number by unweighted methods : (a) 116.8(b) 117.25(c) 115.35(d) 119.37","translation":"भार नसलेल्या पद्धतीनुसार निर्देशांक: (a) 116.8 (b) 117.25 (c) 115.35 (d) 119.37","target_lang":"mr","domain":"technical","complexity":"simple"}
+{"en":"The Bowley’s Price index number is represented in terms of : (a) A. M. of Laspeyre’s and Paasche’s Price index number. (b) G. M. of Laspeyre’s and Paasche’s Price index number. (c) A. M. of Laspeyre’s and Walsh’s price index number. (d) None of these.","translation":"बॉलीचा किंमत निर्देशांक खालीलपैकी कशाच्या संदर्भात दर्शविला जातो: (a) लॅस्पियर आणि पाश्चे यांच्या किंमत निर्देशांकाचा अंकगणितीय मध्य (A. M.) (b) लॅस्पियर आणि पाश्चे यांच्या किंमत निर्देशांकाचा भूमितीय मध्य (G. M.) (c) लॅस्पियर आणि वॉल्श यांच्या किंमत निर्देशांकाचा अंकगणितीय मध्य (A. M.) (d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"Fisher’s price index number equal is : (a) G. M. of Kelly’s price index number and Paasche’s price index number. (b) G. M. of Laspeyre’s and Paasche’s Price index number. (c) G. M. of Bowley’s price index number and Paasche’s price index number. (d) None of these.","translation":"फिशरचा किंमत निर्देशांक कशाच्या बरोबर आहे: (a) केलीच्या किंमत निर्देशांक आणि पाश्चेच्या किंमत निर्देशांकाचा भूमितीय मध्य (G. M.) (b) लॅस्पियर आणि पाश्चे यांच्या किंमत निर्देशांकाचा भूमितीय मध्य (G. M.) (c) बॉलीच्या किंमत निर्देशांक आणि पाश्चेच्या किंमत निर्देशांकाचा भूमितीय मध्य (G. M.) (d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"moderate"}
+{"en":"The price index number using simple G. M. of the n relatives is given by : (a) log I on =  n o 1P 2- log nP (b) log I on =  n o 1P 2+ log nP (c) log I on =  n o 1P log 2nP (d) None of these.","translation":"n संबंधितांच्या साध्या भूमितीय मध्याचा वापर करून किंमत निर्देशांक खालीलप्रमाणे दिला जातो: (a) log I on =  n o 1P 2- log nP (b) log I on =  n o 1P 2+ log nP (c) log I on =  n o 1P log 2nP (d) यापैकी काहीही नाही.","target_lang":"mr","domain":"technical","complexity":"complex"}
\ No newline at end of file