id stringlengths 6 20 | source stringclasses 6
values | instruction stringlengths 11 5.18k | input stringlengths 0 306 | output stringlengths 1 308 | rationale stringlengths 0 2.9k | subject stringclasses 39
values | category stringclasses 7
values |
|---|---|---|---|---|---|---|---|
math_2085 | math_mc | Let $\mathbf{P}$ be the matrix for projecting onto the vector $\begin{pmatrix} 4 \\ -7 \end{pmatrix}.$ Find $\det \mathbf{P}.$ | D | math_Precalculus | mathematics | ||
math_1183 | math_mc | Let $x,$ $y,$ and $z$ be positive real numbers. Find the minimum value of
\[\frac{(x^2 + 3x + 1)(y^2 + 3y + 1)(z^2 + 3z + 1)}{xyz}.\] | C | math_Intermediate Algebra | mathematics | ||
mmlu_aux_train_98012 | mmlu_aux_train | which of these has the most similar component as the earth itself?
A. the stone in the yard
B. a loaf of bread
C. a can of soup
D. a glass of water | A. the stone in the yard | earth_science | earth_science | ||
math_1146 | math_mc | Find all $x$ such that $\lfloor \lfloor 2x \rfloor - 1/2 \rfloor = \lfloor x + 2 \rfloor.$ | A | math_Intermediate Algebra | mathematics | ||
aquarat_3053 | deepmind/aqua_rat | Find the number of trailing zeros in the expansion of (20!*21!*22! ……… *33!)^3!. | A. 468 B. 469 C. 470 D. 467 E. 471 | A. 468 | Let me give you one quick way to solve such questions.
3! = 6 => the answer must be of the form 106n106n
Only A and C have even powers. Hence B C E are out
Out of A and C only A's power is divisible by 3, hence C is out.
Hence A is the answer | college_mathematics | mathematics |
math_158 | math_mc | If $a$, $b$, and $c$ are positive integers satisfying $ab+c = bc+a = ac+b = 41$, what is the value of $a+b+c$? | C | math_Algebra | mathematics | ||
mmlu_aux_train_61140 | mmlu_aux_train | Venus is known as the Earth' "twin" because the planets are so like each other in size. The diameter of Venus is about 7,520 miles (12,100km), about 400 miles (644km) smaller than that of the earth. No other planet comes closer to the earth than Venus. At its nearest approach it is about 25,000,000 miles (402,000,000... | C. It's usually 25,000,000 miles away from the earth. | astronomy | physics | ||
allenai/sciq_11337 | allenai/sciq | What human disease is caused by a defective enzyme that is unable to produce melanin, the pigment responsible for the color of skin and hair?
A. anemia
B. albinism
C. mutations
D. hemophilia | B. albinism | untreated, it produces severe brain damage and mental retardation. Albinism is caused by a defective enzyme that is unable to produce melanin, the pigment responsible for the color of skin and hair. Cystic fibrosis, the most common inherited disease in the United States, blocks pancreatic function and causes thick mucu... | medical_genetics | biology | |
mmlu_aux_train_26055 | mmlu_aux_train | Why should ear, nose, tongue and eyes be called special senses? The basic reason is that these are the channels through which we maintain contact with the surroundings. Though apparently it may feel like these are individual sensory organs, they do show some connections. Interestingly, our hearing is less sharp after w... | C. Your hearing pitch may be decreased. | high_school_biology | biology | ||
NLP4Education_228 | NLP4Education | Given a matrix $\Xm$ of shape $D \times N$ with a singular value decomposition (SVD), $X=USV^\top$, suppose $\Xm$ has rank $K$ and $\Am=\Xm\Xm^\top$.
Which one of the following statements is \textbf{false}?
A. The eigenvalues of $\Am$ are the singular values of $\Xm$.
B. $\Am$ is positive semi-definite, i.e. all eigen... | A. The eigenvalues of $\Am$ are the singular values of $\Xm$. | college_mathematics | mathematics | ||
NLP4Education_298 | NLP4Education | (Infinite Data) Assume that your training data $\mathcal{S}=\left\{\left(\mathbf{x}_{n}, y_{n}\right)\right\}$ is iid and comes from a fixed distribution $\mathcal{D}$ that is unknown but is known to have bounded support. Assume that your family of models contains a finite number of elements and that you choose the bes... | A. The training risk converges to the true risk of the best model as sample size tends to infinity. | machine_learning | computer_science | ||
pythonio_399 | pythonio-mc | Program:
import re
def remove_extra_char(text1):
pattern = re.compile('[\W_]+')
return (pattern.sub('', text1))
Input:
remove_extra_char('**//Google Android// - 12. ')
Output: | B | code | computer_science | ||
math_2206 | math_mc | Find the matrix $\mathbf{P}$ such that for any vector $\mathbf{v},$ $\mathbf{P} \mathbf{v}$ is the projection of $\mathbf{v}$ onto the vector $\begin{pmatrix} 2 \\ -2 \\ -1 \end{pmatrix}.$ | C | math_Precalculus | mathematics | ||
NLP4Education_699 | NLP4Education | For security reasons, you accept the performance and memory overhead introduced by common sanitizers and deploy them in your user-facing production server software. Assuming that all memory safety bugs in your software are detected by the sanitizers, which of the following properties do the sanitizers provide to your c... | B. Integrity of the program data | computer_security | computer_science | ||
aquarat_16730 | deepmind/aqua_rat | In a certain economy, C represents the total amount of consumption in millions of dollars, Y represents the total national income in millions of dollars, and the relationship between these two values is given by the equation C=90+9Y/11. If the total amount of consumption in the economy increases by 99 million dollars, ... | A. 11 B. 22 C. 99 D. 121 E. 171 | D. 121 | Just assume y=11 and C=99
Then C=198 and Y=132
So Y increases by 121
ANSWER:D | college_mathematics | mathematics |
NLP4Education_742 | NLP4Education | A bag contains the letters of LETSPLAY. Someone picks at random 4 letters from the bag without revealing the outcome to you. Subsequently you pick one letter at random among the remaining 4 letters. What is the entropy (in bits) of the random variable that models your choice?
A. $\log_2(4)$
B. $\log_2(8)$
C. $2$
... | A. $\log_2(4)$ | college_mathematics | mathematics | ||
math_551 | math_mc | Matt's four cousins are coming to visit. There are four identical rooms that they can stay in. If any number of the cousins can stay in one room, how many different ways are there to put the cousins in the rooms? | C | math_Counting & Probability | mathematics | ||
allenai/sciq_5936 | allenai/sciq | Bromide is present in brines, which are naturally occurring solutions of what?
A. calcium
B. magnesium
C. salt
D. iron | C. salt | chlorine is added to an aqueous solution of bromide. iodine crystals are added to a solution of potassium bromide. Bromide is present in naturally occurring salt solutions called brines. Based on your answers, propose an effective method to remove bromide from brine. | high_school_chemistry | chemistry | |
NLP4Education_236 | NLP4Education | Recall that we say that a kernel $K: \R \times \R \rightarrow \R$ is valid if there exists $k \in \mathbb{N}$ and $\Phi: \R \rightarrow \R^k$ such that for all $(x, x') \in \R \times \R$, $K(x, x') = \Phi(x)^\top \Phi(x')$. The kernel $K(x, x') = \cos(x + x')$ is a valid kernel.
A. True, because $\cos(x + x')$ can alwa... | B. False, because $K(x,x)$ can take strictly negative values, which is impossible for valid kernels | machine_learning | computer_science | ||
NLP4Education_33 | NLP4Education | Which of the following are parameters involved in the choice made by an order-1 HMM model for PoS tagging knowing that its output is this/Pron is/V a/Det good/Adj question/N and that neither "is" nor "question" can be adjectives, and that "question" can also not be a determiner. (Penalty for wrong ticks.)
A. P(question... | A. P(question|N) | machine_learning | computer_science | ||
math_1488 | math_mc | Let $a$ and $b$ be the two real values of $x$ for which\[\sqrt[3]{x} + \sqrt[3]{20 - x} = 2\]The smaller of the two values can be expressed as $p - \sqrt{q}$, where $p$ and $q$ are integers. Compute $p + q$.
| C | math_Intermediate Algebra | mathematics | ||
allenai/sciq_2108 | allenai/sciq | Chemical symbols are useful to concisely represent the elements present in a substance. the letters usually come from the name of what?
A. discoverer
B. element
C. scientist
D. month | B. element | Chemical symbols are useful to concisely represent the elements present in a substance. The letters usually come from the name of the element. | high_school_chemistry | chemistry | |
aquarat_53154 | deepmind/aqua_rat | Consider the set S = {1, 2, 3, …., 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and with 1000 and have at least 3 elements? | A. 3 B. 4 C. 5 D. 6 E. 7 | D. 6 | Explanation :
We know that it should be an AP, 1st element is 1, and last element 1000.
a = 1, a + (n-1) d = 1000 ; (n-1) d = 999.
So 999 is the product of (n-1) and d. So, we need to see the factors of 999 to see what all values /how many of those values (n-1) and d can assume.The prime factors are 3, 3, 3, and 37.
(9... | college_mathematics | mathematics |
aquarat_31659 | deepmind/aqua_rat | The mean of 40 observations was 36. It was found later that an observation 34 was wrongly taken as 20. The corrected new mean is | A. 76.55 B. 36.35 C. 46.15 D. 16.05 E. 20 | B. 36.35 | Explanation:
Correct Sum = (36 * 40 + 34 - 20) = 1454
Correct mean = = 1454/40 = 36.35
Answer: B | high_school_statistics | mathematics |
aquarat_47689 | deepmind/aqua_rat | The operation # is defined for all nonzero q and y by #y = q + q/y. If a>0, then 1#(1#a) = | A. a B. a+1 C. a/(a+1) D. (a+2)/(a+1) E. (2a+1)/(a+1) | E. (2a+1)/(a+1) | q#y = q + q/y. If a>0, then 1#(1#a) =
You can see that a stands for y and 1 stands for q. I like to work with numbers so I did q=1 a=2 and a=y so y=2
1#a= 1+(1/2)=1.5 so now a is 1.5 --> 1+(1/1.5)=1 2/3 = 5/3
So now you can check by filling in a, which is 2:
A. a --> 2
B. a+1 --> 2+1=3
C. a/(a+1)-->2/(2+1)=2/3
D. (a+2)... | college_mathematics | mathematics |
math_959 | math_mc | Triangle $ABC$ is a right triangle with legs $AB$ and $AC$. Points $X$ and $Y$ lie on legs $AB$ and $AC$, respectively, so that $AX:XB = AY:YC = 1:2$. If $BY = 16$ units, and $CX = 28$ units, what is the length of hypotenuse $BC$? Express your answer in simplest radical form. | C | math_Geometry | mathematics | ||
aquarat_5906 | deepmind/aqua_rat | A certain university will select 2 of 5 candidates eligible to fill a position in the mathematics department and 3 of 8 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates ... | A. 42 B. 70 C. 540 D. 565 E. 560 | E. 560 | 5C2*8C3 = 10*56 = 560
the answer is (E) | college_mathematics | mathematics |
aquarat_45472 | deepmind/aqua_rat | A sheet of paper has statements numbered from 1 to 40. For all values of n from 1 to 40, statement n says: ‘Exactly n of the statements on this sheet are false.’ Which statements are true and which are false? | A. The even numbered statements are true and the odd numbered statements are false. B. The odd numbered statements are true and the even numbered statements are false. C. All the statements are false. D. The 39th statement is true and the rest are false E. The 69th statement is true and the rest are false | B. The odd numbered statements are true and the even numbered statements are false. | Assume there is only one statement is there. The statement should read "Exactly 1 statement on this sheet is false" . If the truth value of the statement is true, then given statement should be false. This is contradiction. If the statement is false, Then the given statement is true. but there is not other true stateme... | formal_logic | mathematics |
mmlu_aux_train_70621 | mmlu_aux_train | Have you ever wanted to stop eating something sweet but you just couldn't ? Is the first thing you do when you get home from school to look in the biscuit tin ? Can you eat a huge bar of chocolate all by yourself ? Can you say "no" to sweets at parties ? If you can't , then there is a reason...perhaps you're sugar add... | A. People who eat sweet regularly. | clinical_knowledge | biology | ||
math_1485 | math_mc | Let $x,$ $y,$ and $z$ be nonzero complex numbers such that $x + y + z = 20$ and
\[(x - y)^2 + (x - z)^2 + (y - z)^2 = xyz.\]Find $\frac{x^3 + y^3 + z^3}{xyz}.$ | D | math_Intermediate Algebra | mathematics | ||
NLP4Education_197 | NLP4Education | $L_1$ regularization often results in sparser solutions than $L_2$ regularization.
A. Always false
B. Only true for linear models
C. TRUE
D. FALSE | C. TRUE | machine_learning | computer_science | ||
aquarat_88799 | deepmind/aqua_rat | Evaluate: 22 + sqrt(- 4 + 6*4*3)=? | A. 4 B. 14 C. 24 D. 34 E. 44 | C. 24 | According to order of operations, inner brackets first where 6?4?3 is first calculated since it has a multiplication and a division.
6*4*3 = 24*3 = 8
Hence
22 + sqrt(- 4 + 6*4*3) = 22 + sqrt(- 4 + 8)
= 22+ sqrt(4) = 22 + 2 = 24
correct answer C | college_mathematics | mathematics |
mmlu_aux_train_75482 | mmlu_aux_train | We each have a memory . That's why we can still remember things after a long time. Some people have very good memories and they can easily learn many things by heart, but some people can only remember things when they say or do them again and again. Many of the great men of the world have got surprising memories. A goo... | D. they have very good memories | high_school_statistics | mathematics | ||
math_1225 | math_mc | Compute
\[\sum_{1 \le a < b < c} \frac{1}{2^a 3^b 5^c}.\](The sum is taken over all triples $(a,b,c)$ of positive integers such that $1 \le a < b < c.$) | C | math_Intermediate Algebra | mathematics | ||
NLP4Education_370 | NLP4Education | The one-time pad is…
A. A perfectly binding commitment scheme.
B. A statistically (but not perfectly) binding commitment scheme.
C. A computationally (but not statistically) binding commitment scheme.
D. Not a commitment scheme. | D. Not a commitment scheme. | computer_security | computer_science | ||
mmlu_aux_train_92693 | mmlu_aux_train | Which of these is the chemical symbol for magnesium?
A. Ma
B. Mg
C. Mn
D. Mu | B. Mg | high_school_chemistry | chemistry | ||
math_1988 | math_mc | Let GCF(a, b) be the abbreviation for the greatest common factor of a and b, and let LCM(c, d) be the abbreviation for the least common multiple of c and d. What is GCF(LCM(8, 14), LCM(7, 12))? | D | math_Prealgebra | mathematics | ||
mmlu_aux_train_6917 | mmlu_aux_train | The computer is fast, and never makes a mistake, while people are too slow, and full of mistakes sometimes. That's what people often say when they talk about computers. For over a quarter of a century, scientists have been making better and better computers. Now a computer can do a lot of everyday jobs wonderfully. It ... | A. Computer | high_school_computer_science | computer_science | ||
mmlu_aux_train_5367 | mmlu_aux_train | Security--for the information on your smartphone, as well as for the phone itself---is a hot topic these days. The truth is that you're packing a lot of sensitive information on your phone, and you should keep it safe. When it comes to physical security, iPhone users would do well to download Find My iPhone, a free app... | C. Lookout | computer_security | computer_science | ||
math_2112 | math_mc | Let $x,$ $y,$ and $z$ be angles such that
\begin{align*}
\cos x &= \tan y, \\
\cos y &= \tan z, \\
\cos z &= \tan x.
\end{align*}Find the largest possible value of $\sin x.$ | D | math_Precalculus | mathematics | ||
aquarat_82012 | deepmind/aqua_rat | In how many ways can 10 engineers and 4 doctors be seated at a round table if all the 4 doctors do not sit together? | A. 13! - (10! × 4!) B. 13! × 4! C. 14! D. 10! × 4! E. None of these | A. 13! - (10! × 4!) | Explanation :
Initially let's find out the total number of ways in which 10 engineers and 4 doctors
can be seated at a round table
In this case, n = total number of persons = 10 + 4 = 14
Hence the total number of ways in which 10 engineers and 4 doctors can be seated at a round table
= (14-1)! = 13! ---(A)
Now let's fi... | college_mathematics | mathematics |
math_234 | math_mc | Suppose the function $f(x)$ is defined on the domain $\{x_1,x_2,x_3\}$, so that the graph of $y=f(x)$ consists of just three points. Suppose those three points form a triangle of area $32$.
The graph of $y = 2f(2x)$ also consists of just three points. What is the area of the triangle formed by those three points? | C | math_Algebra | mathematics | ||
math_711 | math_mc | Triangle $ABC$ is a right triangle with $AC = 7,$ $BC = 24,$ and right angle at $C.$ Point $M$ is the midpoint of $AB,$ and $D$ is on the same side of line $AB$ as $C$ so that $AD = BD = 15.$ Given that the area of triangle $CDM$ may be expressed as $\frac {m\sqrt {n}}{p},$ where $m,$ $n,$ and $p$ are positive integers... | B | math_Geometry | mathematics | ||
math_2186 | math_mc | Let $x = \cos \frac{2 \pi}{7} + i \sin \frac{2 \pi}{7}.$ Compute the value of
\[(2x + x^2)(2x^2 + x^4)(2x^3 + x^6)(2x^4 + x^8)(2x^5 + x^{10})(2x^6 + x^{12}).\] | A | math_Precalculus | mathematics | ||
mmlu_aux_train_92983 | mmlu_aux_train | Which of these explains how a trench can form?
A. two oceanic plates converging
B. two continental plates converging
C. two continental plates diverging
D. two oceanic plates diverging | A. two oceanic plates converging | college_earth_science | earth_science | ||
math_211 | math_mc | Find $a+b+c$ if the graph of the equation $y=ax^2+bx+c$ is a parabola with vertex $(5,3)$, vertical axis of symmetry, and contains the point $(2,0)$. | A | math_Algebra | mathematics | ||
aquarat_769 | deepmind/aqua_rat | A set of data consists of the following 6 numbers: 0, 2, 4, 6,10 and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers? | A. -1 and 9 B. 4 and 4 C. 3 and 5 D. 2 and 6 E. 0 and 8 | E. 0 and 8 | If you are in for some calculations , this is how I got to it
mean = 4
sd = \sqrt{8} = 2.8
Expected values for the SD to not change are - One value below SD from mean is (4 - 2.8) = 1.2 , and one value above SD is (4 + 2.8) = 6.8
This would mean , adding 1.2 ans 6.8 would have no impact on the SD . SD remains the same ... | high_school_statistics | mathematics |
pythonio_594 | pythonio-mc | Program:
import re
def occurance_substring(text,pattern):
for match in re.finditer(pattern, text):
s = match.start()
e = match.end()
return (text[s:e], s, e)
Input:
occurance_substring('python programming, python language','python')
Output: | A | code | computer_science | ||
mmlu_aux_train_94993 | mmlu_aux_train | The sun is a source of which, first and foremost?
A. Light
B. Energy
C. Heat
D. Nutrients) | A. Light | astronomy | physics | ||
mmlu_aux_train_4698 | mmlu_aux_train | Scientists found fish fossils in the desert. What do the fossils tell about this environment when the fish were alive?
A. There was a forest with large trees.
B. There were lakes with water plants.
C. There were mountains with glaciers.
D. There was a desert with large rocks. | B. There were lakes with water plants. | college_biology | biology | ||
NLP4Education_487 | NLP4Education | Let $(G,+), (H,\times)$ be two groups and $f:G\to H$ be an homomorphism. For $x_1,x_2 \in G$, we have:
A. $f(x_1) + f(x_2) = f(x_1) \times f(x_2)$
B. $f(x_1 + x_2) = f(x_1) \times f(x_2)$
C. $f(x_1 + f(x_2)) = f(x_1 \times f(x_2))$
D. $f(x_1 \times x_2) = f(x_1) + f(x_2)$ | B. $f(x_1 + x_2) = f(x_1) \times f(x_2)$ | abstract_algebra | mathematics | ||
NLP4Education_72 | NLP4Education | Our task is to classify whether an animal is a dog (class 0) or a cat (class 1) based on the following features:
\begin{itemize}
\item $x_1$: height
\item $x_2$: length of whiskers
\item $x_3$: thickness of fur
\end{itemize}
We perform standard normal scaling on the t... | A. $w_1 < w_3 < w_2$ | machine_learning | computer_science | ||
math_582 | math_mc | A point in space $(x,y,z)$ is randomly selected so that $-1\le x \le 1$,$-1\le y \le 1$,$-1\le z \le 1$. What is the probability that $x^2+y^2+z^2\le 1$? | C | math_Counting & Probability | mathematics | ||
allenai/sciq_7553 | allenai/sciq | Energy often changes between potential and what other kind of energy?
A. realized
B. magnetic
C. kinetic
D. thermal | C. kinetic | Energy conversion occurs when energy changes from one type or form of energy to another. Energy often changes between potential and kinetic energy. Energy is always conserved during energy conversions. | conceptual_physics | physics | |
math_895 | math_mc | Triangle $ABC$ has $\angle C = 60^{\circ}$ and $BC = 4$. Point $D$ is the midpoint of $BC$. What is the largest possible value of $\tan{\angle BAD}$?
$\mathrm{(A)}\ \frac{\sqrt{3}}{6}\qquad\mathrm{(B)}\ \frac{\sqrt{3}}{3}\qquad\mathrm{(C)}\ \frac{\sqrt{3}}{2\sqrt{2}}\qquad\mathrm{(D)}\ \frac{\sqrt{3}}{4\sqrt{2}-3}\qqua... | C | math_Geometry | mathematics | ||
math_384 | math_mc | Let $t(x) = 3x-8$ and $s(t(x)) = x^2 + 3x - 2$. Find $s(1)$. | C | math_Algebra | mathematics | ||
NLP4Education_734 | NLP4Education | Which of the following is/are true about fuzzing?
A. Black box fuzzing may struggle to find inputs that reach deep into the program.
B. Structure-aware fuzzers never need initial seed inputs.
C. Fuzzing is considered complete when one input triggers a crash.
D. The mutator in structure-aware fuzzing should always gener... | A. Black box fuzzing may struggle to find inputs that reach deep into the program. | computer_security | computer_science | ||
mmlu_aux_train_26028 | mmlu_aux_train | NASA has opened the door to the next generation of space discovery by announcing great plans for a base for humans to live on the surface of the moon forever. The project to build a base on the moon will begin soon after 2020, with astronauts living there within four years. The project comes after several excellent sci... | C. In 1968. | astronomy | physics | ||
math_772 | math_mc | Altitudes $\overline{AX}$ and $\overline{BY}$ of acute triangle $ABC$ intersect at $H$. If $\angle BAC = 61^\circ$ and $\angle ABC = 73^\circ$, then what is $\angle CHX$? | C | math_Geometry | mathematics | ||
mmlu_aux_train_39539 | mmlu_aux_train | There are robots all around us. Some do very complicated jobs like flying airplanes and driving subway trains. and some do one simple job. When an automatic washing machine is switched on, water pours in. The machine waits until the water is warm enough for washing clothes. It does this by "feedback" . Information abou... | A. robots are very popular | high_school_computer_science | computer_science | ||
allenai/sciq_9575 | allenai/sciq | Ionic, covalent, and hydrogen are three important types of what type of interaction between different types of atoms?
A. bonds
B. forms
C. levels
D. conflicts | A. bonds | 2.2 | Chemical Bonds By the end of this section, you will be able to: • Explain the relationship between molecules and compounds • Distinguish between ions, cations, and anions • Identify the key difference between ionic and covalent bonds • Distinguish between nonpolar and polar covalent bonds • Explain how water mole... | college_chemistry | chemistry | |
math_1190 | math_mc | There exists a constant $k$ so that the minimum value of
\[4x^2 - 6kxy + (3k^2 + 2) y^2 - 4x - 4y + 6\]over all real numbers $x$ and $y$ is 0. Find $k.$ | A | math_Intermediate Algebra | mathematics | ||
pythonio_383 | pythonio-mc | Program:
def Check_Vow(string, vowels):
final = [each for each in string if each in vowels]
return(len(final))
Input:
Check_Vow('valid','AaEeIiOoUu')
Output: | A | code | computer_science | ||
aquarat_22126 | deepmind/aqua_rat | If b is greater than 1 , which of the following must be negative? | A. (2 - b)(b - 1) B. (b - 1)/3b C. (1 - b)^2 D. (2 - b)/(1 - b) E. (1 - b^2)/b | E. (1 - b^2)/b | To be -ive, we should remember it should not be zero apart from being positive...
C will always be 0 or positive..
A and D will be zero at b=2..
B will always be positive..
left is E, where the numerator will always be negative and denominator, a positive..
ans E | college_mathematics | mathematics |
NLP4Education_521 | NLP4Education | Plain RSA (with an $\ell$-bit modulus) \dots
A. is commonly used in practice.
B. decrypts in $O(\ell^2)$ time.
C. encrypts in $O(\ell)$ time.
D. has homomorphic properties. | D. has homomorphic properties. | computer_security | computer_science | ||
aquarat_59218 | deepmind/aqua_rat | 3x+4y=10
x^3+y^3=6
What is the minimum value of 3x+11y=? | A. 32 B. 34 C. 35 D. 36 E. 38 | E. 38 | on subtracting 2 eqns we get y=4 and x=-2.
therefore 3x+11y=-6+44
=38.
ANSWER:E | college_mathematics | mathematics |
math_653 | math_mc | Two mathematicians were both born in the last 500 years. Each lives (or will live) to be 100 years old, then dies. Each mathematician is equally likely to be born at any point during those 500 years. What is the probability that they were contemporaries for any length of time? | C | math_Counting & Probability | mathematics | ||
mmlu_aux_train_95130 | mmlu_aux_train | Condensation over night
A. leads to extremely dry conditions
B. can lead to slippery grass
C. causes plants to wilt and die
D. causes black ice on bridges | B. can lead to slippery grass | high_school_physics | physics | ||
aquarat_4246 | deepmind/aqua_rat | If x ≠ 0 and x^3 - (2- x^3)/x^3 = y/x^2, then y = | A. -2-x B. -2+x C. -(x+2) D. -2/x E. 1/x | D. -2/x | x^3 - (2- x^3)/x^3 = y/x^2
-2/x^3 = y/x^2
y = -2/x
Answer : D | college_mathematics | mathematics |
math_486 | math_mc | If I have a $4\times 4$ chess board, in how many ways can I place four distinct pawns on the board such that each column and row of the board contains no more than one pawn? | A | math_Counting & Probability | mathematics | ||
mmlu_aux_train_97647 | mmlu_aux_train | An example of a chemical change is
A. milk to yogurt
B. mixing marbles
C. my chemical romance
D. shredding paper | A. milk to yogurt | high_school_chemistry | chemistry | ||
mmlu_aux_train_5041 | mmlu_aux_train | Humans and many other mammals have unusually efficient internal temperature regulating systems that automatically maintain stable core body temperatures in cold winters and warm summers. In addition, people have developed cultural patterns and technologies that help them adjust to extremes of temperature and humidity .... | D. Because they have internal temperature regulating systems. | college_biology | biology | ||
math_1172 | math_mc | Let $G$ be the set of polynomials of the form $$ P(z)=z^n+c_{n-1}z^{n-1}+\cdots+c_2z^2+c_1z+50, $$where $ c_1,c_2,\dots, c_{n-1} $ are integers and $P(z)$ has distinct roots of the form $a+ib$ with $a$ and $b$ integers. How many polynomials are in $G$? | A | math_Intermediate Algebra | mathematics | ||
mmlu_aux_train_24148 | mmlu_aux_train | Scientists have been puzzled by the phenomenon that migrating birds fly not just in groups all the time, but in "V" formations and they have tried to figure out what benefit birds get from this particular formation. Now, a research group from University of London may have found the answer -- migrating birds fly in a "V... | D. To report new findings about migrating birds' "V" formations. | high_school_biology | biology | ||
allenai/sciq_6160 | allenai/sciq | Hay fever is actually an allergy to what substance, vital to plant reproduction?
A. grass
B. pollen
C. fungi
D. nitrogen | B. pollen | Did you ever hear of hay fever? It’s not really a fever at all. It’s an allergy to plant pollens. People with this type of allergy have symptoms such as watery eyes, sneezing, and a runny nose. A common cause of hay fever is the pollen of ragweed. Many people are also allergic to poison ivy ( Figure below ). Skin conta... | high_school_biology | biology | |
mmlu_aux_train_83583 | mmlu_aux_train | The earth moves round the sun ,and the moon goes round the earth .When our part of the earth turns to the sun ,it is day ,When our part of the earth turns away from the sun ,it is night. The sun is much bigger than the moon .But sometimes the moon looks bigger than the sun, because it's much nearer to the earth. The su... | C. it is much nearer to the earth than the sun | astronomy | physics | ||
math_499 | math_mc | Let $S$ be the increasing sequence of positive integers whose binary representation has exactly $8$ ones. Let $N$ be the 1000th number in $S$. Find the remainder when $N$ is divided by $1000$.
| B | math_Counting & Probability | mathematics | ||
aquarat_81908 | deepmind/aqua_rat | What is the greatest prime factor of (12!11!) + (12!13!)? | A. 41 B. 71 C. 107 D. 157 E. 211 | D. 157 | 12!11! + 12!13!
= 12!11! (1+12*13)
= 12!11!(157)
The answer is D. | college_mathematics | mathematics |
math_1550 | math_mc | Let $m \ge 3$ be an integer and let $S = \{3,4,5,\ldots,m\}$. Find the smallest value of $m$ such that for every partition of $S$ into two subsets, at least one of the subsets contains integers $a$, $b$, and $c$ (not necessarily distinct) such that $ab = c$.
| D | math_Number Theory | mathematics | ||
NLP4Education_288 | NLP4Education | Consider a linear regression problem with $N$ samples $\left\{\left(\boldsymbol{x}_{n}, y_{n}\right)\right\}_{n=1}^{N}$, where each input $\boldsymbol{x}_{n}$ is a $D$-dimensional vector $\{-1,+1\}^{D}$, and all output values are $y_{i} \in \mathbb{R}$. Which of the following statements is correct?
A. Linear regression... | D. None of the above. | machine_learning | computer_science | ||
mmlu_aux_train_29915 | mmlu_aux_train | The longest solar eclipse of the century cast a wide shadow for several minutes over Asia and the Pacific Ocean on 22th July, drawing people outside to watch the sight in the sky. Day turned into night. Temperature turned cooler in cities and villages filled with fans of astronomy. The total eclipse could be seen sta... | A. Not everyone in the world could see the longest eclipse. | astronomy | physics | ||
allenai/sciq_9588 | allenai/sciq | What is the largest class of elements?
A. metals
B. organics
C. acids
D. oils | A. metals | Metals are elements that are good conductors of electricity. They are the largest class of elements. Many metals are shiny, ductile, and malleable. They are also good conductors of heat. Almost all metals are solids are room temperature. | high_school_chemistry | chemistry | |
mmlu_aux_train_29656 | mmlu_aux_train | Passwords are no safeguards Typing your password or credit card number into a computer is a moment's work. But if you think your personal details disappear as soon as you hit the Return key, think again: they can sit on the computer's hard disk for years waiting for a hacker to take them. As people spend more time on t... | C. It's unsafe to store personal information on computers. | computer_security | computer_science | ||
math_901 | math_mc | In quadrilateral $ABCD,\ BC=8,\ CD=12,\ AD=10,$ and $m\angle A= m\angle B = 60^\circ.$ Given that $AB = p + \sqrt{q},$ where $p$ and $q$ are positive integers, find $p+q.$
| A | math_Geometry | mathematics | ||
allenai/sciq_4422 | allenai/sciq | The number of possible isomers increases tremendously as carbon skeletons increase in what?
A. weight
B. size
C. mass
D. variation | B. size | high_school_chemistry | chemistry | ||
pythonio_498 | pythonio-mc | Program:
import re
def remove_char(S):
result = re.sub('[\W_]+', '', S)
return result
Input:
remove_char("Hello1234:, ! Howare33u")
Output: | D | code | computer_science | ||
mmlu_aux_train_93308 | mmlu_aux_train | Gaseous sulfur dioxide is a compound that combines with water in the atmosphere to form acid rain. What is the primary source of sulfur dioxide?
A. volcanic emissions
B. combustion of fossil fuels
C. destruction of tropical forests
D. mining and mineral extraction | B. combustion of fossil fuels | high_school_chemistry | chemistry | ||
math_1494 | math_mc | Let $f : \mathbb{R} \to \mathbb{R}$ be a function such that
\[f(f(x - y)) = f(x) f(y) - f(x) + f(y) - xy\]for all $x,$ $y.$ Find the sum of all possible values of $f(1).$ | B | math_Intermediate Algebra | mathematics | ||
math_501 | math_mc | My grandpa has 10 pieces of art, including 3 prints by Escher. If he hangs the pieces of art in a row in a random order, what is the probability that all three pieces by Escher will be placed consecutively? | D | math_Counting & Probability | mathematics | ||
allenai/sciq_4699 | allenai/sciq | Group 16 is called what?
A. noble gases
B. the acid group
C. metalloids
D. the oxygen group | D. the oxygen group | Group 16 is called the oxygen group. The first three elements in this group are nonmetals. They are followed by one metalloid and one metal. All the elements in the oxygen group have six valence electrons, and all are reactive. Oxygen (O), for example, readily reacts with metals to form compounds such as rust. Oxygen i... | high_school_chemistry | chemistry | |
allenai/sciq_5347 | allenai/sciq | The number of electrons in the outer energy level determines what property of nonmetals?
A. vibration
B. permeability
C. reactivity
D. density | C. reactivity | Some nonmetals are very reactive, whereas others are not reactive at all. It depends on the number of electrons in their outer energy level. | high_school_chemistry | chemistry | |
mmlu_aux_train_56845 | mmlu_aux_train | In China, most people ride bikes to school,or to work,or to places where they want to go.So China is called "kingdom of bicycles". But Americans are a people on the wheel.Wherever you go, you will see cars.There are so many cars that there is a traffic jam here and there.Now, more and more Americans would not consid... | A. bike | high_school_computer_science | computer_science | ||
mmlu_aux_train_92889 | mmlu_aux_train | Which best explains how the Appalachian Mountains formed?
A. an ancient river flooded
B. an earthquake folded land
C. tectonic plates pulled apart
D. tectonic plates collided | D. tectonic plates collided | college_earth_science | earth_science | ||
mmlu_aux_train_42041 | mmlu_aux_train | The coast of the State of Maine is one of the most irregular in the world. A straight line running from the southernmost coastal city to the northernmost coastal city would measure about 225 miles. If you followed the coastline between these points, you would travel more than ten times as far. This irregularity is the... | B. glacier's forcing mountains into the sea | college_biology | biology | ||
pythonio_619 | pythonio-mc | Program:
def mul_even_odd(list1):
first_even = next((el for el in list1 if el%2==0),-1)
first_odd = next((el for el in list1 if el%2!=0),-1)
return (first_even*first_odd)
Input:
mul_even_odd([1,2,3,4,5,6,7,8,9,10])
Output: | A | code | computer_science | ||
allenai/sciq_6611 | allenai/sciq | Mountain building and earthquakes are some of the responses of rocks when subected to what?
A. weather
B. erosion
C. time
D. stress | D. stress | When plates are pushed or pulled, the rock is subjected to stress. Stress can cause a rock to change shape or to break. When a rock bends without breaking, it folds. When the rock breaks, it fractures. Mountain building and earthquakes are some of the responses rocks have to stress. | college_earth_science | earth_science | |
allenai/sciq_5196 | allenai/sciq | The resultant solution will contain the same amount of solute but a greater amount of what?
A. calcium
B. pigment
C. solvent
D. liquid | C. solvent | Many chemicals that we use on a daily basis are transported in a concentrated form but used in a more diluted form. For example, concentrated cleaners are often diluted before they are used. To perform a dilution , pure solvent is added to a concentrated solution in order to make a less concentrated (more dilute) solut... | high_school_chemistry | chemistry | |
allenai/sciq_6794 | allenai/sciq | When is a moving car said to be in dynamic equilibrium?
A. zero net force
B. at rest
C. at homeostasis
D. when accelerating | A. zero net force | Figure 9.3 This car is in dynamic equilibrium because it is moving at constant velocity. There are horizontal and vertical forces, but the net external force in any direction is zero. The applied force F app between the tires and the road is balanced by air friction, and the weight of the car is supported by the normal... | conceptual_physics | physics | |
mmlu_aux_train_62956 | mmlu_aux_train | Walking down a path through some woods in Georgia, I saw a small pool of water ahead on the path. I angled my direction to go around it on the part of the path that wasn't covered by water or mud. As I reached the pool, I was suddenly attacked! Yet I did nothing for the attack. It was so unpredictable and from somewher... | D. To avoid getting his shoes dirty. | high_school_biology | biology | ||
aquarat_39154 | deepmind/aqua_rat | A certain vehicle is undergoing performance adjustments during a set of three trials on an 8-mile track. The first time it travels around the track at a constant rate of p miles per minute, the second time at a constant rate of p^2 miles per minute, and the third time at a constant rate of p^3 miles per minute. If the ... | A. 18 B. 36 C. 60 D. 96 E. 112 minutes | E. 112 minutes | The first journey takes 18 miles whereas the last journey takes 8 miles.
r1= p
r2=p^2
and r3= p^3 so we set up a table like
r x t = d
p x t1 = 8
p^2 x t2= 8
p^3 x t3 = 2 (because 18-16)
so the time taken to complete each leg individually amounts to t1 + t2 + t3 = (8/p) + (8/p^2) + (2/p^3). ----> (equation 1)
On the oth... | college_mathematics | mathematics |
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