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_1313 | math_mc | Let $a_0 = 2,$ $b_0 = 3,$ and
\[a_{n + 1} = \frac{a_n^2}{b_n} \quad \text{and} \quad b_{n + 1} = \frac{b_n^2}{a_n}\]for all $n \ge 0.$ Then $b_8 = \frac{3^m}{2^n}$ for some integers $m$ and $n.$ Enter the ordered pair $(m,n).$ | B | math_Intermediate Algebra | mathematics | ||
aquarat_724 | deepmind/aqua_rat | Given that -1 ≤ v ≤ 1, -2 ≤ u ≤ -0.5, and -2 ≤ z ≤ -0.5 and w = vz/u, then which of the following is necessarily true ? | A. -0.5 ≤ w ≤ -2 B. -4 ≤ w ≤ 4 C. -4 ≤ w ≤ 2 D. -2 ≤ w ≤ -0.5 E. None of these | B. -4 ≤ w ≤ 4 | Explanation :
u is always negative. Hence, for us to have a minimum value of vz/u , vz should be positive.
Also for the least value, the numerator has to be the maximum positive value and the denominator has to be the smallest negative value. In other words, vz has to be 2 and u has to be –0.5.
Hence the minimum value ... | college_mathematics | mathematics |
math_1412 | math_mc | Let $f$ be a function taking the nonnegative integers to the nonnegative integers, such that
\[2f(a^2 + b^2) = [f(a)]^2 + [f(b)]^2\]for all nonnegative integers $a$ and $b.$
Let $n$ be the number of possible values of $f(25),$ and let $s$ be the sum of the possible values of $f(25).$ Find $n \times s.$ | D | math_Intermediate Algebra | mathematics | ||
mmlu_aux_train_84890 | mmlu_aux_train | Did you hear of the supercomputer? Recently, China's Tianhe-1 was ranked as the world's fastest supercomputer, according to a new list of world's TOP 500 supercomputers. It took 200 Chinese scientists two years to build the fastest supercomputer. It can do 2,507 trillion calculations in a second! That means it will... | D. was made by 200 Chinese scientists | college_computer_science | computer_science | ||
mmlu_aux_train_9228 | mmlu_aux_train | Scientists around the world have been studying the warming of waters in the Pacific Ocean known as El Nino . The appearance of El Nino is known to affect the weather around the world. Scientists still do not completely understand it. Yet they now find they can use it to tell about the future in different areas of the ... | B. the warming of waters in the Pacific Ocean | earth_science | earth_science | ||
aquarat_43538 | deepmind/aqua_rat | For which of the following does f(u)−f(v)=f(u−v) for all values of u and v? | A. f(a)=a^2 B. f(a)=a/2 C. f(a)=a+5 D. f(a)=2a−1 E. f(a)=|a| | B. f(a)=a/2 | To solve this easiest way is just put the value and see that if it equals or not.
with option 1. f(u) = u^2 and f(v) = v^2
so L.H.S = u^2 - v^2
and R.H.S = (u-v)^2 ==> u^2 + v^2 -2uv.
so L.H.S not equal to R.H.S
with option 2. f(u) = u/2 and f(v) = v/2
L.H.S = u/2 - v/2 ==> 1/2(u-v)
R.H.S = (u-v)/2
so L.H.S = R.H.S whi... | college_mathematics | mathematics |
aquarat_56489 | deepmind/aqua_rat | For which of the following functions is f(q+b)=f(q)+f(b) for all positive numbers q and b? | A. a) f(x)=x^2 B. b) f(x)=x+1 C. c) f(x)=root x D. d) f(x)=2/x E. e) f(x)= -3x | E. e) f(x)= -3x | f(q+b)=f(q)+f(b) Its E | college_mathematics | mathematics |
mmlu_aux_train_85494 | mmlu_aux_train | Here comes the last term of Junior 3. Terrible! The big exam is coming in less than two months. You still have a lot to do. How will you spend it? We invited three students to share their stories. Dou Yi, 15,Beijing My chemistry used to be poor in the past. I got scores of around 40 on every test. During the last term... | D. Both A and C | high_school_chemistry | chemistry | ||
math_1510 | math_mc | Each of $a_1,$ $a_2,$ $\dots,$ $a_{100}$ is equal to $1$ or $-1.$ Find the minimum positive value of
\[\sum_{1 \le i < j \le 100} a_i a_j.\] | A | math_Intermediate Algebra | mathematics | ||
mmlu_aux_train_98878 | mmlu_aux_train | A circuit is parallel when more than one pathway has flowing what?
A. ideas
B. stocks
C. water
D. zapping energy | D. zapping energy | electrical_engineering | engineering | ||
aquarat_40368 | deepmind/aqua_rat | Set Q consists of the following five numbers: Q = {5, 7, 13, 21, 34}. Which of the following sets has the same standard deviation as Set Q?
I. {35, 38, 43, 51, 64}
II. {10, 16, 26, 42, 68}
III. {46, 59, 67, 72, 75} | A. I only B. III C. IIII D. IIIII E. I, II,III | B. III | (1) Multiplying all the numbers change Standard Deviation
(2) Adding and subtracting all the numbers with the same number keeps the standard deviation same.
If you observe Set I and III are added versions of Set Q .
Set I: 5 has been added to the Set Q
Set III: Subtract each element from 80 and you would find a number ... | high_school_statistics | mathematics |
aquarat_58127 | deepmind/aqua_rat | The probability that a visitor at the mall buys a pack of candy is 40%. If three visitors come to the mall today, what is the probability that exactly two will buy a pack of candy? | A. .288 B. .147 C. .189 D. .063 E. .027 | A. .288 | One case is: candy - candy - no candy
The probability is 4/10*4/10*6/10 = 96/1000
There are 3 such cases, so we should multiply this probability by 3.
P(exactly 2 buy candy) = 96/1000 * 3 = 288/1000 = 0.288
The answer is A. | high_school_statistics | mathematics |
mmlu_aux_train_55890 | mmlu_aux_train | Medical scientists are already putting computer chips directly into the brain to help people who have Parkinson's disease, but in what other ways might computer technology be able to help us? Ray Kurzweil is the author of the successful book The Age Of Intelligent Machines. He is also one of the world's best computer r... | B. a computer research scientist | high_school_computer_science | computer_science | ||
math_607 | math_mc | A boss plans a business meeting at Starbucks with the two engineers below him. However, he fails to set a time, and all three arrive at Starbucks at a random time between 2:00 and 4:00 p.m. When the boss shows up, if both engineers are not already there, he storms out and cancels the meeting. Each engineer is willing t... | D | math_Counting & Probability | mathematics | ||
mmlu_aux_train_95861 | mmlu_aux_train | What causes rock layers to fold on top of each other?
A. construction
B. Violent tremors
C. earthworms
D. tornados | B. Violent tremors | earth_science | earth_science | ||
mmlu_aux_train_59439 | mmlu_aux_train | A little under one-third of U.S. families have no Internet access and do not plan to get it, with most of the holdouts seeing little use for it in their lives, according to a survey released on Friday. Park Associates, a Dallas-based technology market research firm, said 29 percent of U.S. families, or 31 million homes... | B. they can find little value of it | high_school_computer_science | computer_science | ||
math_437 | math_mc | Let $P(x) = x^2 - 3x - 9$. A real number $x$ is chosen at random from the interval $5 \le x \le 15$. The probability that $\lfloor\sqrt{P(x)}\rfloor = \sqrt{P(\lfloor x \rfloor)}$ is equal to $\frac{\sqrt{a} + \sqrt{b} + \sqrt{c} - d}{e}$ , where $a$, $b$, $c$, $d$, and $e$ are positive integers. Find $a + b + c + d + ... | D | math_Counting & Probability | mathematics | ||
allenai/sciq_11027 | allenai/sciq | Hormones cause cellular changes by binding to receptors on these?
A. reach cells
B. fighter cells
C. target cells
D. able cells | C. target cells | 37.2 How Hormones Work Hormones cause cellular changes by binding to receptors on target cells. The number of receptors on a target cell can increase or decrease in response to hormone activity. Hormones can affect cells directly through intracellular hormone receptors or indirectly through plasma membrane hormone rece... | high_school_biology | biology | |
mmlu_aux_train_18058 | mmlu_aux_train | Its often interesting to take a look at some of the lists that arrive toward the end of the year such as top devices, best gadgets, most desirable high-tech gift and more. Apart from cell phones and tablets, and Apple and Samsung products, this year many other gadgets made it on the most wanted list from Yahoo Tech and... | A. 3397 yuan | computer_security | computer_science | ||
math_1580 | math_mc | What is the largest integer that is a divisor of \[
(n+1)(n+3)(n+5)(n+7)(n+9)
\]for all positive even integers $n$? | D | math_Number Theory | mathematics | ||
aquarat_67207 | deepmind/aqua_rat | The arithmetic mean of a data set is 46 and the standard deviation of the set is 4. Which of the following contains the interval two standard deviations from the mean of the set? | A. 38 to 55 B. 38 to 54 C. 48 to 54 D. 80 to 54 E. 38 to 60 | B. 38 to 54 | Arithmetic Mean = 46
SD = 4 (One Interval )
Two SD intervals means 38__42__46 __50__54
answer B | high_school_statistics | mathematics |
math_1842 | math_mc | The landlord of an apartment building needs to purchase enough digits to label all of the apartments from 100 through 125 on the first floor and 200 through 225 on the second floor. The digits can only be purchased in a package that contains one of each digit 0 through 9. How many packages must the landlord purchase? | C | math_Prealgebra | mathematics | ||
mmlu_aux_train_37656 | mmlu_aux_train | Skipping classes, particularly big lectures where an absence is likely to go undetected, is a tradition among college undergraduates. These days, however, some professors say they're seeing more _ , as students make the most of new technologies as learning aids. Americ Azevedo taught an "Introduction to Computers" at ... | A. so many undergraduates relied on digital learning aids | college_computer_science | computer_science | ||
math_1158 | math_mc | Find $a$ if $a$ and $b$ are integers such that $x^2 - x - 1$ is a factor of $ax^{17} + bx^{16} + 1$. | B | math_Intermediate Algebra | mathematics | ||
allenai/sciq_10483 | allenai/sciq | Which layer is found below the lithosphere?
A. magnetosphere
B. troposphere
C. stratosphere
D. asthenosphere | D. asthenosphere | The asthenosphere is below the lithosphere. The asthenosphere is also in the upper mantle. This layer is solid, but it can flow and bend. A solid that can flow is like silly putty. | college_earth_science | earth_science | |
math_1202 | math_mc | The equations of the asymptotes of a hyperbola are $y = 2x+5$ and $y = -2x+1.$ Given that the hyperbola passes through the point $(0, 7),$ the standard form for the equation of the hyperbola is \[\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1,\]where $a,$ $b$, $h,$ and $k$ are constants with $a, b > 0.$ Find $a + h.$ | C | math_Intermediate Algebra | mathematics | ||
allenai/sciq_2703 | allenai/sciq | Some women experience cramping and pain before and during what monthly cycle?
A. reproduction
B. deformation
C. menstruation
D. inflammation | C. menstruation | Some women experience cramping and pain before and during menstruation. | high_school_biology | biology | |
math_1621 | math_mc | If $f(x)$ is a function, then we define the function $f^{(n)}(x)$ to be the result of $n$ applications of $f$ to $x$, where $n$ is a positive integer. For example, $f^{(3)}(x)=f(f(f(x)))$.
We define the $\textit{order}$ of an input $x$ with respect to $f$ to be the smallest positive integer $m$ such that $f^{(m)}(x)=x... | B | math_Number Theory | mathematics | ||
math_2153 | math_mc | Let $\mathbf{A}$ and $\mathbf{B}$ be matrices such that
\[\mathbf{A} + \mathbf{B} = \mathbf{A} \mathbf{B}.\]If $\mathbf{A} \mathbf{B} = \begin{pmatrix} 20/3 & 4/3 \\ -8/3 & 8/3 \end{pmatrix},$ find $\mathbf{B} \mathbf{A}.$ | A | math_Precalculus | mathematics | ||
aquarat_45861 | deepmind/aqua_rat | if A=2^65 AND B=2^64+2^63.....+2^0 | A. A is larger than B by 2^64 times B. B is larger than A by 1 C. A is larger than B by 1 D. A is equal to B E. None | C. A is larger than B by 1 | lets say A : 2^4=16 , B: 2^3+2^2+2^1+2^0 = 15 so A is larger than B by 1 always
ANSWER:C | college_mathematics | mathematics |
allenai/sciq_1101 | allenai/sciq | Single bonds allow the atoms they join to rotate freely about the what?
A. nucleus
B. bond axis
C. electron shell
D. atomic orbit | B. bond axis | college_chemistry | chemistry | ||
aquarat_74101 | deepmind/aqua_rat | If YWVSQ is 25 - 24 - 21 - 19 - 17, Then MLIGF | A. 13 - 11 - 9 - 7 - 8 B. 13 - 11 - 9 - 7 - 6 C. 13 - 11 - 9 - 7 - 7 D. 13 - 11 - 9 - 7 - 3 E. 13 - 11 - 9 - 7 - 1 | A. 13 - 11 - 9 - 7 - 8 | MLIGF = 13 - 11 - 9 - 7 - 8
Note: this is a dummy question. Dont answer these questions
Answer:A | formal_logic | mathematics |
mmlu_aux_train_2374 | mmlu_aux_train | Which list gives the correct order of substances from the lowest melting point to the highest?
A. oxygen, water, iron
B. water, iron, oxygen
C. oxygen, iron, water
D. iron, oxygen, water | A. oxygen, water, iron | high_school_chemistry | chemistry | ||
mmlu_aux_train_24471 | mmlu_aux_train | My father was, by nature, a cheerful, kindly man.Until he was thirty-four years old he worked as a farm-hand for Thomas Butterworth near the town of Bidwell, Ohio.On Saturday evenings he drove his horse into town to spend a few hours in social intercourse with other farm-hands.He was quite happy in his position in life... | B. gives you a philosophical insight into life | college_mathematics | mathematics | ||
mmlu_aux_train_21447 | mmlu_aux_train | Sure, human dads can play games with their kids and help with homework, but can they give birth? Daddy sea horses can! This Father's Day, while you're praising your daddy, you may also remember that some of the best dads in the world can be found in the animal kingdom: Sea horses: The "Mr. Moms" in the sea, male sea ho... | B. A Darwin's rhea | high_school_biology | biology | ||
aquarat_65222 | deepmind/aqua_rat | If, when the two parties of knights encounter one another after a month, exactly one knight changes from one travelling party to the other travelling party, that knight must be | A. P B. Q C. R D. S E. T | B. Q | Q because Q always have to travel in northern route
ANSWER:B | abstract_algebra | mathematics |
aquarat_68846 | deepmind/aqua_rat | How many different sets of positive square integers K, each greater than 1, add up to 75? | A. 1 B. 4 C. 7 D. 11 E. 13 | E. 13 | E = 13 is the correct answer. | college_mathematics | mathematics |
NLP4Education_123 | NLP4Education | When computing HITS, the initial values
A. Are set all to 1
B. Are set all to 1/n
C. Are set all to 1/sqrt(n)
D. Are chosen randomly | C. Are set all to 1/sqrt(n) | college_computer_science | computer_science | ||
NLP4Education_715 | NLP4Education | Which of the following statement(s) is/are true? To achieve memory safety for C, ...
A. pointer arithmetic must be checked/restricted
B. all control-flow must be validated against a model
C. the standard library must be formally verified
D. a strict specification of program functionality is required | A. pointer arithmetic must be checked/restricted | computer_security | computer_science | ||
aquarat_91889 | deepmind/aqua_rat | For each positive integer,the quantitySn is defined such thatSn+1=(Sn)^2 -S(n+1).in addition ,S2=1.then which of the following must be true. | A. a)S4 +S3 +1=0 B. b)(S1)^2 +S4 +2=0 C. c) ifS1=-1thenS4 is also equal to-1. D. d) ifS4 =-7thenS1=-2. E. e) ifS1 =-3thenS4=-7 | A. a)S4 +S3 +1=0 | Since all the answers include S4, let's start from there.
S4=S2^2-S3
S3=S1^2-S2
Substituting S3 into the first equation we get:
S4=S2^2-(S1^2-S2)
Since S2=1
S4=1-(S1^2-1)
S4=2-S1^2
We need S1^2 in order to calculate S4.
E) provides S1 and from there we can calculate S4:
S4=2-(-3)^2
S4=-7
Correct.
As a side note, I woul... | college_mathematics | mathematics |
math_1167 | math_mc | Let $x_1,$ $x_2,$ $x_3,$ $\dots,$ $x_{100}$ be positive real numbers such that $x_1^2 + x_2^2 + x_3^2 + \dots + x_{100}^2 = 1.$ Find the minimum value of
\[\frac{x_1}{1 - x_1^2} + \frac{x_2}{1 - x_2^2} + \frac{x_3}{1 - x_3^2} + \dots + \frac{x_{100}}{1 - x_{100}^2}.\] | D | math_Intermediate Algebra | mathematics | ||
allenai/sciq_11182 | allenai/sciq | What is the middle layer that hair pass through before exiting at the surface of the skin?
A. cuticle
B. dermis
C. epithelial tissue
D. epidermis | D. epidermis | Hair follicles are the structures where hairs originate. Hairs grow out of follicles, pass through the epidermis, and exit at the surface of the skin. | high_school_biology | biology | |
allenai/sciq_4757 | allenai/sciq | The motor thus acts as a generator whenever its coil does what?
A. stops
B. rotates
C. oscillates
D. revolves | B. rotates | 23.6 Back Emf It has been noted that motors and generators are very similar. Generators convert mechanical energy into electrical energy, whereas motors convert electrical energy into mechanical energy. Furthermore, motors and generators have the same construction. When the coil of a motor is turned, magnetic flux chan... | conceptual_physics | physics | |
allenai/sciq_4723 | allenai/sciq | How do bees communicate to tell other bees where food is located?
A. mating dance
B. wing flapping
C. waggle dance
D. high pitch noise | C. waggle dance | Animals may communicate by sight with gestures, body postures, or facial expressions. Look at the cat in Figure below . There’s no mistaking the meaning of its arched back, standing hair, and exposed fangs. It’s clearly saying “stay away, or else!” Bees communicate with a waggle dance. They use it to tell other bees wh... | high_school_biology | biology | |
mmlu_aux_train_26165 | mmlu_aux_train | Almost all of us have been there: A sense of uneasiness strikes us when we see the battery running low on the smartphone. While today's smartphones enable us to surf the Internet, take pictures and play music, their limited, sometimes annoyingly short battery life has started to make people full of memories of early mo... | C. 4 | college_chemistry | chemistry | ||
mmlu_aux_train_6475 | mmlu_aux_train | Forty-two of the fifty American states offered some kind of public online learning this past school year.One state,Michigan,now requires all students to have an online learning experience before they finish high school.Even the idea of a school has changed since the rise ofthe Internet in the 1990s. A new report from t... | D. has online classes and no real classrooms | high_school_computer_science | computer_science | ||
mmlu_aux_train_6879 | mmlu_aux_train | I believe that it is important to be brought up with a firm belief in the good. I was fortunate in this respect. My parents not only gave me a happy home, but they had me study half a dozen foreign languages and made it possible for me to travel in other countries. This made me more tolerant and helped me to bridge man... | C. She got married in Czechoslovakia. | high_school_biology | biology | ||
allenai/sciq_4046 | allenai/sciq | What is the shorter loop of the cardiovascular system?
A. metabolic circulation
B. pulmonary circulation
C. venous circulation
D. pulmonary edema | B. pulmonary circulation | Pulmonary circulation is the shorter loop of the cardiovascular system. It carries blood between the heart and lungs. Oxygen-poor blood flows from the heart to the lungs. In the lungs, the blood absorbs oxygen and releases carbon dioxide. Then the oxygen-rich blood returns to the heart. | high_school_biology | biology | |
mmlu_aux_train_38921 | mmlu_aux_train | The European Union on Monday prohibited the use of X-ray body scanners in European airports, parting ways with the U. S. Transportation Security Administration, which has used hundreds of the scanners as a way to screen millions of airline passengers for explosives hidden under clothing. The European Commission, which... | D. They won't risk causing cancer. | computer_security | computer_science | ||
allenai/sciq_8641 | allenai/sciq | What is the general name for a solid material that is formed via a natural process?
A. mineral
B. plasma
C. gas
D. chemical | A. mineral | A mineral is a solid material that forms by a natural process. A mineral can be made of an element or a compound. It has a specific chemical composition. Its chemical composition is different from other minerals. Each type of mineral has physical properties that differ from others. These properties include crystal stru... | high_school_chemistry | chemistry | |
pythonio_31 | pythonio-mc | Program:
def radix_sort(nums):
RADIX = 10
placement = 1
max_digit = max(nums)
while placement < max_digit:
buckets = [list() for _ in range( RADIX )]
for i in nums:
tmp = int((i / placement) % RADIX)
buckets[tmp].append(i)
a = 0
for b in range( RADIX )... | B | code | computer_science | ||
math_1214 | math_mc | Suppose that $x$ and $y$ are positive real numbers such that $x^2-xy+2y^2=8$. Then the maximum possible value of $x^2+xy+2y^2$ can be expressed in simplest form as $\frac{a + b \sqrt{c}}{d},$ where $a,$ $b,$ $c,$ $d$ are positive integers. Find $a + b + c + d.$ | B | math_Intermediate Algebra | mathematics | ||
allenai/sciq_479 | allenai/sciq | Which hormone helps cells absorb sugar from the blood?
A. cortisol
B. insulin
C. estrogen
D. adrenaline | B. insulin | Endocrine system: A high concentration of sugar in the blood triggers secretion of insulin by an endocrine gland called the pancreas. Insulin is a hormone that helps cells absorb sugar from the blood. | high_school_biology | biology | |
math_1657 | math_mc | A subset of the integers $1,2,\cdots,100$ has the property that none of its members is 3 times another. What is the largest number of members such a subset can have?
$\text{(A) } 50\quad \text{(B) } 66\quad \text{(C) } 67\quad \text{(D) } 76\quad \text{(E) } 78$
| A | math_Number Theory | mathematics | ||
mmlu_aux_train_56631 | mmlu_aux_train | Which are you more likely to have wath you at sny given mement--your cell phone or your wallet? Soon you may be able to throw your wallet away and pay for things with a quick wave of your smart phone over an electroue scannet. In January, Starbucks announced that customers could start using their phones to buy coffee i... | B. The boom of pay by phone business. | computer_security | computer_science | ||
math_1944 | math_mc | Acme Corporation has released an alphabet soup in which each of the vowels (A, E, I, O, U) of the English alphabet appears five times (and the consonants do not appear at all). How many five-letter words can be formed from a bowl of Acme Vowel Soup? (Note: The words do not have to be actual words in English!) | B | math_Prealgebra | mathematics | ||
allenai/sciq_3330 | allenai/sciq | Any sample of matter that has the same physical and chemical properties throughout the sample is called what?
A. type
B. element
C. substance
D. molecule | C. substance | Elements and Compounds Any sample of matter that has the same physical and chemical properties throughout the sample is called a substance. There are two types of substances. A substance that cannot be broken down into chemically simpler components is an element. Aluminum, which is used in soda cans, is an element. A s... | high_school_chemistry | chemistry | |
pythonio_453 | pythonio-mc | Program:
def find_ind(key, i, n,
k, arr):
ind = -1
start = i + 1
end = n - 1;
while (start < end):
mid = int(start +
(end - start) / 2)
if (arr[mid] - key <= k):
ind = mid
start = mid + 1
else:
end = mid
return ind
def removals(arr, n, k):
ans = n - 1
arr.sort()
for i in ... | B | code | computer_science | ||
math_336 | math_mc | The graph of $y=\frac{5x^2-9}{3x^2+5x+2}$ has a horizontal asymptote at $y=a$. What is $a$? | D | math_Algebra | mathematics | ||
aquarat_36778 | deepmind/aqua_rat | Let the polynomials be:
P1(x)=3x2−7x+3,
P2(x)=−5x2−4x+2,
P1(x)+P2(x)= | A. 2x2 + 11x - 7 B. -2x2 - 11x + 5 C. -2x2 - 11x + 6 D. 2x2 - 9x + 7 E. None of these | B. -2x2 - 11x + 5 | Solution:
P1(x)+P2(x)=(3x2−7x+3)+(−5x2−4x+2)=P1(x)+P2(x)=(3x2−7x+3)+(−5x2−4x+2)=
3x2−7x+3−5x2−4x+2=3x2−7x+3−5x2−4x+2=
−2x2−11x+5
Answer B | college_mathematics | mathematics |
mmlu_aux_train_63899 | mmlu_aux_train | A job used to be the next step after a diploma. But now, young people aren't in any rush to start working. Less than 78 % of people aged 20 to 34 either have jobs or are looking for work, according to the Bureau of Labor Statistics (USA). That's down from the peak of 83 % in 2000, and the lowest since the 1970s. The bi... | B. they have to get more advanced degrees to earn more | high_school_statistics | mathematics | ||
math_1463 | math_mc | Let $g(x) = x^5 + x^4 + x^3 + x^2 + x + 1.$ What is the remainder when the polynomial $g(x^{12})$ is divided by the polynomial $g(x)$? | D | math_Intermediate Algebra | mathematics | ||
allenai/sciq_10433 | allenai/sciq | Cnvs result from regions of what being duplicated or deleted inconsistently within the population?
A. cytoplasm
B. DNA
C. genes
D. genome | D. genome | college_biology | biology | ||
mmlu_aux_train_56645 | mmlu_aux_train | To switch or not to switch, that is the question.Google's announcement of its Nexus One smartphone happened over a week ago and I'm still receiving lots of e-mails from readers asking the same question: Should they give up their iPhone for the Nexus One? Some people with iPhones, disappointed by American Telephone&Tel... | C. Because of the limited service and high cost. | computer_security | computer_science | ||
math_700 | math_mc | How many continuous paths from $A$ to $B$, along segments of the figure, do not revisit any of the six labeled points?
[asy]
draw((0,0)--(3,0)--(3,2)--(0,2)--(0,0)--cycle,linewidth(2));
draw((0,2)--(1,0)--(3,2)--(0,2)--cycle,linewidth(2));
draw((0,2)--(1.5,3.5)--(3,2),linewidth(2));
label("$A$",(1.5,3.5),N);
label("$... | C | math_Counting & Probability | mathematics | ||
pythonio_238 | pythonio-mc | Program:
import re
pattern = 'fox'
text = 'The quick brown fox jumps over the lazy dog.'
def find_literals(text, pattern):
match = re.search(pattern, text)
s = match.start()
e = match.end()
return (match.re.pattern, s, e)
Input:
find_literals('Its been a very crazy procedure right', 'crazy')
Output: | A | code | computer_science | ||
aquarat_58894 | deepmind/aqua_rat | In the faculty of Reverse-Engineering, 250 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 80% of the total? | A. 515. B. 545. C. 618. D. 674. E. 666. | D. 674. | Answer is D :674
Solution : Total number of students studying both are 423 + 250 - 134 = 539 (Subtracting the 134 since they were included in the both the other numbers already).
So 80% of total is 539, so 100% is approx. 674. | college_mathematics | mathematics |
math_778 | math_mc | A regular octagon $ABCDEFGH$ has sides of length two. Find the area of $\bigtriangleup ADG$. Express your answer in simplest radical form. | D | math_Geometry | mathematics | ||
mmlu_aux_train_42357 | mmlu_aux_train | Scientists are worried that an asteroid will possibly hit the earth in 2036. If scientists are right, planet earth is 24 years away from a major disaster. Scientists have been monitoring the progress of a 390-metre-wide asteroid ever since it was discovered last June. They have announced that it could hit the earth, c... | B. the asteroid named Apophis might hit the earth in 2036. | astronomy | physics | ||
allenai/sciq_1024 | allenai/sciq | What kind of pipettes are suitable for measuring very small amounts of liquids?
A. macropipettes
B. frozen pipettes
C. micropipettes
D. clutch pipettes | C. micropipettes | Pipettes are small, but important tools in many biology labs. Micropipettes, such as the ones shown here, are calibrated to measure very small amounts of liquids. For example, 100 microliters (100 µL) is about half the volume of your little finger tip; or even 1 µL, which is much smaller than a drop of water. | college_biology | biology | |
pythonio_193 | pythonio-mc | Program:
import heapq
def expensive_items(items,n):
expensive_items = heapq.nlargest(n, items, key=lambda s: s['price'])
return expensive_items
Input:
expensive_items([{'name': 'Item-1', 'price': 101.1},{'name': 'Item-2', 'price': 555.22}, {'name': 'Item-3', 'price': 45.09}],2)
Output: | C | code | computer_science | ||
math_1219 | math_mc | Let $\omega$ be a nonreal root of $z^3 = 1.$ Find the number of ordered pairs $(a,b)$ of integers such that $|a \omega + b| = 1.$ | A | math_Intermediate Algebra | mathematics | ||
allenai/sciq_241 | allenai/sciq | To measure what changes that occur in chemical reactions, chemists usually use a related thermodynamic quantity, calledenthalpy?
A. entropy
B. evaporation
C. ion exchange
D. energy | D. energy | (a) Initially, the system (a copper penny and concentrated nitric acid) is at atmospheric pressure. (b) When the penny is added to the nitric acid, the volume of NO2 gas that is formed causes the piston to move upward to maintain the system at atmospheric pressure. In doing so, the system is performing work on its surr... | college_chemistry | chemistry | |
pythonio_297 | pythonio-mc | Program:
MAX=1000;
def replace_spaces(string):
string=string.strip()
i=len(string)
space_count=string.count(' ')
new_length = i + space_count*2
if new_length > MAX:
return -1
index = new_length-1
string=list(string)
for f in range(i-2, new_length-2):
string.append('0')
for j in ran... | A | code | computer_science | ||
math_424 | math_mc | Points $A(3,5)$ and $B(7,10)$ are the endpoints of a diameter of a circle graphed in a coordinate plane. How many square units are in the area of the circle? Express your answer in terms of $\pi$. | B | math_Algebra | mathematics | ||
math_1120 | math_mc | Let $x$ and $y$ be positive real numbers such that
\[\frac{1}{x + 2} + \frac{1}{y + 2} = \frac{1}{3}.\]Find the minimum value of $x + 2y.$ | A | math_Intermediate Algebra | mathematics | ||
mmlu_aux_train_26197 | mmlu_aux_train | Money is the root of all evil and new study claims there may be some truth behind the saying.Scientists at the University of California, Berkeley, US,announced on February 27 that rich people are more likely to do unethical things, such as lie or cheat, than poorer people. The scientists did a series of eight experim... | A. draw readers' attention to the research | high_school_statistics | mathematics | ||
mmlu_aux_train_39972 | mmlu_aux_train | That summer I drank every day, everywhere I went. I had a bottle in my drawer next to me and a bottle next to my bed. I never did another drug, but I drank so much that my family finally asked a priest for help. My father gave me a bottle of medicine for alcoholism that produces unpleasant symptoms when users drink alc... | D. He believed it could prevent him drinking. | clinical_knowledge | biology | ||
NLP4Education_246 | NLP4Education | Matrix Factorizations: If we compare SGD vs ALS for optimizing a matrix factorization of a $D \times N$ matrix, for large $D, N$
A. Per iteration, SGD and ALS have identical computational cost.
B. Per iteration, ALS has a higher computational cost than SGD.
C. Per iteration, SGD's cost does not depend on $D$ or $N$.
D.... | B. Per iteration, ALS has a higher computational cost than SGD. | machine_learning | computer_science | ||
math_1187 | math_mc | Find the maximum value of
\[\cos \theta_1 \sin \theta_2 + \cos \theta_2 \sin \theta_3 + \cos \theta_3 \sin \theta_4 + \cos \theta_4 \sin \theta_5 + \cos \theta_5 \sin \theta_1,\]over all real numbers $\theta_1,$ $\theta_2,$ $\theta_3,$ $\theta_4,$ and $\theta_5.$ | B | math_Intermediate Algebra | mathematics | ||
math_940 | math_mc | Side $AB$ of regular hexagon $ABCDEF$ is extended past $B$ to point $X$ such that $AX = 3AB$. Given that each side of the hexagon is $2$ units long, what is the length of segment $FX$? Express your answer in simplest radical form. | D | math_Geometry | mathematics | ||
allenai/sciq_5058 | allenai/sciq | Saturated hydrocarbons get their name because they are saturated with what atoms?
A. oxygen
B. hydrogen
C. nitrogen
D. helium | B. hydrogen | Saturated hydrocarbons have only single bonds between carbon atoms, so the carbon atoms are bonded to as many hydrogen atoms as possible. In other words, they are saturated with hydrogen atoms. | high_school_chemistry | chemistry | |
allenai/sciq_1361 | allenai/sciq | What are all of the living or once-living aspects of the environment called?
A. abiotic factors
B. photic factors
C. fossils
D. biotic factors | D. biotic factors | Biotic factors are all of the living or once-living aspects of the environment. They include all the organisms that live there as well as the remains of dead organisms. | high_school_biology | biology | |
pythonio_775 | pythonio-mc | Program:
def remove_list_range(list1, leftrange, rigthrange):
result = [i for i in list1 if (min(i)>=leftrange and max(i)<=rigthrange)]
return result
Input:
remove_list_range([[2], [0], [1, 2, 3], [0, 1, 2, 3, 6, 7], [9, 11], [13, 14, 15, 17]],1,3)
Output: | D | code | computer_science | ||
aquarat_31305 | deepmind/aqua_rat | Of the 80 electronics components that a factory must manufacture, 60 percent would be most e¢ ciently manufactured by Machine A and the remaining 40 percent would be most efficiently manufactured by Machine B, though either machine could manufacture any of the 80 components. If 60 percent of the components were manufac... | A. 80 B. 32 C. 33 D. 35 E. 36 | A. 80 | A can manufacture 60 % of 80 efficiently, which is 48.
B can manufacure 40 % of 80 efficiently, which is 32.
Now 60 % of 80 are produced by A. This means 48 parts. Since A can produce 48 efficiently, all 48 are produced efficiently. Rest (32) is produced by B, which can produce max. 32 parts efficiently.
Hence parts th... | college_mathematics | mathematics |
math_546 | math_mc | Define a regular $n$-pointed star to be the union of $n$ line segments $P_1P_2, P_2P_3,\ldots, P_nP_1$ such that
the points $P_1, P_2,\ldots, P_n$ are coplanar and no three of them are collinear,
each of the $n$ line segments intersects at least one of the other line segments at a point other than an endpoint,
all of t... | C | math_Counting & Probability | mathematics | ||
math_2138 | math_mc | Let $\mathbf{p}$ and $\mathbf{q}$ be two three-dimensional unit vectors such that the angle between them is $30^\circ.$ Find the area of the parallelogram whose diagonals correspond to $\mathbf{p} + 2 \mathbf{q}$ and $2 \mathbf{p} + \mathbf{q}.$ | C | math_Precalculus | mathematics | ||
mmlu_aux_train_2783 | mmlu_aux_train | Which most likely contributes to the rotational pattern of a hurricane that develops in the Atlantic Ocean?
A. Gulf Stream
B. Coriolis effect
C. low relative humidity
D. high-pressure systems | B. Coriolis effect | college_earth_science | earth_science | ||
math_1418 | math_mc | The function $f(x),$ defined for $0 \le x \le 1,$ has the following properties:
(i) $f(0) = 0.$
(ii) If $0 \le x < y \le 1,$ then $f(x) \le f(y).$
(iii) $f(1 - x) = 1 - f(x)$ for all $0 \le x \le 1.$
(iv) $f \left( \frac{x}{3} \right) = \frac{f(x)}{2}$ for $0 \le x \le 1.$
Find $f \left( \frac{2}{7} \right).$ | C | math_Intermediate Algebra | mathematics | ||
NLP4Education_753 | NLP4Education | Consider the group $(\mathbb{Z} / 23 \mathbb{Z}^*, \cdot)$. Find how many elements of the group are generators of the group. (Hint: $5$ is a generator of the group.)
A. 10
B. 22
C. 11
D. 2 | A. 10 | abstract_algebra | mathematics | ||
mmlu_aux_train_1902 | mmlu_aux_train | Four solid balls, each with a different mass, are moving at the same speed. Which ball would require the most force to stop its motion?
A. ball with a mass of 5 kg
B. ball with a mass of 10 kg
C. ball with a mass of 15 kg
D. ball with a mass of 20 kg | D. ball with a mass of 20 kg | conceptual_physics | physics | ||
aquarat_24549 | deepmind/aqua_rat | Find the remainder W when 12^190 is divided by 1729 ? | A. 12 B. 1 C. 1728 D. 1717 E. 4 | D. 1717 | 12^(190) can be written as. ((12^3)^63)* 12. 12^3 when divided by 1729 gives a remainder W -1. so in the numerator we have -12. Now acccording to remainder theorm the answer will be 1729-12=1717.D | college_mathematics | mathematics |
NLP4Education_142 | NLP4Education | Considering the transaction below, which one is WRONG?
|Transaction ID |Items Bought|
|--|--|
|1|Tea|
|2|Tea, Yoghurt|
|3|Tea, Yoghurt, Kebap|
|4 |Kebap |
|5|Tea, Kebap|
A. {Yoghurt} -> {Kebap} has 50% confidence
B. {Yoghurt, Kebap} has 20% support
C. {Tea} has the highest support
D. {Yoghurt} has the lowest support a... | D. {Yoghurt} has the lowest support among all itemsets | college_mathematics | mathematics | ||
NLP4Education_413 | NLP4Education | Which of the following algorithms is a stream cipher?
A. FOX
B. IDEA
C. RC4
D. AES | C. RC4 | computer_security | computer_science | ||
mmlu_aux_train_10648 | mmlu_aux_train | The language used by scientists to explain complex ideas can be difficult and sometimes even boring. The language, with its Latin words and long scientific terms, could be one reason some people avoid learning about science, especially children. American Danielle Dixson is a marine biologist. She wants to make science ... | C. The language usually contains complicated words and terms. | college_biology | biology | ||
mmlu_aux_train_2332 | mmlu_aux_train | Charisma has a goldfish she keeps in a tank. She planted several underwater plants in the bottom of the tank. How are the goldfish and the plants in the tank similar?
A. Both add oxygen to the water.
B. Both perform photosynthesis.
C. Both are made up of cells.
D. Both eat food. | C. Both are made up of cells. | high_school_biology | biology | ||
NLP4Education_744 | NLP4Education | Is $(\mathbb{Z} / 8\mathbb{Z}^*, \cdot)$ isomorphic to $(\mathbb{Z} / k\mathbb{Z}, +)$ for some $k$?
A. Yes, for $k = 4$
B. Yes, for $k = 8$
C. Yes, for some integer $k > 1$
D. No, there is no such $k$ | D. No, there is no such $k$ | abstract_algebra | mathematics | ||
math_639 | math_mc | Objects $A$ and $B$ move simultaneously in the coordinate plane via a sequence of steps, each of length one. Object $A$ starts at $(0,0)$ and each of its steps is either right or up, both equally likely. Object $B$ starts at $(5,7)$ and each of its steps is either left or down, both equally likely. Which of the followi... | D | math_Counting & Probability | mathematics | ||
math_188 | math_mc | Let $f(x) = (x+2)^2-5$. If the domain of $f$ is all real numbers, then $f$ does not have an inverse function, but if we restrict the domain of $f$ to an interval $[c,\infty)$, then $f$ may have an inverse function. What is the smallest value of $c$ we can use here, so that $f$ does have an inverse function? | A | math_Algebra | mathematics | ||
pythonio_429 | pythonio-mc | Program:
def last_Two_Digits(N):
if (N >= 10):
return
fac = 1
for i in range(1,N + 1):
fac = (fac * i) % 100
return (fac)
Input:
last_Two_Digits(7)
Output: | A | code | computer_science |
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