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_1028 | math_mc | An equilateral triangle is inscribed in the ellipse whose equation is $x^2+4y^2=4$. One vertex of the triangle is $(0,1)$, one altitude is contained in the y-axis, and the square of the length of each side is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
| C | math_Geometry | mathematics | ||
math_72 | math_mc | Simplify $\dfrac{5+12i}{2-3i}$. Your answer should be of the form $a+bi$, where $a$ and $b$ are both real numbers and written as improper fractions (if necessary). | A | math_Algebra | mathematics | ||
pythonio_356 | pythonio-mc | Program:
def find_Min_Sum(a,b,n):
a.sort()
b.sort()
sum = 0
for i in range(n):
sum = sum + abs(a[i] - b[i])
return sum
Input:
find_Min_Sum([4,1,8,7],[2,3,6,5],4)
Output: | A | code | computer_science | ||
allenai/sciq_3557 | allenai/sciq | What type of craniates have backbones?
A. vertebrates
B. invertebrates
C. larva
D. juveniles | A. vertebrates | 34.3 Vertebrates are craniates that have a backbone. | high_school_biology | biology | |
math_273 | math_mc | An infinite geometric series has common ratio $-1/5$ and sum $16.$ What is the first term of the series? | B | math_Algebra | mathematics | ||
NLP4Education_37 | NLP4Education | Consider the following lexicon $L$:
boy : Adj, N
boys : N
blue : Adj, N
drink : N, V
drinks : N, V
Nice : Adj, N
When using an order-1 HMM model (using $L$) to tag the word sequence: "Nice boys drink blue drinks" does the tag of drink depend on the tag of nice?
A. Yes, since previous tags always ... | B. No, the hypotheses of the HMM make the two tags independent from each other. | college_computer_science | computer_science | ||
math_680 | math_mc | Five standard six-sided dice are rolled. We are told there is no three-of-a-kind, but there is a pair of dice that show the same number. These two dice are set aside, and the other three dice are re-rolled. What is the probability that after re-rolling these three dice, at least three of the five dice show the same ... | C | math_Counting & Probability | mathematics | ||
aquarat_83013 | deepmind/aqua_rat | If d + xy = d and x is not equal to 0, which of the following must be true? | A. x=0 B. x+y=0 C. x<y D. y=0 E. x=d | D. y=0 | d + xy = d --> xy=0. Since x is not equal to 0, thus y = 0.
Answer: D. | abstract_algebra | mathematics |
mmlu_aux_train_20581 | mmlu_aux_train | LAST week, the College Board announced that it was revising the SAT (Scholastic Assessment Test) in an effort to make it more acceptable to test-takers, teachers, college admission officers and the public more generally. Test-takers who receive lower scores than they have hoped for are likely to be concerned about thei... | B. They may not get satisfactory scores and it influences their admission to college. | high_school_statistics | mathematics | ||
math_640 | math_mc | Joe will randomly select two letters from the word CAMP, four letters from the word HERBS, and three letters from the word GLOW. What is the probability that he will have all of the letters from the word PROBLEM? Express your answer as a common fraction. | B | math_Counting & Probability | mathematics | ||
mmlu_aux_train_95295 | mmlu_aux_train | Fish move best through water when their fins are?
A. Large [Collect]
B. Long
C. Small
D. Short | A. Large [Collect] | high_school_biology | biology | ||
allenai/sciq_8397 | allenai/sciq | Strong, stable bonds between carbon atoms produce complex molecules containing chains, branches, and rings; the chemistry of these compounds is called what?
A. animal chemistry
B. inorganic chemistry
C. organic chemistry
D. nuclear chemistry | C. organic chemistry | Summary 20.1 Hydrocarbons Strong, stable bonds between carbon atoms produce complex molecules containing chains, branches, and rings. The chemistry of these compounds is called organic chemistry. Hydrocarbons are organic compounds composed of only carbon and hydrogen. The alkanes are saturated hydrocarbons—that is, hyd... | high_school_chemistry | chemistry | |
math_225 | math_mc | Suppose the function $f$ has all real numbers in its domain and range and is invertible. Some values of $f$ are given by the following table: $$\begin{array}{c || c | c | c | c | c}
x & 1 & 2 & 3 & 4 & 5 \\
\hline
f(x) & 2 & 3 & 5 & 7 & 8
\end{array}$$What is the value of $f(f(3)) + f(f^{-1}(4)) + f^{-1}(f^{-1}(5))?$ I... | B | math_Algebra | mathematics | ||
pythonio_859 | pythonio-mc | Program:
def remove_tuple(test_list):
res = [sub for sub in test_list if not all(ele == None for ele in sub)]
return (str(res))
Input:
remove_tuple([(1, 2), (2, None), (3, None), (24, 3), (None, None )] )
Output: | D | code | computer_science | ||
pythonio_421 | pythonio-mc | Program:
def min_jumps(arr, n):
jumps = [0 for i in range(n)]
if (n == 0) or (arr[0] == 0):
return float('inf')
jumps[0] = 0
for i in range(1, n):
jumps[i] = float('inf')
for j in range(i):
if (i <= j + arr[j]) and (jumps[j] != float('inf')):
jumps[i] = min(jumps[i], jumps[j] + 1)
break
... | C | code | computer_science | ||
math_1294 | math_mc | Two of the roots of
\[ax^3 + (a + 2b) x^2 + (b - 3a) x + (8 - a) = 0\]are $-2$ and 3. Find the third root. | B | math_Intermediate Algebra | mathematics | ||
math_1902 | math_mc | Angle PQR is a right angle. The three quadrilaterals shown are squares. The sum of the areas of the three squares is 338 square centimeters. What is the number of square centimeters in the area of the largest square?
[asy]
draw((0,0)--(12,0)--(0,5)--cycle);
dot((0,0));
dot((12,0));
dot((0,5));
draw((0,0)--(0,5)--(-5,5... | D | math_Prealgebra | mathematics | ||
math_1586 | math_mc | When the greatest common divisor and least common multiple of two integers are multiplied, their product is 200. How many different values could be the greatest common divisor of the two integers? | C | math_Number Theory | mathematics | ||
mmlu_aux_train_94108 | mmlu_aux_train | Jake is testing how light affects plant growth. He grows two plants in identical pots with the same amount of water and fertilizer. Jake grows one of the plants in the sun, and the other in the shade. Which part of Jake's process indicates that there is a control for this investigation?
A. He is growing plants in iden... | C. He is growing one plant out of the sun. | high_school_biology | biology | ||
aquarat_56321 | deepmind/aqua_rat | In the faculty of Reverse-Engineering, 230 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. 649. E. 666. | D. 649. | Answer is D :649
Solution : Total number of students studying both are 423 + 230 - 134 = 519 (Subtracting the 134 since they were included in the both the other numbers already).
So 80% of total is 519, so 100% is approx. 649. | college_mathematics | mathematics |
math_467 | math_mc | How many triangles with positive area are there whose vertices are points in the $xy$-plane whose coordinates are integers $(x,y)$ satisfying $1\le x\le 4$ and $1\le y\le 4$?
$\text{(A) } 496\quad \text{(B) } 500\quad \text{(C) } 512\quad \text{(D) } 516\quad \text{(E) } 560$
| A | math_Counting & Probability | mathematics | ||
math_808 | math_mc | $ABCDE$ is a regular pentagon. $AP$, $AQ$ and $AR$ are the perpendiculars dropped from $A$ onto $CD$, $CB$ extended and $DE$ extended, respectively. Let $O$ be the center of the pentagon. If $OP = 1$, then find $AO + AQ + AR$.
[asy]
unitsize(2 cm);
pair A, B, C, D, E, O, P, Q, R;
A = dir(90);
B = dir(90 - 360/5... | A | math_Geometry | mathematics | ||
math_1080 | math_mc | A machine-shop cutting tool has the shape of a notched circle, as shown. The radius of the circle is $\sqrt{50}$ cm, the length of $AB$ is $6$ cm and that of $BC$ is $2$ cm. The angle $ABC$ is a right angle. Find the square of the distance (in centimeters) from $B$ to the center of the circle.
[asy] size(150); default... | D | math_Geometry | mathematics | ||
math_785 | math_mc | In triangle $ABC$, $AB=20$ and $AC=11$. The angle bisector of $\angle A$ intersects $BC$ at point $D$, and point $M$ is the midpoint of $AD$. Let $P$ be the point of the intersection of $AC$ and $BM$. The ratio of $CP$ to $PA$ can be expressed in the form $\dfrac{m}{n}$, where $m$ and $n$ are relatively prime positive ... | A | math_Geometry | mathematics | ||
allenai/sciq_3141 | allenai/sciq | Red algae and green algae are the closest relatives of what?
A. land plants
B. water plants
C. transfer plants
D. arctic plants | A. land plants | 28.5 Red algae and green algae are the closest relatives of land plants. | high_school_biology | biology | |
mmlu_aux_train_67855 | mmlu_aux_train | Teachers say the digital age has had a good and a not-so-good influence on the American teenagers. More than 2,000 high school teachers took an online survey. 75 percent of the teachers said the Internet and digital search tools have had a "mostly good" use for their students' research habits and skills, But 87 percent... | D. 87% | high_school_statistics | mathematics | ||
mmlu_aux_train_95938 | mmlu_aux_train | Energy may be transferred to an object without being plugged in, such as with
A. an electric grill
B. an electric stove
C. an electronic torch
D. a microwave oven | C. an electronic torch | conceptual_physics | physics | ||
allenai/sciq_8583 | allenai/sciq | The variation in a sample can be represented by what quantity, which means the total spread of values?
A. range
B. mode
C. variety
D. median | A. range | The variation in a sample can be represented by the range, or the total spread of values. | high_school_statistics | mathematics | |
math_52 | math_mc | What is the length of the segment of the number line whose endpoints satisfy $|x-\sqrt[5]{16}|=3$? | D | math_Algebra | mathematics | ||
NLP4Education_336 | NLP4Education | Select what is true about the Baum-Welch algorithm. A penalty will be applied for any incorrect answers.
A. The algorithm always converges towards a global maximum of the parameters estimated.
B. You cannot randomly initialize the parameters of the algorithm.
C. It uses expectation maximization to estimate parameters o... | C. It uses expectation maximization to estimate parameters of the Hidden Markov Model. | machine_learning | computer_science | ||
pythonio_817 | pythonio-mc | Program:
from itertools import groupby
def extract_elements(numbers, n):
result = [i for i, j in groupby(numbers) if len(list(j)) == n]
return result
Input:
extract_elements([1, 1, 3, 4, 4, 5, 6, 7],2)
Output: | B | code | computer_science | ||
math_1907 | math_mc | In rectangle $ABCD$, $AB = 6$ cm, $BC = 8$ cm, and $DE = DF$. The area of triangle $DEF$ is one-fourth the area of rectangle $ABCD$. What is the length in centimeters of segment $EF$? Express your answer in simplest radical form.
[asy]
draw((0,0)--(0,24)--(32,24)--(32,0)--cycle);
draw((13,24)--(32,5));
label("$A$",(0,... | C | math_Prealgebra | mathematics | ||
pythonio_68 | pythonio-mc | Program:
def remove_datatype(test_tuple, data_type):
res = []
for ele in test_tuple:
if not isinstance(ele, data_type):
res.append(ele)
return (res)
Input:
remove_datatype((7, 1.1, 2, 2.2), float)
Output: | A | code | computer_science | ||
mmlu_aux_train_73390 | mmlu_aux_train | I have a robot friend, Robbi. It looks like my toy car because it moves on four wheels. It is always helpful. "Come on, Robbi! Bring me milk." "Yes, Sandy," says Robbi. It goes to the kitchen and comes back with a glass of milk. It can find milk among orange juice, water, apple juice. Do you think Robbi is a waiter onl... | A. Robbi is the name of a robot. | high_school_computer_science | computer_science | ||
aquarat_19010 | deepmind/aqua_rat | If f(x) = 12 - x^2/2 and f(2k) = 4k, what is one possible value for k? | A. 2 B. 3 C. 4 D. 6 E. 8 | C. 4 | First of all, see thisGMAT blog postand check the related lesson linked below for some background on function notation.
We can plug anything in for x and get a result. You can find f(1), for example, by plugging in 1 where x is, and you would get 12 - 1/2 = 11.5. Or we could find f(2), which would be 12 - 4/2 = 10.
So ... | college_mathematics | mathematics |
math_960 | math_mc | [asy] pair A = (0,0), B = (7,4.2), C = (10, 0), D = (3, -5), E = (3, 0), F = (7,0); draw(A--B--C--D--cycle,dot); draw(A--E--F--C,dot); draw(D--E--F--B,dot); markscalefactor = 0.1; draw(rightanglemark(B, A, D)); draw(rightanglemark(D, E, C)); draw(rightanglemark(B, F, A)); draw(rightanglemark(D, C, B)); MP("A",(0,0),W);... | B | math_Geometry | mathematics | ||
math_1885 | math_mc | Find $PQ$ in the triangle below.
[asy]
unitsize(1inch);
pair P,Q,R;
P = (0,0);
Q= (sqrt(3),0);
R = (0,1);
draw (P--Q--R--P,linewidth(0.9));
draw(rightanglemark(Q,P,R,3));
label("$P$",P,S);
label("$Q$",Q,S);
label("$R$",R,N);
label("$9\sqrt{3}$",R/2,W);
label("$30^\circ$",(1.25,0),N);
[/asy] | D | math_Prealgebra | mathematics | ||
math_906 | math_mc | The nine points of this grid are equally spaced horizontally and vertically. The distance between two neighboring points is 1 unit. What is the area, in square units, of the region where the two triangles overlap?
[asy]
size(80);
dot((0,0)); dot((0,1));dot((0,2));dot((1,0));dot((1,1));dot((1,2));dot((2,0));dot((2,1)... | B | math_Geometry | mathematics | ||
math_1936 | math_mc | Simplify: $$\dfrac{\sqrt{338}}{\sqrt{288}}+\dfrac{\sqrt{150}}{\sqrt{96}}.$$Express your answer as a common fraction. | D | math_Prealgebra | mathematics | ||
NLP4Education_557 | NLP4Education | Tick the \textbf{non-commutative} operation.
A. $+ $ (addition) over $\mathbb{Z}$
B. $\times$ (multiplication) over $\mathbb{Z}$
C. $-$ (subtraction) over $\mathbb{Z}$
D. $\oplus$ (exclusive-or) | C. $-$ (subtraction) over $\mathbb{Z}$ | abstract_algebra | mathematics | ||
mmlu_aux_train_14267 | mmlu_aux_train | La Gomera is the only place in the world which has a whistle language. We do not know how and why it began because we do not know the complete history of the island. But we can certainly imagine the reasons for the beginning of the whistle language. There are many deep valleys on the island. A person on one side of a ... | D. the whistle language will help pass the message to the doctor | high_school_biology | biology | ||
math_997 | math_mc | Joe has exactly enough paint to paint the surface of a cube whose side length is 2. It turns out that this is also exactly enough paint to paint the surface of a sphere. If the volume of this sphere is $\frac{K \sqrt{6}}{\sqrt{\pi}}$, then what is $K$? | D | math_Geometry | mathematics | ||
mmlu_aux_train_62689 | mmlu_aux_train | Scientists have claimed a milestone in the drive for new energy--development of the first practical artificial leaf, an advanced solar cell that imitates the process,called photosynthesis ,that green plants use to make sunlight and water into energy. "A practical artificial leaf has been a dream of scientists for decad... | D. providing electricity for the poor family at a low cost | college_chemistry | chemistry | ||
allenai/sciq_11136 | allenai/sciq | The kinetic energy of molecules is generally proportionate to what other property that they have?
A. mass
B. variation
C. precipitation
D. temperature | D. temperature | The average kinetic energy of the molecules is proportional to the temperature of the sample. | college_physics | physics | |
pythonio_743 | pythonio-mc | Program:
import heapq as hq
def raw_heap(rawheap):
hq.heapify(rawheap)
return rawheap
Input:
raw_heap([25, 44, 68, 21, 39, 23, 89])
Output: | B | code | computer_science | ||
pythonio_33 | 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 )... | C | code | computer_science | ||
mmlu_aux_train_96720 | mmlu_aux_train | There are many changes that can occur to the earth, quickly or overtime. Which would occur over millions of years?
A. earthquake
B. canyon
C. tornado
D. Tsunami | B. canyon | earth_science | earth_science | ||
mmlu_aux_train_19672 | mmlu_aux_train | "I don't want to buy a traditional yearbook. I can keep and share memories of my high school on the Internet."You may often hear this from many American high school students now. Instead of buying a book, more and more students choose to sign up at My Yearbook.com. My Yearbook.com was created by two teenagers, Catherin... | A. Going online for yearbooks | high_school_computer_science | computer_science | ||
aquarat_54424 | deepmind/aqua_rat | If air is called green , green is called blue, blue is called tangerine, sky is called yellow, yellow is called water and water is called pink, then what is the color of clear sky ? | A. Blue B. Sky C. Water D. Tangerine E. Black | D. Tangerine | Explanation:
The colour of clear sky is 'blue' and as given, 'blue' is called 'tangerine'.
So, the colour of clear sky is 'tangerine'.
Answer: D | formal_logic | mathematics |
math_2036 | math_mc | In order to compute the area of a particular circle, Juan first measures the length of its diameter. The actual diameter is 20 cm, but Juan's measurement has an error of up to $20\%$. What is the largest possible percent error, in percent, in Juan's computed area of the circle? | B | math_Prealgebra | mathematics | ||
math_619 | math_mc | A game show offers a contestant three prizes A, B and C, each of which is worth a whole number of dollars from $$ 1$ to $$ 9999$ inclusive. The contestant wins the prizes by correctly guessing the price of each prize in the order A, B, C. As a hint, the digits of the three prices are given. On a particular day, the dig... | B | math_Counting & Probability | mathematics | ||
NLP4Education_677 | NLP4Education | Tick the \emph{correct} assertion. Assume that $C$ is an arbitrary random permutation.
A. $\mathsf{BestAdv}_n(C,C^\ast)=\mathsf{Dec}^n_{\left|\left|\left|\cdot\right|\right|\right|_\infty}(C)$
B. $\mathsf{BestAdv}_n(C,C^\ast)=\mathsf{Dec}^{n/2}_{\left|\left|\left|\cdot\right|\right|\right|_\infty}(C)$
C. $E(\mathsf{DP}... | D. $\mathsf{BestAdv}_n(C,C^\ast)=\frac{1}{2}\mathsf{Dec}^n_{\left|\left|\cdot\right|\right|_a}(C)$ | computer_security | computer_science | ||
pythonio_239 | 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('Hardest choices required strongest will', 'will')
Output: | C | code | computer_science | ||
math_1613 | math_mc | Let $d_1 = a^2 + 2^a + a \cdot 2^{(a+1)/2}$ and $d_2 = a^2 + 2^a - a \cdot 2^{(a+1)/2}$. If $1 \le a \le 251$, how many integral values of $a$ are there such that $d_1 \cdot d_2$ is a multiple of $5$?
| B | math_Number Theory | mathematics | ||
aquarat_19297 | deepmind/aqua_rat | 9.4 , 9.9 , 9.9 , 9.9 , 10.0 , 10.2 , 10.2 , 10.5
The mean and the standard deviation of the 8 numbers shown above is 10 and 0.3 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean? | A. 90% B. 85% C. 80% D. 75% E. 70% | D. 75% | D. 75% | high_school_statistics | mathematics |
mmlu_aux_train_35353 | mmlu_aux_train | Many of the world's pollution problems have been caused by the crowding of large groups of people into the cities. Supply for the needs of the people leads to further pollution by industry. If the rapid increase of world population in countries continues at the present rate, there may be much greater harm to human bein... | B. population pollution | high_school_biology | biology | ||
math_210 | math_mc | For how many positive integers $n$ does $1+2+\cdots+n$ evenly divide $6n$? | A | math_Algebra | mathematics | ||
mmlu_aux_train_2123 | mmlu_aux_train | How many atoms are in one formula unit of magnesium hydroxide, Mg(OH)_{2}?
A. 6
B. 5
C. 4
D. 3 | B. 5 | high_school_chemistry | chemistry | ||
math_189 | math_mc | Given that the graphs of $y=h(x)$ and $y=j(x)$ intersect at $(2,2),$ $(4,6),$ $(6,12),$ and $(8,12),$ there is one point where the graphs of $y=h(2x)$ and $y=2j(x)$ must intersect. What is the sum of the coordinates of that point? | A | math_Algebra | mathematics | ||
math_80 | math_mc | Jack walked up a hill at a speed of $(x^2-11x-22)$ miles per hour. Meanwhile, Jill walked a total distance of $(x^2-3x-54)$ miles in $(x+6)$ hours. If Jack and Jill walked at the same speed, what is that speed, in miles per hour? | C | math_Algebra | mathematics | ||
mmlu_aux_train_4843 | mmlu_aux_train | A student heated a pan of soup on a stove. While stirring the soup with a metal spoon, the student noticed the spoon became very warm. What is the most likely reason the spoon became warm?
A. The stirring action heated the spoon.
B. Warm air in the room heated the spoon.
C. Heat from the soup was transferred to the sp... | C. Heat from the soup was transferred to the spoon. | conceptual_physics | physics | ||
allenai/sciq_1777 | allenai/sciq | What occurs when force is applied to a moving object?
A. inertia
B. acceleration
C. transmission
D. stimulation | B. acceleration | Acceleration occurs when a force is applied to a moving object. | conceptual_physics | physics | |
allenai/sciq_6910 | allenai/sciq | Which theory describes the distribution of electrons in molecules in much the same way that the distribution of electrons in atoms is described using atomic orbitals?
A. atomic orbital theory
B. atomic distribution theory
C. molecular distribution theory
D. molecular orbital theory | D. molecular orbital theory | Molecular orbital theory describes the distribution of electrons in molecules in much the same way that the distribution of electrons in atoms is described using atomic orbitals. Using quantum mechanics, the behavior of an electron in a molecule is still described by a wave function, Ψ, analogous to the behavior in an ... | college_chemistry | chemistry | |
pythonio_772 | pythonio-mc | Program:
def length_Of_Last_Word(a):
l = 0
x = a.strip()
for i in range(len(x)):
if x[i] == " ":
l = 0
else:
l += 1
return l
Input:
length_Of_Last_Word("python language")
Output: | A | code | computer_science | ||
aquarat_12495 | deepmind/aqua_rat | If |z|/w = 3,which of the following must be true? | A. z = -3w B. z = 3w C. z^2 = 9w^2 D. z^2 = 9w^3 E. z^3 = 27w^3 | C. z^2 = 9w^2 | |z|/w = 3.
|z| = 3w.
Then z = 3w or -3w and so z^2 = 9w^2.
The answer is C. | college_mathematics | mathematics |
allenai/sciq_8490 | allenai/sciq | Under certain conditions, electric current causes what type of field?
A. seismic
B. magnetic
C. light
D. kinetic | B. magnetic | Electricity and magnetism are inextricably linked. Under certain conditions, electric current causes a magnetic field. Under other conditions, a magnetic field can cause an electric current. A moving charged particle creates a magnetic field around it. Additionally, when a moving charged particle moves through a differ... | electrical_engineering | engineering | |
allenai/sciq_447 | allenai/sciq | When food is scarce, starving cells secrete a molecule that stimulates neighboring cells to do what?
A. compete
B. aggregate
C. die off
D. hoard energy | B. aggregate | high_school_biology | biology | ||
pythonio_334 | pythonio-mc | Program:
def get_product(val) :
res = 1
for ele in val:
res *= ele
return res
def find_k_product(test_list, K):
res = get_product([sub[K] for sub in test_list])
return (res)
Input:
find_k_product([(7, 8, 9), (3, 5, 7), (10, 11, 21)], 0)
Output: | A | code | computer_science | ||
aquarat_33142 | deepmind/aqua_rat | How many ways are there for 3 males and 4 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall? | A. 6 B. 36 C. 72 D. 100 E. 720 | B. 36 | So Mary has her own chair, fixed position. Other 3 females around the table can sit in 3! ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 3 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males... | college_mathematics | mathematics |
math_1414 | math_mc | Write $x^{10} + x^5 + 1$ as the product of two polynomials with integer coefficients. | C | math_Intermediate Algebra | mathematics | ||
math_2131 | math_mc | Let $\mathbf{a},$ $\mathbf{b},$ and $\mathbf{c}$ be nonzero vectors, no two of which are parallel, such that
\[(\mathbf{a} \times \mathbf{b}) \times \mathbf{c} = \frac{1}{3} \|\mathbf{b}\| \|\mathbf{c}\| \mathbf{a}.\]Let $\theta$ be the angle between $\mathbf{b}$ and $\mathbf{c}.$ Find $\sin \theta.$ | B | math_Precalculus | mathematics | ||
aquarat_12254 | deepmind/aqua_rat | If air is called green , green is called blue, blue is called sky, sky is called yellow, yellow is called water and water is called pink, then what is the color of clear sky ? | A. Blue B. Sky C. Water D. Yellow E. Black | B. Sky | Explanation:
The colour of clear sky is 'blue' and as given, 'blue' is called 'sky'.
So, the colour of clear sky is 'sky'.
Answer: B | formal_logic | mathematics |
math_986 | math_mc | Rectangle $ABCD$ is inscribed in triangle $EFG$ such that side $AD$ of the rectangle is on side $EG$ of the triangle, as shown. The triangle's altitude from $F$ to side $EG$ is 7 inches, and $EG = 10 \text{ inches}$. The length of segment $AB$ is equal to half the length of segment $AD$. What is the area of rectangle $... | C | math_Geometry | mathematics | ||
NLP4Education_615 | NLP4Education | Tick the \textbf{true} assertion. A first preimage attack on a hash function H is \ldots
A. … given $x$ find $y$ such that $H(x)=y$
B. … given $x$ find $x'\neq x$ such that $H(x)=H(x')$
C. … given $y$ find $x$ such that $H(x)=y$
D. … find $x$ and $x'$ such that $x'\neq x$ and $H(x)=H(x')$ | C. … given $y$ find $x$ such that $H(x)=y$ | computer_security | computer_science | ||
allenai/sciq_10356 | allenai/sciq | A measure of how close a series of measurements are to one another is what?
A. calculation
B. reflection
C. density
D. precision | D. precision | precision: A measure of how close a series of measurements are to one another. Precise measurements are highly reproducible, even if the measurements are not near the correct value. | high_school_physics | physics | |
allenai/sciq_3808 | allenai/sciq | Any organism that causes disease is called what?
A. a parasite
B. a microbe
C. a virus
D. a pathogen | D. a pathogen | You have ten times as many bacterial cells as human cells in your body. Luckily for you, most of these bacteria are harmless. However, some of them can cause disease. Any organism that causes disease is called a pathogen . Diseases caused by bacterial pathogens include food poisoning, strep throat, and Lyme disease. | high_school_biology | biology | |
pythonio_243 | pythonio-mc | Program:
def floor_Min(A,B,N):
x = max(B - 1,N)
return (A*x) // B
Input:
floor_Min(10,20,30)
Output: | B | code | computer_science | ||
allenai/sciq_3069 | allenai/sciq | What are the two types of earth crust?
A. reflective and continental
B. micro and continental
C. amorphous and continental
D. oceanic and continental | D. oceanic and continental | The crust is less than 1% of Earth by mass. The two types are oceanic crust and continental crust. | college_earth_science | earth_science | |
NLP4Education_63 | NLP4Education | Consider the following joint distribution on $X$ and $Y$, where both random variables take on the values $\{0,1\}$: $p(X=0, Y=0)=0.1$, $p(X=0, Y=1)=0.2$, $p(X=1, Y=0)=0.3$, $p(X=1, Y=1)=0.4$. You receive $X=1$. What is the largest probability of being correct you can achieve when predicting $Y$ in this case?
A. $\frac{... | C. $\frac{4}{7}$ | high_school_statistics | mathematics | ||
aquarat_31923 | deepmind/aqua_rat | Find the arithmetic mean W of all roots of the following equation- see an attachment. | A. 2 B. 1 C. 0.5 D. -1/3 E. 0.3 | C. 0.5 | arithmetic mean W your answer C and E are same, can you correct one of them please. thanks.C | college_mathematics | mathematics |
math_1266 | math_mc | Let $A = (1,0)$ and $B = (5,4).$ Let $P$ be a point on the parabola $y^2 = 4x.$ Find the smallest possible value of $AP + BP.$ | A | math_Intermediate Algebra | mathematics | ||
allenai/sciq_5486 | allenai/sciq | What are bacteria that stain purple are called?
A. gram-positive bacteria
B. complex bacteria
C. gram-negative bacteria
D. gram-neutral bacteria | A. gram-positive bacteria | Bacteria that stain purple are called gram-positive bacteria. They have a thick cell wall without an outer membrane. | college_biology | biology | |
pythonio_305 | pythonio-mc | Program:
def move_zero(num_list):
a = [0 for i in range(num_list.count(0))]
x = [ i for i in num_list if i != 0]
x.extend(a)
return (x)
Input:
move_zero([0,1,0,1,1])
Output: | C | code | computer_science | ||
mmlu_aux_train_8695 | mmlu_aux_train | Windows 8, apart from Windows 95, is the biggest surprise and the only version of Microsoft' s operating system that has been changed from the core when compared to its former one. However, a recent study has shown that under 20% of business owners would be willing to upgrade to the new version of Windows. The reason f... | A. fast rate | computer_security | computer_science | ||
math_1952 | math_mc | Express as a fraction in lowest terms: $0.\overline{1} + 0.\overline{01}$ | B | math_Prealgebra | mathematics | ||
mmlu_aux_train_93035 | mmlu_aux_train | Which process of the water cycle transports water from plants to clouds?
A. precipitation
B. transpiration
C. condensation
D. sublimation | B. transpiration | high_school_biology | biology | ||
mmlu_aux_train_58596 | mmlu_aux_train | The card using a built-in voice-recognition chip requires users to give a spoken password that it recognizes. The idea is to prevent thieves from using a stolen card to buy goods online. A model built by engineers in California packs a microphone, a loudspeaker, a battery and a voice-recognition chip into a standard-s... | D. It makes fraud more difficult. | computer_security | computer_science | ||
allenai/sciq_5876 | allenai/sciq | Group 16 is called the oxygen group. what is the only metalloid in this group?
A. gallium
B. beryllium
C. tellurium
D. cadmium | C. tellurium | Group 16 is called the oxygen group. Tellurium is the only metalloid in this group, which also contains three nonmetals and one metal. | high_school_chemistry | chemistry | |
aquarat_56480 | deepmind/aqua_rat | If x = 1 + √2, then what is the value of x4 - 4x3 + 4x2 + 4? | A. -1 B. 0 C. 5 D. 2 E. 3 | C. 5 | Answer
x = 1 + √2
∴ x4 - 4x3 + 4x2 + 5 = x2(x2 - 4x + 4) + 4
= x2(x - 2)2 + 4
= (1 + √2)2(1 + √2 - 2)2 + 4
=(√2 + 1)2 (√2 - 1)2 + 4
=[(√2)2 - (1)2]2 + 4
=(2 - 1)2 =1 + 4=5
Correct Option: C | college_mathematics | mathematics |
math_202 | math_mc | Solve for $c$: $$\sqrt{4+\sqrt{8+4c}}+ \sqrt{2+\sqrt{2+c}} = 2+2\sqrt{2}$$ | C | math_Algebra | mathematics | ||
allenai/sciq_8533 | allenai/sciq | What are the pores in plants that keep certain gases and liquids in and out called?
A. stigmata
B. chloroplasts
C. lesions
D. stomata | D. stomata | Additional Land Plant Adaptations As plants adapted to dry land and became independent of the constant presence of water in damp habitats, new organs and structures made their appearance. Early land plants did not grow above a few inches off the ground, and on these low mats, they competed for light. By evolving a shoo... | high_school_biology | biology | |
aquarat_57869 | deepmind/aqua_rat | The moon revolves around the earth at a speed of approximately 1.03 kilometers per second. This approximate speed is how many kilometers per hour? | A. 60 B. 61.2 C. 62.5 D. 3,708 E. 3,672 | D. 3,708 | moon revolves around the earth at a speed of 1.02kilometers per second.
one hour equal to 60 minutes.
one minute equals to 60 seconds. so one hour equals to 3600seconds.
so one hour, speed= 1.03*3600=3708kilometers per hour.
Option D is correct | high_school_physics | physics |
aquarat_20300 | deepmind/aqua_rat | If 20! × 20!/20^n is an integer, what is the largest possible value of n? | A. 20 B. 16 C. 8 D. 4 E. 1 | C. 8 | 20! × 20!/20^n is an integer.
Or 20! × 20!/(2^2n*5^n)
This means we need to find the power of 5 in the numerator. We can safely say that the number of powers of 5 will be lower than the number of powers of 4 in the numerator.
Largest power of 5 in 20! = [20/5] + [20/25] = 4
Since there are 2 20!'s, power of 4 in the nu... | college_mathematics | mathematics |
allenai/sciq_5435 | allenai/sciq | What is the second line of defense?
A. inflammatory response
B. rejection of foreign bodies
C. fight or flight
D. immune response | A. inflammatory response | The second line of defense includes the inflammatory response and phagocytosis by nonspecific leukocytes. | high_school_biology | biology | |
mmlu_aux_train_99511 | mmlu_aux_train | You can etch the surface of a windshield with
A. a sponge
B. feathers
C. soft cloth
D. jasper | D. jasper | high_school_chemistry | chemistry | ||
aquarat_45675 | deepmind/aqua_rat | If a certain sample of data has a mean of 21.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean? | A. 12.0 B. 13.5 C. 17.0 D. 23.5 E. 26.5 | B. 13.5 | Value ismore than 2.5SDfrom the mean means that the distance between the mean and the value must be more than 2.5*SD=7.5. So the value must be either less than 21-7.5=13.5or more than 21+7.5=28.5.
Answer: B. | high_school_statistics | mathematics |
aquarat_3844 | deepmind/aqua_rat | The probability of pulling a black ball out of a glass jar is 1/X. The probability of pulling a black ball out of a glass jar and breaking the jar is 1/Y. What is the probability of breaking the jar? | A. 1/(XY). B. X/Y. C. Y/X. D. 1/(X+Y). E. 1/(X-Y). | B. X/Y. | Let the probability of breaking the jar= n
n*1/X = 1/Y
n= X/Y
B is the answer | college_mathematics | mathematics |
mmlu_aux_train_6282 | mmlu_aux_train | Everyone may all have the experience of feeling anxious and stressed when having a rough day or having some troubles. Different people may choose different ways to deal with it, and for most people a break for a 10-minute walk may be quite useful.www.zxxk.com Anyway, here is another way around: to get a piece of chewin... | B. gum chewers tend to be less stressed | college_biology | biology | ||
mmlu_aux_train_11635 | mmlu_aux_train | Some people in Manchester, Britain, will soon be paying for goods and services with so-called "smart" credit cards. These cards are more secure than the traditional magnetic-strip version and can be used to travel on buses, check bank accounts and do shopping. The Manchester project is one of the biggest smart card sch... | C. it has a silicon chip in it | computer_security | computer_science | ||
math_420 | math_mc | Juan, Carlos and Manu take turns flipping a coin in their respective order. The first one to flip heads wins. What is the probability that Manu will win? Express your answer as a common fraction. | C | math_Algebra | mathematics |
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