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_1321 | math_mc | Let $z$ be a complex number such that $|z - 5 - i| = 5.$ Find the minimum value of
\[|z - 1 + 2i|^2 + |z - 9 - 4i|^2.\] | C | math_Intermediate Algebra | mathematics | ||
math_1349 | math_mc | Let $x$ and $y$ be real numbers such that
\[xy - \frac{x}{y^2} - \frac{y}{x^2} = 3.\]Find the sum of all possible values of $(x - 1)(y - 1).$ | C | math_Intermediate Algebra | mathematics | ||
pythonio_10 | pythonio-mc | Program:
def count_ways(n):
A = [0] * (n + 1)
B = [0] * (n + 1)
A[0] = 1
A[1] = 0
B[0] = 0
B[1] = 1
for i in range(2, n+1):
A[i] = A[i - 2] + 2 * B[i - 1]
B[i] = A[i - 1] + B[i - 2]
return A[n]
Input:
count_ways(8)
Output: | D | code | computer_science | ||
aquarat_2524 | deepmind/aqua_rat | Set A = {1, 2, 3, 4, 5, 6, q}
Which of the following possible values for q would cause Set A to have the smallest standard deviation? | A. 1 B. 2.5 C. 3 D. 3.5 E. 7 | D. 3.5 | I agree. The mean of the set q =1,2,3,4,5,6 is 3.5 . Now if we add one extra number to the set, in order for the standard deviation to be minimum, that number must be as close as possible to the original set (1,2,3,4,5,6). Therefore we have to choose the number closest to 3,5 from the options we have, leaving D as the ... | college_mathematics | mathematics |
NLP4Education_472 | NLP4Education | Birthday attacks ...
A. are equivalent to exhaustive search.
B. can be used to find collisions in hash functions.
C. are used to break Google Calendars.
D. imply that a majority of people is born in Spring. | B. can be used to find collisions in hash functions. | computer_security | computer_science | ||
allenai/sciq_6617 | allenai/sciq | Electrons are located at fixed distances from the nucleus, what are they called?
A. Energy layers
B. Positive levels
C. energy concentrations
D. energy levels | D. energy levels | Electrons are located at fixed distances from the nucleus, called energy levels. You can see the first three energy levels in the Figure below . The diagram also shows the maximum possible number of electrons at each energy level. | high_school_physics | physics | |
mmlu_aux_train_62776 | mmlu_aux_train | When newspapers and radio describe the damage caused by a hurricane named Hazel,girls named Hazel are probably teased by their friends.To keep out of trouble,the Weather Bureau says, "Any _ between hurricane names and the names of particular girls is purely accidental. " Some women became angry because hurricanes ... | C. others often make fun of them. | high_school_computer_science | computer_science | ||
allenai/sciq_5321 | allenai/sciq | Insulin and glucagon help keep blood glucose levels in the normal range because of what type of effects?
A. sympathetic
B. opportunistic
C. ABNORMALISTIC
D. antagonistic | D. antagonistic | college_biology | biology | ||
NLP4Education_404 | NLP4Education | Which one of these is a closed set?
A. $\mathbb{Z}$ with addition
B. $\mathbb{Z}^\star$ with addition
C. $\mathbb{Z}^\star$ with subtraction
D. $\mathbb{Z} - \{0\}$ with division | A. $\mathbb{Z}$ with addition | abstract_algebra | mathematics | ||
mmlu_aux_train_80454 | mmlu_aux_train | Mary is from the U.S.A. She has two brothers. Now her family are in China. Her father, Mr. Peterson teaches English in Xihu Middle School. And her mother works in the same school. She teaches English, too. Mary likes red clothes very much. Her mother likes red clothes a lot, too. Mary is a nice girl student. She is in ... | D. Mrs. Peterson, Mr. Peterson and Mary. | high_school_computer_science | computer_science | ||
pythonio_803 | pythonio-mc | Program:
def reverse_list_lists(lists):
for l in lists:
l.sort(reverse = True)
return lists
Input:
reverse_list_lists([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]])
Output: | C | code | computer_science | ||
mmlu_aux_train_93660 | mmlu_aux_train | A scientist is searching for areas where new solar systems might form. What feature is the scientist looking for?
A. a star similar to our Sun
B. a cloud of dust and gas
C. an oxygen-rich atmosphere
D. a gravitational acceleration of 9.8 m/sec2 | B. a cloud of dust and gas | astronomy | physics | ||
allenai/sciq_4574 | allenai/sciq | Solid bedrock vibrates less and therefore does less of what to bedrock?
A. damage
B. butress
C. dampen
D. block | A. damage | Ground type. Solid bedrock vibrates less than soft sediments, so there is less damage on bedrock. Sometimes sediments become saturated with water. They then undergo liquefaction and become like quicksand ( Figure below ). Soil on a hillside may become a landslide. | conceptual_physics | physics | |
mmlu_aux_train_19404 | mmlu_aux_train | Our planet is home to about seven billion people. Since the 1990s, population experts have predicted the number would grow to nine billion before it begins to slow down and possibly decrease. But a new report predicts the world's population is likely to increase to almost 11 billion by 2100. Based on the most modern st... | B. Africa. | high_school_statistics | mathematics | ||
mmlu_aux_train_97317 | mmlu_aux_train | Which of the following is an example of electrical insulation?
A. Ethernet cables
B. stove burners
C. movie cameras
D. air conditioning | A. Ethernet cables | electrical_engineering | engineering | ||
mmlu_aux_train_36733 | mmlu_aux_train | Don't you think your schoolbag is too heavy to bear? The e-schoolbag will free you from the weight. It is said that e-schoolbags are going to be brought into use in Chinese middle schools soon. An experiment with several hundred e-schoolbags will begin in seven cities: Beijing, Shanghai, Dalian, Shenzhen, Chongqing, Ta... | D. It can phone somebody. | high_school_computer_science | computer_science | ||
math_100 | math_mc | Two arithmetic sequences $A$ and $B$ both begin with 30 and have common differences of absolute value 10, with sequence $A$ increasing and sequence $B$ decreasing. What is the absolute value of the difference between the 51st term of sequence $A$ and the 51st term of sequence $B$? | B | math_Algebra | mathematics | ||
allenai/sciq_3100 | allenai/sciq | What are the two basic parts that all flowering plants have in common?
A. stalk and petiole
B. blade and petiole
C. leaf and petiole
D. metal and petiole | B. blade and petiole | Flowering vascular plants also have diverse leaves. However, the leaves of all flowering plants have two basic parts in common: the blade and petiole. The blade of the leaf is the relatively wide, flat part of the leaf that gathers sunlight and undergoes photosynthesis. The petiole is the part that attaches the leaf to... | high_school_biology | biology | |
aquarat_97013 | deepmind/aqua_rat | If |q|=−q, which of the following must be true? | A. q≥0 B. q≤0 C. q2>x D. x3<0 E. 2x<x | B. q≤0 | |q| =-q means absolute value of q is equal to negative of q. Since absolute value cannot be negative hence negative of q should result in a non negative number. It means q is a non positive number i.e. q<0. Answer is B | college_mathematics | mathematics |
allenai/sciq_8975 | allenai/sciq | What is the main function of the cardiovascular system?
A. transporting substances around the body
B. excretion of food waste
C. coordinate bones and muscles
D. respiration of air | A. transporting substances around the body | The main function of the cardiovascular system is transporting substances around the body. Figure above shows some of the substances that are transported in the blood. They include hormones, oxygen, nutrients from digested food, and cellular wastes. Transport of all these materials is necessary to maintain homeostasis ... | high_school_biology | biology | |
aquarat_79243 | deepmind/aqua_rat | A function f(x) is said to reflect onitself if, y = f(x) and x = f(y). Which of the following function reflects on itself? | A. f(x) = (4x + 3) / (3x - 9) B. f(x) = (4x + 3) / (3x - 2) C. f(x) = (4x + 3) / (3x - 9) D. f(x) = (4x + 3) / (3x - 1) E. f(x) = (4x + 3) / (3x - 4) | E. f(x) = (4x + 3) / (3x - 4) | (a) f(x) = x = f(y)
y = x = f(y) Hence (a) is true.
(b) f(x) = 2x+1x−22x+1x−2 = y
xy - 2y = 2x + 1
xy - 2x = 1 + 2y
x(y - 2) = 1 + 2y
x = 1+2yy−21+2yy−2 Hence (b) is also true.
Similarly if we check for options (c) & (d), they will also hold true, hence t he answer is option (e).
Answer:E | college_mathematics | mathematics |
mmlu_aux_train_51971 | mmlu_aux_train | As any parent with an iPhone or an iPod Touch knows, mobile apps can be an engaging and entertaining experience for kids. Now, a new study of PBS Kids suggests that the experience can be an educational one as well. The study, which was administered by PBS under a grant from the Department of Education, first tested t... | C. Smart phones make kids learn more. | high_school_statistics | mathematics | ||
allenai/sciq_11039 | allenai/sciq | What are the three most common protective devices?
A. fuses, circuit breaks & surge protectors
B. fuses , fabrication breaks & surge protectors
C. tranistors, resistors & diodes
D. fuses , circuit breaks & surge claws | A. fuses, circuit breaks & surge protectors | There are multiple ways to prevent these situations from occurring. The three most common protective devices are fuses, circuit breakers, and surge protectors. | electrical_engineering | engineering | |
aquarat_36635 | deepmind/aqua_rat | For which of the following does p(a)−p(b)=p(a−b) for all values of a and b? | A. p(x)=x^2 B. p(x)=x/2 C. p(x)=x+5 D. p(x)=2x−1 E. p(x)=|x| | B. p(x)=x/2 | To solve this easiest way is just put the value and see that if it equals or not.
with option 1. p(a) = a^2 and p(b) = b^2
so L.H.S = a^2 - b^2
and R.H.S = (a-b)^2 ==> a^2 + b^2 -2ab.
so L.H.S not equal to R.H.S
with option 2. p(a) = a/2 and p(b) = b/2
L.H.S = a/2 - b/2 ==> 1/2(a-b)
R.H.S = (a-b)/2
so L.H.S = R.H.S whi... | college_mathematics | mathematics |
math_1168 | math_mc | Consider the set of 30 parabolas defined as follows: all parabolas have as focus the point $(0,0)$ and the directrix lines have the form $y=ax+b$ with $a$ and $b$ integers such that $a\in \{-2,-1,0,1,2\}$ and $b\in \{-3,-2,-1,1,2,3\}$. No three of these parabolas have a common point. How many points in the plane are on... | D | math_Intermediate Algebra | mathematics | ||
allenai/sciq_6062 | allenai/sciq | What is the largest part of the brain?
A. stem
B. cerebrum
C. cerebellum
D. limbic system | B. cerebrum | The cerebrum is the largest part of the brain. It controls conscious functions such as reasoning, language, sight, touch, and hearing. It is divided into two hemispheres, or halves. The hemispheres are very similar but not identical to one another. They are connected by a thick bundle of axons deep within the brain. Ea... | anatomy | biology | |
pythonio_8 | pythonio-mc | Program:
import heapq as hq
def heap_queue_largest(nums,n):
largest_nums = hq.nlargest(n, nums)
return largest_nums
Input:
heap_queue_largest( [25, 35, 22, 85, 14, 65, 75, 22, 58],5)
Output: | D | code | computer_science | ||
allenai/sciq_2077 | allenai/sciq | What changes from heat or pressure during metamorphism?
A. carbohydrates
B. fossils
C. grains
D. minerals | D. minerals | Metamorphism does not cause a rock to melt completely. It only causes the minerals to change by heat or pressure. If the rock melts completely, it will cool to become an igneous rock. | college_geology | earth_science | |
aquarat_54041 | deepmind/aqua_rat | If the probability that Brendon, Daniel and Kane score more than 700 on the GMAT is 0.4, 0.5 and 0.6 respectively, what is the probability that at least 2 of them score less than 700? | A. 0.12 B. 0.38 C. 0.40 D. 0.5 E. 0.6 | D. 0.5 | The probability that Brendon, Daniel and Kane score less than or equal to 700 on the GMAT is 0.4, 0.5 and 0.6 respectively,
All three score less than 700 = 0.6*0.5*0.4 = 0.12;
Brendon and Daniel score less than or equal to 700, while Kane scores more than 700 = 0.6*0.5*0.6 = 0.18;
Brendon and Kane score less than or eq... | high_school_statistics | mathematics |
aquarat_83900 | deepmind/aqua_rat | How many zeroes are there at the end of the number N, if N = 70! + 140! ? | A. 8 B. 12 C. 16 D. 20 E. 24 | C. 16 | The number of zeroes at the end of 70! will be less than the number of zeroes at the end of 140!
Hence it is sufficient to calculate the number of zeroes at the end of 70!
The number of zeroes = [70/5] + [70/25] + [70/125] = 14 + 2 + 0 = 16
The answer is C. | college_mathematics | mathematics |
math_966 | math_mc | Consider all quadrilaterals $ABCD$ such that $AB=14$, $BC=9$, $CD=7$, and $DA=12$. What is the radius of the largest possible circle that fits inside or on the boundary of such a quadrilateral?
$\textbf{(A)}\ \sqrt{15} \qquad \textbf{(B)}\ \sqrt{21} \qquad \textbf{(C)}\ 2\sqrt{6} \qquad \textbf{(D)}\ 5 \qquad \textbf{(... | A | math_Geometry | mathematics | ||
NLP4Education_99 | NLP4Education | Given the following teleporting matrix (E) for nodes A, B and C:
[0 ½ 0]
[0 0 0]
[0 ½ 1]
and making no assumptions about the link matrix (R), which of the following is correct:
(Reminder: columns are the probabilities to leave the respective node.)
A. A random walker can never reach node A
B. A random... | D. A random walker can always leave node B | college_mathematics | mathematics | ||
mmlu_aux_train_98517 | mmlu_aux_train | Which acts as an insulator for electricity?
A. A metal ring
B. A battery
C. A door hinge
D. Beeswax | D. Beeswax | high_school_physics | physics | ||
aquarat_14790 | deepmind/aqua_rat | Nr Books bought Nr of People
5 7
6 3
7 3
8 2
What is the median of books bought per person? | A. a) 2 B. b) 4 C. c) 6 D. d) 8 E. e) 18 | C. c) 6 | 5,5,5,5,5,5,5,6,6,6,7,7,7,8,8
so you will observer that the median of the list is 6.
Ans C | high_school_statistics | mathematics |
mmlu_aux_train_77073 | mmlu_aux_train | The survey was done among 29,760 students at 100 US high schools. The results suggest that in the past year, 30 percent of US high school students have stolen from a store. And 64 percent may have cheated on a test. However, 93 percent of the students said they were satisfied with their honesty. And 77 percent said,"... | C. They are not so honest as older generations | high_school_statistics | mathematics | ||
mmlu_aux_train_1166 | mmlu_aux_train | Which sentence about the periodic table of elements is true?
A. All elements in period 2 are metals.
B. All elements in group 18 are metals.
C. Metals are found on the left side of the periodic table.
D. Metals are found on the right side of the periodic table. | C. Metals are found on the left side of the periodic table. | high_school_chemistry | chemistry | ||
mmlu_aux_train_94145 | mmlu_aux_train | In Rutherford's experiment, what caused some high-energy particles to bounce off the metal, while most pass straight through?
A. light waves
B. magnetic waves
C. positive charges
D. negative charges | C. positive charges | college_physics | physics | ||
pythonio_689 | pythonio-mc | Program:
import math
def round_up(a, digits):
n = 10**-digits
return round(math.ceil(a / n) * n, digits)
Input:
round_up(123.01247,2)
Output: | D | code | computer_science | ||
mmlu_aux_train_9682 | mmlu_aux_train | "Does my smile look big in this?" Future fitting-room mirrors in clothing stores could subtly adjust your reflection to make you look - and hence feel - happier, encouraging you to like what you see. That's the idea behind the Emotion Evoking System developed by Shigeo Yoshida and colleagues at the University of Tokyo ... | A. To see whether one's feeling can be unconsciously affected. | machine_learning | computer_science | ||
mmlu_aux_train_88417 | mmlu_aux_train | A large number of people in the world eat fast food .Whenever you go into a fast food restaurant , you can see lots of people enjoying their meals there. How do you know in which country people like fast food best ? The English people are the world's biggest fans of fast food , while the French are the least interested... | D. the English | high_school_statistics | mathematics | ||
aquarat_55459 | deepmind/aqua_rat | If x > 3000, then the value of (3x)/(2 x^1.21 - 1111^1.3) is closest to? | A. 1/6 B. 1/3 C. 10/21 D. 4/10 E. 3/2 | D. 4/10 | assume x = 3002
(3x)/(2 x^1.21 - 1111^1.3) = 9006 / (2 * (3002)^1.21 - 1111^1.3)
=9006 / 23154
= = 4 /10
D | college_mathematics | mathematics |
allenai/sciq_7127 | allenai/sciq | What is required for communication?
A. transmission and weight of signals
B. lack and reception of signals
C. transmission and reception of signals
D. weight and reception of signals | C. transmission and reception of signals | college_computer_science | computer_science | ||
pythonio_269 | pythonio-mc | Program:
def min_Jumps(a, b, d):
temp = a
a = min(a, b)
b = max(temp, b)
if (d >= b):
return (d + b - 1) / b
if (d == 0):
return 0
if (d == a):
return 1
else:
return 2
Input:
min_Jumps(11,14,11)
Output: | B | code | computer_science | ||
aquarat_54666 | deepmind/aqua_rat | If each data point in a certain set Q is increased by a factor of 9, what happens with the set's standard deviation? | A. Doesn't Change B. Increases by Factor 9 C. Decreases by Factor 9 D. Increases by 9 E. Can't be determined | B. Increases by Factor 9 | Standard deviation questions will always be conceptual in nature, because the GMAT does not require that you be able to calculate standard deviation.Veritasteaches a concept known as themapping strategyfor data sufficiency, which helps make a problem like this easily understandable. The mapping strategy is just looking... | high_school_statistics | mathematics |
mmlu_aux_train_69202 | mmlu_aux_train | An expensive car speeding down the main street of a small town was soon over-taken by a young motorcycle policeman. As he started to take out the ticket, the woman in the car said proudly. "Before you go any further, young man, I think you should know that the mayor of this city is a good friend of mine." The officer d... | C. the driver was driving too fast | conceptual_physics | physics | ||
math_1963 | math_mc | The tail of a 1-mile long train exits a tunnel exactly 3 minutes after the front of the train entered the tunnel. If the train is moving 60 miles per hour, how many miles long is the tunnel? | A | math_Prealgebra | mathematics | ||
allenai/sciq_963 | allenai/sciq | Why do players with more mass often have a larger impact in football?
A. momentum is larger
B. Velocity is larger
C. kinetic energy is lower
D. potential energy is lower | A. momentum is larger | Figure 28.18 Momentum is an important concept for these football players from the University of California at Berkeley and the University of California at Davis. Players with more mass often have a larger impact because their momentum is larger. For objects moving at relativistic speeds, the effect is even greater. (cr... | high_school_physics | physics | |
aquarat_84387 | deepmind/aqua_rat | Suppose the operation * is dened on the set of integers by a*b = a+2b.
Then for every two integers a and b, the value of a*(b*a) is the same
as | A. a*b B. b*a C. (3a)*b D. b*(4a) E. (5a)*b | E. (5a)*b | One checks which of the choices is the same as a(ba) = a(b+2a) = a+2(b+2a) =
a +2b +4a = 5a + 2b. Since (5a) b = 5a + 2b, the answer is (e).
correct answer E | abstract_algebra | mathematics |
math_826 | math_mc | In triangle $ABC$, altitudes $AD$, $BE$, and $CF$ intersect at the orthocenter $H$. If $\angle ABC = 49^\circ$ and $\angle ACB = 12^\circ$, then find the measure of $\angle BHC$, in degrees. | A | math_Geometry | mathematics | ||
mmlu_aux_train_4317 | mmlu_aux_train | Which type of scientist would study the relationship between simple machines and energy?
A. chemist
B. biologist
C. physicist
D. geologist | C. physicist | conceptual_physics | physics | ||
allenai/sciq_3843 | allenai/sciq | What type of digestion is chewing an example of?
A. fluid
B. electromagnetic
C. mechanical
D. gravity | C. mechanical | high_school_biology | biology | ||
aquarat_8503 | deepmind/aqua_rat | If ABC is a quarter circle and a smaller circle is inscribed in it; if radius of quarter circle is 1.414units. Find the radius of smaller circle | A. 0.48 B. 0.58 C. 0.68 D. 0.78 E. 0.88 | B. 0.58 | if r be radius of smaller circle then
distance b/n centres = √2 * r
so, r + r√2 = R here,R = 1.414 =√2
=> r=(√2 -1)R
r = 0 .586 unit
ANSWER:B | college_mathematics | mathematics |
aquarat_11499 | deepmind/aqua_rat | If f(x)= 5x^3- 4x+8 and g(y)= 6y-4, then g(f(x)) = | A. 11x^2+4x+4 B. 11x^2-12x+44 C. 30x^3-24x+44 D. 30x^3+4x+4 E. 30x^3-12x+44 | C. 30x^3-24x+44 | g(f(x)) = 6(f(x)) -4 = 6(5x^3- 4x+8) - 4 = 30x^3-24x+44 =>C | college_mathematics | mathematics |
aquarat_85799 | deepmind/aqua_rat | Let the polynomials be:
P1(x)=3x2−7x+6,
P2(x)=−5x2−4x+2,
P1(x)+P2(x)= | A. 2x2 + 11x - 7 B. -2x2 - 11x + 8 C. -2x2 - 11x + 6 D. 2x2 - 9x + 7 E. None of these | B. -2x2 - 11x + 8 | Solution:
P1(x)+P2(x)=(3x2−7x+6)+(−5x2−4x+2)=P1(x)+P2(x)=(3x2−7x+6)+(−5x2−4x+2)=
3x2−7x+6−5x2−4x+2=3x2−7x+6−5x2−4x+2=
−2x2−11x+8
Answer B | college_mathematics | mathematics |
pythonio_281 | pythonio-mc | Program:
def increment_numerics(test_list, K):
res = [str(int(ele) + K) if ele.isdigit() else ele for ele in test_list]
return res
Input:
increment_numerics(["Flutter", "451", "is", "44", "96", "Magnificent", "12"] , 33)
Output: | A | code | computer_science | ||
math_1699 | math_mc | Find the value of $a$ that satisfies the equation $293_{a}+468_{a}=73B_{a}$, where $B_{a}=11_{10}$. | B | math_Number Theory | mathematics | ||
aquarat_79697 | deepmind/aqua_rat | a^2*b^2+a^2+b^2=259
b^2*c^2+b^2+c^2=1299
c^2*a^2+c^2+a^2=499
then find b=? | A. 2 B. 3 C. 4 D. 5 E. 6 | D. 5 | adding 1 to all equqtions.,we get them modified to the following form
(a^2+1)(b^2+1)=260
(b^2+1)(c^2+1)=1300
(c^2+1)(a^2+1)=500
by corresponding mul and div we get a=3,b=5,c=7
ANSWER:D | college_mathematics | mathematics |
math_1197 | math_mc | Let $S$ denote the value of the sum
\[\sum_{n = 1}^{9800} \frac{1}{\sqrt{n + \sqrt{n^2 - 1}}}\]
$S$ can be expressed as $p + q \sqrt{r}$, where $p, q,$ and $r$ are positive integers and $r$ is not divisible by the square of any prime. Determine $p + q + r$.
| B | math_Intermediate Algebra | mathematics | ||
mmlu_aux_train_15110 | mmlu_aux_train | Children who see their parents drunk are twice likely to get drunk themselves, a survey of young teenagers has suggested. Poor parental supervision also raises the chances of teenage drinking, said the Joesph Rowntree Foundation. If parents don't know where their children are on a Saturday night, or let them watch film... | C. About 2800. | high_school_statistics | mathematics | ||
pythonio_590 | pythonio-mc | Program:
def odd_Num_Sum(n) :
j = 0
sm = 0
for i in range(1,n + 1) :
j = (2*i-1)
sm = sm + (j*j*j*j)
return sm
Input:
odd_Num_Sum(4)
Output: | A | code | computer_science | ||
math_1864 | math_mc | Two adjacent sides of a rhombus form a $60$-degree angle. If each side of the rhombus measures $2$ cm, what is the area of the rhombus, in square centimeters? Express your answer in simplest radical form. | A | math_Prealgebra | mathematics | ||
math_730 | math_mc | Find the area of rhombus $ABCD$ given that the radii of the circles circumscribed around triangles $ABD$ and $ACD$ are $12.5$ and $25$, respectively.
| D | math_Geometry | mathematics | ||
mmlu_aux_train_78028 | mmlu_aux_train | When you're not at home,many worries may start to crowd your mind.Did I turn the coffee maker off?Did I lock the door?Are the kids doing their homework or watching television?With a smart home,you can quiet all of these worries. A smart home is a home with a communication network.This network connects devices ,such as ... | C. mobile phones | electrical_engineering | engineering | ||
mmlu_aux_train_33100 | mmlu_aux_train | Johnny Smith was a good math student at a high school. He loved his computer. He came home early every day, then he worked with it till midnight. But Johnny was not a good English student, not good at all. He got an F in his English class. One day after school Johnny joined his computer to the computer in his high scho... | D. his own house | high_school_computer_science | computer_science | ||
math_290 | math_mc | The values of $f$, $g$, $h$ and $j$ are 5, 6, 7 and 8, but not necessarily in that order. What is the largest possible value of the sum of the four products $fg$, $gh$, $hj$ and $fj$? | D | math_Algebra | mathematics | ||
pythonio_210 | pythonio-mc | Program:
def binomial_Coeff(n,k):
C = [0] * (k + 1);
C[0] = 1; # nC0 is 1
for i in range(1,n + 1):
for j in range(min(i, k),0,-1):
C[j] = C[j] + C[j - 1];
return C[k];
def sum_Of_product(n):
return binomial_Coeff(2 * n,n - 1);
Input:
sum_Of_product(1)
Output: | A | code | computer_science | ||
mmlu_aux_train_63337 | mmlu_aux_train | The human brain contains ten thousand million cells and each of these may have a thousand connections. Such enormous numbers used to discourage us and cause us to dismiss the possibility of making a machine with human-like ability, but now that we have grown used to moving forward at such a pace we can be less sure. Qu... | C. By either programming it or changing its structure | machine_learning | computer_science | ||
math_1334 | math_mc | Let \[P(x) = (2x^4 - 26x^3 + ax^2 + bx + c)(5x^4 - 80x^3 + dx^2 + ex + f),\]where $a, b, c, d, e, f$ are real numbers. Suppose that the set of all complex roots of $P(x)$ is $\{1, 2, 3, 4, 5\}.$ Find $P(6).$ | C | math_Intermediate Algebra | mathematics | ||
math_2094 | math_mc | There is an angle $\theta$ in the range $0^\circ < \theta < 45^\circ$ which satisfies
\[\tan \theta + \tan 2 \theta + \tan 3 \theta = 0.\]Calculate $\tan \theta$ for this angle. | A | math_Precalculus | mathematics | ||
mmlu_aux_train_31316 | mmlu_aux_train | Geologists have been studying volcanoes for a long time.Though they have learned a great deal,they still have not discovered the cause of volcanic action.They know that the inside of the earth is very hot,but they are not sure exactly what causes the great heat.Some geologists have thought that the heat is caused by th... | D. not sure | earth_science | earth_science | ||
aquarat_79147 | deepmind/aqua_rat | Eva’s grade was in the 80th percentile out of 80 grades in her class. In another class of 70 students there were 30 grades higher than Eva’s. If nobody had Eva’s grade, then Eva was what percentile of the two classes combined? | A. 84 B. 80 C. 74 D. 69 E. 65 | E. 65 | Being in 80% percentile out of 80 grades means Eva was 65th (from the least grade) in the class (as long as nobody had Eva's grades), she outscored 64.
In another class her grade would rank her 41 (from the least grade out of 71, 70+Eva), 40 had the grades lower than Eva.
So in combined classes she outscored 64+40=104.... | high_school_statistics | mathematics |
mmlu_aux_train_1840 | mmlu_aux_train | Which of the following will reduce a home electric bill?
A. using cloth napkins rather than paper towels
B. drying clothes on a clothesline on sunny days
C. keeping appliances plugged in when not in use
D. using incandescent light bulbs in the lamps | B. drying clothes on a clothesline on sunny days | electrical_engineering | engineering | ||
mmlu_aux_train_99477 | mmlu_aux_train | Jenny was outside facing her house holding a compass. The needle of the compass was facing her house. Staying in one place she turned around and around, stopping several times. She noticed that whichever way she faced
A. the compass's needle was facing straight ahead
B. the compass's needle was facing the house
C. the... | B. the compass's needle was facing the house | conceptual_physics | physics | ||
math_745 | math_mc | Twelve congruent disks are placed on a circle $C$ of radius 1 in such a way that the twelve disks cover $C$, no two of the disks overlap, and so that each of the twelve disks is tangent to its two neighbors. The resulting arrangement of disks is shown in the figure below. The sum of the areas of the twelve disks can be... | C | math_Geometry | mathematics | ||
allenai/sciq_9361 | allenai/sciq | Similar to the coil on a stove, changes in what reflect an increase in the temperature of a star?
A. color
B. rotation
C. direction
D. texture | A. color | Think about the coil of an electric stove as it heats up. The coil changes in color as its temperature rises. When you first turn on the heat, the coil looks black. The air a few inches above the coil begins to feel warm. As the coil gets hotter, it starts to glow a dull red. As it gets even hotter, it becomes a bright... | astronomy | physics | |
NLP4Education_437 | NLP4Education | Which of the following ciphers is based on arithmetics over the finite field $\mathrm{GF}(2^8)$?
A. AES
B. DES
C. A5/1
D. RC4 | A. AES | computer_security | computer_science | ||
math_229 | math_mc | Jose invested $\$50,\!000$ for $2$ years at an annual interest rate of $4$ percent compounded yearly. Patricia invested $\$50,\!000$ for the same period of time, at the same interest rate, but the interest was compounded quarterly. To the nearest dollar, how much more money did Patricia's investment earn than that of J... | B | math_Algebra | mathematics | ||
mmlu_aux_train_25506 | mmlu_aux_train | Dear Victor: I am a college student. Nowadays games on the net are very popular with college students. Some of my roommates are very interested in them. They not only play games in their free time, but also keep talking about them at night when lights are off, and they regard games as part of life. I've begged them to... | A. playing computer games | high_school_computer_science | computer_science | ||
aquarat_13950 | deepmind/aqua_rat | If sy + z = s(y + z), which of the following must be true? | A. x = 0 and z = 0 B. s= 1 and y = 1 C. s = 1 and z = 0 D. s = 1 or y = 0 E. s = 1 or z = 0 | E. s = 1 or z = 0 | sy + z = sy + sz
z = sz
case 1: z not= 0, s = z/z = 1
case 2: z = 0, 0 = s0 = 0
Combining 2 cases: s = 1 or z =0
E. is the answer. | abstract_algebra | mathematics |
mmlu_aux_train_99005 | mmlu_aux_train | Which of the following likely make up a path for electrical energy to travel to a device?
A. steel or copper
B. rice or beans
C. peaches or cream
D. cotton and solar | A. steel or copper | electrical_engineering | engineering | ||
math_2009 | math_mc | Simplify $\frac{\sqrt{507}}{\sqrt{48}}-\frac{\sqrt{175}}{\sqrt{112}}$. | D | math_Prealgebra | mathematics | ||
pythonio_454 | 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 | ||
allenai/sciq_8764 | allenai/sciq | What do you call reversible changes that do not change matter’s chemical makeup or chemical properties?
A. potential changes
B. chemical changes
C. physical changes
D. element changes | C. physical changes | A change of state occurs whenever matter changes from one state to another. Changes of state are physical changes in matter. They are reversible changes that do not change matter’s chemical makeup or chemical properties. | high_school_chemistry | chemistry | |
allenai/sciq_2805 | allenai/sciq | What is the term for the sudden movement of large blocks of rock and soil down a slope?
A. torrent
B. hurricane
C. sludge
D. slump | D. slump | Less dramatic types of mass wasting move Earth materials slowly down a hillside. Slump is the sudden movement of large blocks of rock and soil down a slope. ( Figure below ). All the material moves together in big chunks. Slumps may happen when a layer of slippery, wet clay is underneath the rock and soil on a hillside... | college_geology | earth_science | |
aquarat_89974 | deepmind/aqua_rat | Define q* by the equation q* = π-q. Then ((−π)*)* = | A. −2π B. -1 C. −π D. 2π E. 4π | C. −π | for q* f(f(−π)) = f(π − (−π)) = f(π + π) = f(2π) = π − 2π = −π=C | college_mathematics | mathematics |
aquarat_78810 | deepmind/aqua_rat | Which of the following is not an odd function? | A. f(x) = -x3 B. f(x) = x5 C. f(x) = x2 - x D. f(x) = |x|3 E. None of these | D. f(x) = |x|3 | Solution:
An odd function is a function whose value reverses in sign for a reversal in sign of its argument. i.e. f(x) = -f(-x).
Except f(x) = |x|3 all other functions mentioned in the choices change values.
Answer D | college_mathematics | mathematics |
math_755 | math_mc | Rhombus $PQRS$ is inscribed in rectangle $ABCD$ so that vertices $P$, $Q$, $R$, and $S$ are interior points on sides $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, and $\overline{DA}$, respectively. It is given that $PB=15$, $BQ=20$, $PR=30$, and $QS=40$. Let $m/n$, in lowest terms, denote the perimeter of $ABCD$. ... | D | math_Geometry | mathematics | ||
allenai/sciq_7164 | allenai/sciq | The molecular formula is still c 4 h 10 , which is the same formula as?
A. carbon hydroxide
B. chlorine
C. butane
D. propane | C. butane | The name of this molecule is 2-methylpropane. The molecular formula is still C 4 H 10 , which is the same formula as butane. A structural isomer is one of multiple molecules that have the same molecular formula, but different structural formulas. Butane and 2-methylpropane are structural isomers. | high_school_chemistry | chemistry | |
NLP4Education_6 | NLP4Education | What is the content of the inode?
A. Filename
B. String with the name of the owner
C. File size
D. Capacity of the whole file system | C. File size | computer_security | computer_science | ||
aquarat_7179 | deepmind/aqua_rat | If abc ≠ 1 and the sum of the reciprocals of a, b, and c equals the reciprocal of the product of a, b, and c, then a = | A. (1 + bc)/(b + c) B. (1 – bc)/(b + c) C. (1 + b + c)/(bc) D. (1 – b – c)/(bc) E. (1 – b – c)/(b + c) | C. (1 + b + c)/(bc) | Answer is C though it took me around 4 minutes to get that. | abstract_algebra | mathematics |
mmlu_aux_train_27455 | mmlu_aux_train | Right is right. Right? Of course. But is left wrong? Well, the Romans used to think so. They thought left-handed people were mistakes of nature. Latin, the language of the Romans, had many words that expressed this view. Some words we use today still have this meaning. The Latin word "dexter" means "right". The English... | C. He can use either his left hand or his right hand. | high_school_biology | biology | ||
math_562 | math_mc | Point $(x,y)$ is randomly picked from the rectangular region with vertices at $(0,0),(2008,0),(2008,2009),$ and $(0,2009)$. What is the probability that $x > 2y$? Express your answer as a common fraction. | D | math_Counting & Probability | mathematics | ||
math_419 | math_mc | The integers $G$ and $H$ are chosen such that
\[\frac{G}{x+5}+\frac{H}{x^2-4x}=\frac{x^2-2x+10}{x^3+x^2-20x}\]for all real values of $x$ except $-5$, $0$, and $4$. Find $H/G$. | D | math_Algebra | mathematics | ||
pythonio_420 | 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
... | D | code | computer_science | ||
math_611 | math_mc | An 8 by 8 checkerboard has alternating black and white squares. How many distinct squares, with sides on the grid lines of the checkerboard (horizontal and vertical) and containing at least 5 black squares, can be drawn on the checkerboard?
[asy]
draw((0,0)--(8,0)--(8,8)--(0,8)--cycle);
draw((1,8)--(1,0));
draw((7,8)-... | A | math_Counting & Probability | mathematics | ||
math_101 | math_mc | What is the shortest distance from the origin to the circle defined by $x^2-24x +y^2+10y +160=0$? | B | math_Algebra | mathematics | ||
mmlu_aux_train_66882 | mmlu_aux_train | You're jogging at a steady pace, enjoying your favorite music through your headphones. Your breath is short and your heart is pumping. Your legs feel like they couldn't carry you any faster. And then you hear the groan of a zombie over your right shoulder. You must run or be eaten. The zombie apocalypse isn't ... | D. create a virtual health game | computer_science | computer_science | ||
allenai/sciq_8393 | allenai/sciq | What can all living things sense and respond to in their environment?
A. warmth
B. wind
C. sunlight
D. stimuli | D. stimuli | All living things can sense and respond to stimuli in their environment. Stimuli might include temperature, light, or gravity. | high_school_biology | biology | |
pythonio_839 | pythonio-mc | Program:
def previous_palindrome(num):
for x in range(num-1,0,-1):
if str(x) == str(x)[::-1]:
return x
Input:
previous_palindrome(120)
Output: | C | code | computer_science | ||
mmlu_aux_train_33620 | mmlu_aux_train | If You Decide to Go to the Moon By Faith Mcnulty, Steven Kellogg(illustrator)---This book is written in the second person and tells you the most important information you need to know if you go to the moon. I especially appreciate the information on how to get home. You know, just in case... Discover Space By Cynthia P... | B. introduce some books about astronomy | astronomy | physics |
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