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_1278 | math_mc | Let $c$ be a complex number. Suppose there exist distinct complex numbers $r$, $s$, and $t$ such that for every complex number $z$, we have
\[
(z - r)(z - s)(z - t) = (z - cr)(z - cs)(z - ct).
\]Compute the number of distinct possible values of $c$. | D | math_Intermediate Algebra | mathematics | ||
allenai/sciq_41 | allenai/sciq | What phenomenon is primarily the result of plate tectonic motions?
A. volcanoes
B. tsunamis
C. eruption
D. earthquake | D. earthquake | Earthquakes are primarily the result of plate tectonic motions. What type of stress would cause earthquakes at each of the three types of plate boundaries?. | college_earth_science | earth_science | |
math_2203 | math_mc | Compute the distance between the parallel lines given by
\[\begin{pmatrix} 2 \\ -3 \end{pmatrix} + t \begin{pmatrix} 1 \\ -7 \end{pmatrix}\]and
\[\begin{pmatrix} 1 \\ -5 \end{pmatrix} + s \begin{pmatrix} 1 \\ -7 \end{pmatrix}.\] | B | math_Precalculus | mathematics | ||
aquarat_84713 | deepmind/aqua_rat | Evaluate combination
96C94=96!/(94)!(2)! | A. 6170 B. 5560 C. 4170 D. 4560 E. None of these | D. 4560 | Explanation:
nCr=n!/(r)!(n−r)!
96C94=96!/(94)!(2)!
=96*95*94!/(94)!(2)!
=96*95/2∗1
=4560
Option D | college_mathematics | mathematics |
allenai/sciq_6887 | allenai/sciq | What is the atomic number?
A. Speed of electrons
B. number of protons
C. Number of neutrons
D. Number of electrons | B. number of protons | In the modern periodic table, elements are organized by atomic number. The atomic number is the number of protons in an atom of an element. This number is unique for each element, so it seems like an obvious way to organize the elements. (Mendeleev used atomic mass instead of atomic number because protons had not yet b... | high_school_chemistry | chemistry | |
mmlu_aux_train_42545 | mmlu_aux_train | People tend to become more personal and hide less of themselves when using email.Researchers from Open University in Britain have found in a recent study that there are good reasons for this. The team of researchers asked 83 pairs of students, all strangers to each other, to solve a problem.They had to discuss this que... | A. how people open up when emailing | high_school_computer_science | computer_science | ||
allenai/sciq_8544 | allenai/sciq | When the energy of the earthquake reaches shore, it forms a huge wave called?
A. a typhoon
B. a surge
C. a tidal wave
D. a tsunami | D. a tsunami | When an earthquake occurs under the ocean, it sends waves through the water as well as the ground. When the energy of the earthquake reaches shore, it forms a huge wave called a tsunami. | earth_science | earth_science | |
aquarat_45307 | deepmind/aqua_rat | A voltmeter is used: | A. 22 B. 266 C. 27 D. 26 E. 81 | C. 27 | Explanation:
Answer: Option C | electrical_engineering | engineering |
mmlu_aux_train_11226 | mmlu_aux_train | We live in a digital world now, and a student's technology needs have changed. For the early years, when you are in primary school, you can get by with no technology at all. Even if you have a computer, it's a good idea to get children familiar with libraries. At this age, trips to the library are like family outings. ... | D. go to libraries to read more books | high_school_computer_science | computer_science | ||
mmlu_aux_train_98676 | mmlu_aux_train | Baking soda can react chemically with what?
A. oxidized alcohol
B. sunlight
C. dirt
D. wind | A. oxidized alcohol | high_school_chemistry | chemistry | ||
NLP4Education_307 | NLP4Education | For optimizing a matrix factorization problem in the recommender systems setting, as the number of observed entries increases but all $K, N, D$ are kept constant, the computational cost of the matrix inversion in Alternating Least-Squares increases.
A. Always increases
B. Always decreases
C. Remains constant
D. Increas... | C. Remains constant | machine_learning | computer_science | ||
mmlu_aux_train_92823 | mmlu_aux_train | During a rainstorm, leaves wash down a gully on a hillside. The water slows down at the foot of the hill and fans out, depositing the leaves. What geologic structure is formed in a similar way?
A. a basalt column
B. a stalactite
C. a fault line
D. a delta | D. a delta | college_science | earth_science | ||
pythonio_820 | pythonio-mc | Program:
def smallest_multiple(n):
if (n<=2):
return n
i = n * 2
factors = [number for number in range(n, 1, -1) if number * 2 > n]
while True:
for a in factors:
if i % a != 0:
i += n
break
if (a == factors[-1] and i % a ==... | A | code | computer_science | ||
allenai/sciq_7096 | allenai/sciq | What kind of fossils are excellent markers for correlating the ages of sedimentary rocks?
A. vertiscom
B. foram
C. agonum
D. euglena | B. foram | college_biology | biology | ||
pythonio_516 | pythonio-mc | Program:
def sum_Of_Subarray_Prod(arr,n):
ans = 0
res = 0
i = n - 1
while (i >= 0):
incr = arr[i]*(1 + res)
ans += incr
res = incr
i -= 1
return (ans)
Input:
sum_Of_Subarray_Prod([1,2,3,4],4)
Output: | D | code | computer_science | ||
allenai/sciq_8151 | allenai/sciq | What is the process in which a liquid boils and changes to a gas?
A. melting
B. freezing
C. sublimation
D. vaporization | D. vaporization | The process in which a liquid boils and changes to a gas is called vaporization . The temperature at which a liquid boils is its boiling point. The boiling point of water is 100°C (212°F). Other types of matter may have higher or lower boiling points. For example, the boiling point of table salt is 1413°C. The boiling ... | high_school_chemistry | chemistry | |
math_402 | math_mc | Tim wants to invest some money in a bank which compounds quarterly with an annual interest rate of $7\%$. To the nearest dollar, how much money should he invest if he wants a total of $\$60,\!000$ at the end of $5$ years? | D | math_Algebra | mathematics | ||
NLP4Education_198 | NLP4Education | Which method can be used for dimensionality reduction?
A. SVM
B. Decision Trees
C. PCA
D. Random Forest | C. PCA | machine_learning | computer_science | ||
mmlu_aux_train_17384 | mmlu_aux_train | The prefix = st1 /USgovernment has announced plans to list polar bears as a threatened species because of concerns that the ice where they live is melting. But as the BBC's Owen Clegg reports, theUSplans are also important for other reasons. It's estimated that there are no more than twenty-five thousand polar bears li... | A. It is that the floating ice upon which they survive melts away. | college_biology | biology | ||
math_505 | math_mc | Let $S$ be the set of points whose coordinates $x,$ $y,$ and $z$ are integers that satisfy $0\le x\le2,$ $0\le y\le3,$ and $0\le z\le4.$ Two distinct points are randomly chosen from $S.$ The probability that the midpoint of the segment they determine also belongs to $S$ is $m/n,$ where $m$ and $n$ are relatively prime ... | D | math_Counting & Probability | mathematics | ||
allenai/sciq_6693 | allenai/sciq | What is the force that causes objects to fall down to the ground?
A. motion
B. velocity
C. pull
D. gravity | D. gravity | Regardless of what gravity is — a force between masses or the result of curves in space and time — the effects of gravity on motion are well known. You already know that gravity causes objects to fall down to the ground. Gravity affects the motion of objects in other ways as well. | conceptual_physics | physics | |
mmlu_aux_train_92689 | mmlu_aux_train | Over geologic time, global mean sea level has varied significantly. Which change is most likely responsible for an increase in global mean sea level?
A. erosion of sediment from a mountain range
B. mass extinction of marine organisms
C. formation of an ocean trench
D. melting of polar ice caps | D. melting of polar ice caps | college_earth_science | earth_science | ||
mmlu_aux_train_18923 | mmlu_aux_train | A mobile phone is no longer just a phone -- it is also a music player, video camera and personal organizer. And mobile phones with television programming are just around the corner. But the more functions cell phone manufacturers add, the greater the amount of power the phones use and the less practical running them on... | B. it is inconvenient to use | electrical_engineering | engineering | ||
pythonio_341 | pythonio-mc | Program:
from itertools import zip_longest, chain, tee
def exchange_elements(lst):
lst1, lst2 = tee(iter(lst), 2)
return list(chain.from_iterable(zip_longest(lst[1::2], lst[::2])))
Input:
exchange_elements([25,35,45,55,75,95])
Output: | B | code | computer_science | ||
allenai/sciq_11546 | allenai/sciq | What are the two most common causes of diseases?
A. bacteria and protazoa
B. nutritional deficiencies
C. bacteria and viruses
D. viruses and protazoa | C. bacteria and viruses | Today most people realize that microorganisms, such as bacteria or viruses, are the cause of disease. This concept is known as the germ theory of disease, one of the few scientific theories in the field of the life sciences. Although it seems obvious now, people did not always understand the cause of disease. How does ... | high_school_biology | biology | |
math_2155 | math_mc | Let $\mathcal{C}$ be the hyperbola $y^2 - x^2 = 1$. Given a point $P_0$ on the $x$-axis, we construct a sequence of points $(P_n)$ on the $x$-axis in the following manner: let $\ell_n$ be the line with slope 1 passing passing through $P_n$, then $P_{n+1}$ is the orthogonal projection of the point of intersection of $\... | C | math_Precalculus | mathematics | ||
allenai/sciq_2510 | allenai/sciq | What type of isomers contain the same number of atoms of each kind but differ in which atoms are bonded to one another?
A. structural isomers
B. unique isomers
C. constitutional isomers
D. different isomers | A. structural isomers | Isomers that contain the same number of atoms of each kind but differ in which atoms are bonded to one another are called structural isomers. Isobutane and n-butane are examples of structural isomers. One kind of isomerism consists of two compounds that have the same empirical formula but differ in the number of formul... | college_chemistry | chemistry | |
pythonio_710 | pythonio-mc | Program:
def sort_tuple(tup):
n = len(tup)
for i in range(n):
for j in range(n-i-1):
if tup[j][0] > tup[j + 1][0]:
tup[j], tup[j + 1] = tup[j + 1], tup[j]
return tup
Input:
sort_tuple([("Amana", 28), ("Zenat", 30), ("Abhishek", 29),("Nikhil", 21), ("B", "C")])
Output: | D | code | computer_science | ||
mmlu_aux_train_94481 | mmlu_aux_train | In what section of Earth do earthquakes happen?
A. crust
B. mantle
C. inner core
D. outer core | A. crust | earth_science | earth_science | ||
math_337 | math_mc | The function $\lfloor x\rfloor$ is defined as the largest integer less than or equal to $x$. For example, $\lfloor 5.67\rfloor = 5$, $\lfloor -\tfrac 14\rfloor = -1$, and $\lfloor 8\rfloor = 8$.
What is the range of the function $$f(x) = \lfloor x\rfloor - x~?$$Express your answer in interval notation. | A | math_Algebra | mathematics | ||
mmlu_aux_train_54294 | mmlu_aux_train | One night in February 1962, John H. Glenn, Jr. flew overprefix = st1 /Australia. The man in the Mercury capsule was alone, but friendly voices reached him by radio. Over the dark land 100 miles below, he saw sparkling lights. It marked the city of Perth, where people had turned on their lights as a greeting to him. ... | A. greet Glenn | astronomy | physics | ||
math_1922 | math_mc | Equilateral triangle $ABC$ and square $BCDE$ are coplanar, as shown. What is the number of degrees in the measure of angle $CAD$?
[asy]
size(70);
draw((0,0)--(20,0)--(20,20)--(0,20)--cycle);
draw((0,20)--(10,37.3)--(20,20));
draw((10,37.3)--(20,0));
label("$A$",(10,37.3),N);
label("$B$",(0,20),W);
label("$C$",(20,20),... | A | math_Prealgebra | mathematics | ||
allenai/sciq_6019 | allenai/sciq | The composition of the magma determines if the rock is mafic, felsic, or what?
A. intermediate
B. variable
C. porous
D. magnetic | A. intermediate | The composition of the magma determines if the rock is mafic, felsic, or intermediate. | college_geology | earth_science | |
mmlu_aux_train_18638 | mmlu_aux_train | Science has told us too much about the moon that it is fairly easy to imagine what it would be like to get there. It is certainly not a friendly place. Since there is no air or water, there can be no life of any kind. There is not much variety of scenery either. For mile after mile there are only flat plains of dust wi... | D. all of the above | astronomy | physics | ||
mmlu_aux_train_17628 | mmlu_aux_train | Below is an introduction to Top 5 Teen Magazines from the US and the UK. J-14 Marked to preteen and teenage girls ages 11-19, J-14 --a shortened name of "Just For Teens" --is packed with features like teen gossip, quizzes, fashion advice, posters, and celebrity interviews in every issue. Some of the magazine's most po... | B. Advice on fashion. | high_school_computer_science | computer_science | ||
aquarat_24056 | deepmind/aqua_rat | Given a set of n rays in a plane, we define a reversal as the operation of reversing precisely one ray and obtaining a new set of n rays.
Q1: if n = 2001 and if k reversals are performed such that all the rays are reversed, then a possible value of k is
a. 4000 b. 4002 c. 2011 d. 1999 | A. 2336 B. 2011 C. 1366 D. 288 E. 1232 | B. 2011 | there are n rays. If we reverse all of them, we would have a complete reversed set after n reversals. After that any reversal that we perform has to be undone with another reversal to obtain complete reversal. We can have a complete reversal after k reversals if k = n + 2m (m ∈ N). i.e., k could be some number greater ... | abstract_algebra | mathematics |
math_262 | math_mc | Compute the value of $x$ such that
$\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\cdots\right)\left(1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\cdots\right)=1+\frac{1}{x}+\frac{1}{x^2}+\frac{1}{x^3}+\cdots$. | D | math_Algebra | mathematics | ||
pythonio_767 | pythonio-mc | Program:
def ntimes_list(nums,n):
result = map(lambda x:n*x, nums)
return list(result)
Input:
ntimes_list([1, 2, 3, 4, 5, 6, 7],3)
Output: | D | code | computer_science | ||
math_513 | math_mc | Albert starts to make a list, in increasing order, of the positive integers that have a first digit of 1. He writes $1, 10, 11, 12, \ldots$ but by the 1,000th digit he (finally) realizes that the list would contain an infinite number of elements. Find the three-digit number formed by the last three digits he wrote (the... | B | math_Counting & Probability | mathematics | ||
mmlu_aux_train_22885 | mmlu_aux_train | Do you sleep well? Some people get off to sleep as soon as their head hits the pillow, but many others are not so lucky. In fact, the lack of quality sleep has become a public health issue around the world. According to me World Association of Sleep Medicine, 45 percent of the world's population suffer from sleep prob... | B. Modern technology. | clinical_knowledge | biology | ||
aquarat_73075 | deepmind/aqua_rat | If ‘POOJA’ is coded as ‘SRRMD’, then ‘PRIYA’ is coded as | A. THGFE B. GVFED C. FREDCV D. SULBD E. SUUNF | D. SULBD | P= 16 = 16+3 = 19 = S
O = 15 =15+3 =18 = R
SIMILARLY,
P = 16 = 16+3 = 19 = S
R = 18 = 18+3 = 21 = U
I = 9 = 9+3 = 12 = L
Y = 25 = 25 +3 = 28 = B
A = 1 = 1+3 = 4 = D
SO ANS IS
SULBD | formal_logic | mathematics |
allenai/sciq_11592 | allenai/sciq | What happens to most of the energy in a trophic level as it passes to the next higher level?
A. it is transferred
B. it is lost
C. it stays the same
D. it increases | B. it is lost | high_school_biology | biology | ||
math_484 | math_mc | Cities $A$, $B$, $C$, $D$, and $E$ are connected by roads $\widetilde{AB}$, $\widetilde{AD}$, $\widetilde{AE}$, $\widetilde{BC}$, $\widetilde{BD}$, $\widetilde{CD}$, and $\widetilde{DE}$. How many different routes are there from $A$ to $B$ that use each road exactly once? (Such a route will necessarily visit some citie... | C | math_Counting & Probability | mathematics | ||
aquarat_94835 | deepmind/aqua_rat | A train 100 m long passes a man, running at 15 km/hr in the same direction in which the train is going, in 20 seconds. The speed of the train is: | A. 16 km/hr. B. 33 km/hr. C. 21 km/hr. D. 49 km/hr. E. 76 km/hr. | B. 33 km/hr. | Speed of the train relative to man =100/20m/sec=5 m/sec.
=5 x 18/5 km/hr
= 18 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x - 15) km/hr.
x - 15 = 18
x = 33 km/hr.
ANSWER:B | high_school_physics | physics |
aquarat_65406 | deepmind/aqua_rat | A 6% stock yields 8%.The market value of the stock is : | A. Rs. 48 B. Rs. 75 C. Rs. 96 D. Rs. 133.33 E. None | B. Rs. 75 | Solution
For an income of Rs. 8, investment = Rs. 100.
For an income of Rs. 6, investment = Rs.(100/8x6) = Rs. 75.
∴ Market value of Rs.100 stock = Rs. 75.
Answer B | college_mathematics | mathematics |
NLP4Education_389 | NLP4Education | Let $G$ be a group generated by $g$. What is the discrete logarithm problem?
A. Find $y$ such that $g^x = y$ for a given $x$.
B. Find $x$ such that $g^x = y$ for a given $y$.
C. Find $x, y$ such that $g^x = y$.
D. Find $x, x'$ such that $g^x = g^{x'}$ and $x \ne x'$. | B. Find $x$ such that $g^x = y$ for a given $y$. | abstract_algebra | mathematics | ||
mmlu_aux_train_70109 | mmlu_aux_train | Most young boys don't like growing flowers and watering them. But for 16-year-old Angus,working in the garden isn't just a hobby -- it has changed his life. Angus has a special illness and his IQ is lower than a normal boy. Six months ago, he started learning how to grow flowers. Now, he spends hours in the garden grow... | B. learn how to grow flowers | high_school_biology | biology | ||
aquarat_11142 | deepmind/aqua_rat | If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 13.2
II. 12.3
III. 9.3 | A. I only B. I and II only C. II only D. III only E. I and III only | D. III only | Mean = 12
SD = 1.3
2 SD above mean = 12+2*1.3 = 14.6
2 SD below mean = 12-2*1.3 = 9.4
12.3 and 13.2 lies in the range of 2SD from mean
Answer: Option D | high_school_statistics | mathematics |
allenai/sciq_424 | allenai/sciq | What kind of mountainous formation can often be found near trenches?
A. caves
B. craters
C. volcanoes
D. earthquakes | C. volcanoes | deep sea trenches : Trenches are found in the sea. Some are near the edges of continents. Trenches are found near chains of active volcanoes. An example is the line of the very deepest blue, off of western South America. | earth_science | earth_science | |
math_1118 | math_mc | The vertices $V$ of a centrally symmetric hexagon in the complex plane are given by \[V=\left\{ \sqrt{2}i,-\sqrt{2}i, \frac{1}{\sqrt{8}}(1+i),\frac{1}{\sqrt{8}}(-1+i),\frac{1}{\sqrt{8}}(1-i),\frac{1}{\sqrt{8}}(-1-i) \right\}.\]For each $j$, $1\leq j\leq 12$, an element $z_j$ is chosen from $V$ at random, independentl... | D | math_Intermediate Algebra | mathematics | ||
math_251 | math_mc | The red parabola shown is the graph of the equation $x = ay^2 + by + c$. Find $a+b+c$.
[asy]
size(150);
real ticklen=3;
real tickspace=2;
real ticklength=0.1cm;
real axisarrowsize=0.14cm;
pen axispen=black+1.3bp;
real vectorarrowsize=0.2cm;
real tickdown=-0.5;
real tickdownlength=-0.15inch;
real tickdownbase=0.3;
re... | D | math_Algebra | mathematics | ||
math_1019 | math_mc | Let $ABCDEF$ be a regular hexagon, and let $G,H,I$ be the midpoints of sides $AB,CD,EF$ respectively. If the area of $\triangle GHI$ is $225$, what is the area of hexagon $ABCDEF$? | C | math_Geometry | mathematics | ||
aquarat_775 | deepmind/aqua_rat | A pharmaceutical company received $2 million in royalties on the first $12; million in sales of generic equivalent of one of its products and then $4 million in royalties on the next $48 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $12 million in sales to t... | A. 20% B. 25% C. 30% D. 50% E. 55% | D. 50% | change in ratio of royalties to sales = 2/12 -4/48 = 1/12
% decrease = (1/12)/(2/12) *100 = 50% (approx)
Answer: D) | college_mathematics | mathematics |
NLP4Education_660 | NLP4Education | Tick the assertion related to an open problem.
A. NP ⊆ IP.
B. P ⊆ IP.
C. PSPACE = IP.
D. NP = co-NP. | D. NP = co-NP. | computer_security | computer_science | ||
aquarat_55321 | deepmind/aqua_rat | Series E(n) is such that i*E(i) = j*E(j) for any pair of positive integers (i, j). If E(1) is a positive integer, which of the following is possible?
I. 2*E(100) = E(99) + E(98)
II. E(1) is the only integer in the series
III. The series does not contain negative numbers | A. I only B. II only C. IIII only D. IIIII only E. I, IIIII | D. IIIII only | First thing I want to understand is this relation: i*E(i) = j*E(j) for any pair of positive integers. I will take examples to understand it.
When i = 1 and j = 2, E(1) = 2*E(2)
So E(2) = E(1)/2
When i = 1 and j = 3, E(1) = 3*E(3)
So E(3) = E(1)/3
I see it now. The series is: E(1), E(1)/2, E(1)/3, E(1)/4 and so on...
II... | college_mathematics | mathematics |
NLP4Education_618 | NLP4Education | Tick the \textbf{false} assertion. Assume that $C$ is a random permutation.
A. $\mathrm{BestAdv}_n(C,C^*) = \frac{1}{2}\mathrm{Dec}^n_{\left|\left|\left|\cdot\right|\right|\right|_a}(C)$
B. $\mathrm{BestAdv}_n^{n.a.}(C,C^*) = \frac{1}{2}\mathrm{Dec}^n_{\left|\left|\left|\cdot\right|\right|\right|_\infty}(C)$
C. $\mathb... | D. $\mathrm{Dec}^n(C\circ C) \leq \mathrm{Dec}^n(C)^2$ | computer_security | computer_science | ||
mmlu_aux_train_28129 | mmlu_aux_train | Not long ago, many people believed that babies only wanted food and to be kept warm and dry. Some people thought babies were not able to learn things until they were five or six months old. Yet doctors in the United States say babies begin learning on their first day of life. The Eunice Kennedy Shriver National Institu... | D. at or after five or six months old | high_school_biology | biology | ||
math_2026 | math_mc | The figure shows a square of side $y$ units divided into a square of side $x$ units and four congruent rectangles. What is the perimeter, in units, of one of the four congruent rectangles? Express your answer in terms of $y$. [asy]
size(4cm);
defaultpen(linewidth(1pt)+fontsize(12pt));
draw((0,0)--(0,4)--(4,4)--(4,0)--c... | A | math_Prealgebra | mathematics | ||
NLP4Education_328 | NLP4Education | If A={a} and B={b}, select all strings that belong to (A ⊗ B)+
A penalty will be applied for any wrong answers selected.
A. (a,bb)
B. (aaa,bb)
C. (a,b)
D. (aa,bbb) | C. (a,b) | abstract_algebra | mathematics | ||
math_2192 | math_mc | Let $P$ be a plane passing through the origin. When $\begin{pmatrix} 5 \\ 3 \\ 5 \end{pmatrix}$ is projected onto plane $P,$ the result is $\begin{pmatrix} 3 \\ 5 \\ 1 \end{pmatrix}.$ When $\begin{pmatrix} 4 \\ 0 \\ 7 \end{pmatrix}$ is projected onto plane $P,$ what is the result? | A | math_Precalculus | mathematics | ||
aquarat_94897 | deepmind/aqua_rat | Find the remainder T 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 T-1. so in the numerator we have -12. Now acccording to remainder theorm the answer will be 1729-12=1717.D | college_mathematics | mathematics |
math_769 | math_mc | A circle with center $O$ has radius 25. Chord $\overline{AB}$ of length 30 and chord $\overline{CD}$ of length 14 intersect at point $P$. The distance between the midpoints of the two chords is 12. The quantity $OP^2$ can be represented as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find th... | B | math_Geometry | mathematics | ||
math_354 | math_mc | Suppose functions $g$ and $f$ have the properties that $g(x)=3f^{-1}(x)$ and $f(x)=\frac{24}{x+3}$. For what value of $x$ does $g(x)=15$? | C | math_Algebra | mathematics | ||
aquarat_73843 | deepmind/aqua_rat | What are the next two letters in the following series and why?
W A T N T L I T F S _ _
*Hint : Look into the title of the Riddle | A. A and W B. A and E C. B and W D. A and C E. S and W | A. A and W | A
A and W.
The letters are the first letters of the words in the question. Thus, the next two letters are A and W. | formal_logic | mathematics |
allenai/sciq_4403 | allenai/sciq | Water is the solvent in solutions called acids and?
A. bases
B. proteins
C. nutrients
D. alkalines | A. bases | Water is the solvent in solutions called acids and bases. To understand acids and bases, it is important to know more about pure water, in which nothing is dissolved. In pure water (such as distilled water), a tiny fraction of water molecules naturally breaks down, or dissociates, to form ions. An ion is an electricall... | high_school_chemistry | chemistry | |
allenai/sciq_2880 | allenai/sciq | What type of rocks are very useful for determining the deformation history of an area?
A. sedimentary
B. crystalline
C. igneous
D. limestone | A. sedimentary | Sedimentary rocks are very useful for determining the deformation history of an area. | college_geology | earth_science | |
pythonio_44 | pythonio-mc | Program:
def check_string(str1):
messg = [
lambda str1: any(x.isupper() for x in str1) or 'String must have 1 upper case character.',
lambda str1: any(x.islower() for x in str1) or 'String must have 1 lower case character.',
lambda str1: any(x.isdigit() for x in str1) or 'String must have 1 number.'... | C | code | computer_science | ||
allenai/sciq_1429 | allenai/sciq | What is an attitude of doubt about the truthfulness of claims that lack empirical evidence?
A. conspiracy
B. speculation
C. independent variable
D. skepticism | D. skepticism | Skepticism is an attitude of doubt about the truthfulness of claims that lack empirical evidence. Scientific skepticism , also referred to as skeptical inquiry, questions claims based on their scientific verifiability rather than simply accepting claims based on faith or anecdotes. Scientific skepticism uses critical t... | formal_logic | mathematics | |
NLP4Education_658 | NLP4Education | Consider an arbitrary cipher $C$ and a uniformly distributed random permutation $C^*$ on $\{0,1\}^n$. Tick the \textbf{false} assertion.
A. $\mathsf{Dec}^1(C)=0$ implies $C=C^*$.
B. $\mathsf{Dec}^1(C)=0$ implies $[C]^1=[C^*]^1$.
C. $\mathsf{Dec}^1(C)=0$ implies that $C$ is perfectly decorrelated at order 1.
D. $\mathsf... | A. $\mathsf{Dec}^1(C)=0$ implies $C=C^*$. | computer_security | computer_science | ||
mmlu_aux_train_50904 | mmlu_aux_train | Large areas of the Amazon rainforest were grassland until just 2,000 years ago when it has been found. Researchers say the find gives new light on the Amazon's history - and show it was a savannah rather than the high forest it is today. They believe much of the area was grassland until a natural shift to a wetter cl... | B. History of the Amazon rainforests. | college_biology | biology | ||
pythonio_509 | pythonio-mc | Program:
import re
def replace_specialchar(text):
return (re.sub("[ ,.]", ":", text))
Input:
replace_specialchar('a b c,d e f')
Output: | C | code | computer_science | ||
aquarat_64658 | deepmind/aqua_rat | If $10,000,000 is the initial amount placed in an account that collects 7% annual interest, which of the following compounding rates would produce the largest total amount after two years? | A. compounding annually B. compounding quarterly C. compounding daily D. compounding monthly E. All four of these would produce the same total | C. compounding daily | Answer = C Compounding daily
This will produce the maximum yield as the interest accured each day will be added the very next day to the Principal amount for further computation of interest.
This process will be repeated every day till the amount matures
Compounding annually will give least returns | college_mathematics | mathematics |
allenai/sciq_3965 | allenai/sciq | What is the cause of existence of molecular solids and liquids?
A. attractive forces
B. few forces
C. popular forces
D. negative forces | A. attractive forces | college_chemistry | chemistry | ||
NLP4Education_669 | NLP4Education | Tick the \emph{true} assertion. A distinguishing attack against a block cipher\dots
A. is a probabilistic attack.
B. succeeds with probability $1$.
C. outputs the secret key.
D. succeeds with probability $0$. | A. is a probabilistic attack. | computer_security | computer_science | ||
math_105 | math_mc | Find the product of all real values of $r$ for which $\frac{1}{2x}=\frac{r-x}{7}$ has exactly one real solution. | B | math_Algebra | mathematics | ||
aquarat_19310 | deepmind/aqua_rat | A survey was sent to 70 customers, 7 of whom responded. Then the survey was redesigned and sent to another 63 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey? | A. 2% B. 6% C. 4% D. 28% E. 63% | C. 4% | case 1: (7/70)=x/100
x=10%
case 2: (9/63)=y/100
y=14%
So percent increase is =(y-x)=(14-10)%=4%
Answer is C | high_school_statistics | mathematics |
mmlu_aux_train_63608 | mmlu_aux_train | If you ask Americans whether or not they think their former president George W. Bush is smart, most of them will probably tell you they don't think so. However, Bush's IQ score is estimated to be above 120, which puts him in the top ten percent of the population. It doesn't seem to make sense. How come someone with suc... | B. mental faculties | formal_logic | mathematics | ||
math_1061 | math_mc | A circle of radius 1 is surrounded by 4 circles of radius $r$ as shown. What is $r$?
[asy]
unitsize(0.6cm);
for(int i=0; i<2; ++i){
for(int j=0; j<2; ++j){
draw(Circle((-2.4+4.8i,-2.4+4.8j),2.4),linewidth(0.7));
draw((-2.4+4.8i,-2.4+4.8j)--(-0.7+4.8i,-0.7+4.8j));
label("$r$",(-1.5+4.8i,-1.5+4.8j),SE);
};
}
draw(Circle... | A | math_Geometry | mathematics | ||
mmlu_aux_train_59338 | mmlu_aux_train | About l,500 years ago the Japanese imported many aspects of Chinese culture :the writing system, political institutions, and perhaps the most important, Buddhism. Buddhist priests were expected to eat only vegetables, and tofu, made from the soybean, was a very important food in their diet.When Buddhism was introduced ... | B. it was a very important food in the diet of Buddhist priests | high_school_biology | biology | ||
allenai/sciq_8240 | allenai/sciq | What is used to convert concentrations to collisions per second?
A. frequency factor
B. particles factor
C. collision meter
D. speeds factor | A. frequency factor | The frequency factor is used to convert concentrations to collisions per second. Equation 14.39 is known as the Arrhenius equation and summarizes the collision model of chemical kinetics, where T is the absolute temperature (in K) and R is the ideal gas constant [8.314 J/(K·mol)]. Ea indicates the sensitivity of the re... | high_school_chemistry | chemistry | |
NLP4Education_110 | NLP4Education | Data being classified as unstructured or structured depends on the:
A. Level of human involvement
B. Degree of abstraction
C. Amount of data
D. Type of physical storage | B. Degree of abstraction | college_computer_science | computer_science | ||
NLP4Education_53 | NLP4Education | Consider: Non-terminals: S (top-level), NP (for "noun phrase"), VP (for "verbal phrase"), N (for "Noun"), V (for "Verb"), Det (for "Determiner"). PoS tags: N, V, Det Terminals: I, yesterday, in, rain, went, home, the, cat, go Out of the following, select the ones which are possible valid "syntactic rules" as defined in... | A. NP → Det N | formal_logic | mathematics | ||
allenai/sciq_10742 | allenai/sciq | The posterior pituitary is an extension of what anatomical structure?
A. hypothalamus
B. brain stem
C. hippocampus
D. frontal lobe | A. hypothalamus | anatomy | biology | ||
mmlu_aux_train_7071 | mmlu_aux_train | Generations of Americans have been brought up to believe that a good breakfast is essential to one's life. Eating breakfast at the start of the day, we have been told, and told again, is as necessary as putting gasoline in the family car before starting a trip. But for many people, the thought of food as the first thin... | D. breakfast is not as important as we thought before | high_school_statistics | mathematics | ||
math_1315 | math_mc | Find the remainder when $x^{100}$ is divided by $(x + 1)^3.$ | B | math_Intermediate Algebra | mathematics | ||
NLP4Education_425 | NLP4Education | Tick the \emph{incorrect} assertion. The Diffie-Hellman key agreement protocol \ldots
A. allows two participants to set up a key so that they can communicate securely.
B. requires the hardness of the Discrete Logarithm problem.
C. uses ElGamal encryption in order to establish the key.
D. is easy to break when working o... | C. uses ElGamal encryption in order to establish the key. | computer_security | computer_science | ||
math_1742 | math_mc | What is $\frac{1357_{9}}{100_{4}}-2460_{8}+5678_{9}$? Express your answer in base 10. | C | math_Number Theory | mathematics | ||
NLP4Education_788 | NLP4Education | Let $G_1, G_2$, be valid generator matrices of dimensions $\mathbb F^{k_i \times n_i}$, all over the same field $\mathbb F$. Recall that ``valid'' means that for all $i$, $k_i \leq n_i$ and $\text{rank}(G_i) = k_i$. True or false: Assuming $k_1 = k_2$ and $n_1=n_2$, the matrix $G_{7} + G_{8}$ is also a valid generator... | B. Always false | abstract_algebra | mathematics | ||
allenai/sciq_11494 | allenai/sciq | What type of boiling point do nonmetals normally have?
A. even
B. odd
C. low
D. high | C. low | Properties of nonmetals include a relatively low boiling point, so many nonmetals are gases. Nonmetals are also poor conductors of heat, and solid nonmetals are dull and brittle. | high_school_chemistry | chemistry | |
NLP4Education_518 | NLP4Education | MD5 is
A. a secure block cipher
B. a broken block cipher
C. a secure hash function
D. a broken hash function | D. a broken hash function | computer_security | computer_science | ||
mmlu_aux_train_35846 | mmlu_aux_train | Charles Darwin (1809 - 1882) was a great naturalist, famous for his theory of evolution . One day two boys decided to play a trick on the great man. They took the body of a centipede , the head of a beetle , the leg of a grasshopper , and the wings of a butterfly, and glued them together. Putting the strange creatu... | B. 73 | high_school_biology | biology | ||
math_1728 | math_mc | What is the least positive integer $n$ such that $n^2 - n$ is divisible by some but not all integer values of $k$ when $1\leq k \leq n$? | B | math_Number Theory | mathematics | ||
mmlu_aux_train_92928 | mmlu_aux_train | If a classroom experiment involves the use of several unidentified chemical solutions, which factor would be most important in maintaining safety during the experiment?
A. The classroom would be fairly cold.
B. The classroom would have poor lighting.
C. The classroom would have good ventilation.
D. The classroom would... | C. The classroom would have good ventilation. | high_school_chemistry | chemistry | ||
allenai/sciq_7814 | allenai/sciq | What type of metal is a good conductor of electricity?
A. copper
B. Aluminium
C. zinc
D. Tin | A. copper | Copper is a good conductor of electricity. That's why electric wires are often made of copper. They are covered with a protective coating of plastic, which does not conduct electricity. | high_school_chemistry | chemistry | |
math_483 | math_mc | We call a number a mountain number if its middle digit is larger than any other digit. For example, 284 is a mountain number. How many 3-digit mountain numbers are there? | A | math_Counting & Probability | mathematics | ||
aquarat_9243 | deepmind/aqua_rat | 300 first-time customers of a fashion store were surveyed for their shopping experience right after leaving the store. 60% of the customers in the survey had purchased clothes for less than $100. 40% of the customers in the survey reported they were overall satisfied with their purchase. 65% of the customers that had p... | A. 1 B. 25 C. 35 D. 45 E. 75 | A. 1 | Out of 300 - 180 purchased for less than 100$120 for more
Out of 300 - 120 responded as satisfied and 180 responded disatisfied
Out of 180 ( Purchased less than 100$) - 65% = 117 responded as satisfied, So remaining Satisfied are 120 - 117 = 3
so 3 is what percentage of 300 - 1%
So the answer should be A | high_school_statistics | mathematics |
NLP4Education_493 | NLP4Education | If we need to create a channel that protects confidentiality and we have at our disposal a channel that protects integrity and authenticity, we need to use
A. symmetric key encryption.
B. message authentication codes.
C. public key encryption.
D. digital signatures. | C. public key encryption. | computer_security | computer_science | ||
allenai/sciq_970 | allenai/sciq | The symbol for each what is usually the first letter or two of its name?
A. property
B. material
C. state
D. element | D. element | high_school_chemistry | chemistry | ||
math_1396 | math_mc | Let $A = (-3, 0),$ $B=(-2,1),$ $C=(2,1),$ and $D=(3,0).$ Suppose that point $P$ satisfies \[PA + PD = PB + PC = 8.\]Then the $y-$coordinate of $P,$ when simplified, can be expressed in the form $\frac{-a + b \sqrt{c}}{d},$ where $a,$ $b,$ $c,$ $d$ are positive integers. Find $a + b + c + d.$ | C | math_Intermediate Algebra | mathematics | ||
math_115 | math_mc | What is the sum of the squares of the coefficients of $4(x^4 + 3x^2 + 1)$? | D | math_Algebra | mathematics |
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