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 |
|---|---|---|---|---|---|---|---|
pythonio_808 | pythonio-mc | Program:
def find_Extra(arr1,arr2,n) :
for i in range(0, n) :
if (arr1[i] != arr2[i]) :
return i
return n
Input:
find_Extra([1,3,5,7,9,11],[1,3,5,7,9],5)
Output: | C | code | computer_science | ||
math_2018 | math_mc | In the diagram, $AB = 13\text{ cm},$ $DC = 20\text{ cm},$ and $AD = 5\text{ cm}.$ What is the length of $AC,$ to the nearest tenth of a centimeter?
[asy]
draw((0,0)--(5,12)--(21,12)--(5,0)--cycle,black+linewidth(1));
draw((5,12)--(5,0),black+linewidth(1));
draw((0,0)--(21,12),black+linewidth(1));
draw((5,0)--(5,0.5)--... | C | math_Prealgebra | mathematics | ||
mmlu_aux_train_89935 | mmlu_aux_train | Since the first Earth Day started on April 22, 1970, people around the world have been encouraged to protect the environment and natural resources.Gaylord Nelson started this holiday.On the first Earth Day, 20 million people took part in Earth Day events. Earth Day activities can include learning something about techno... | C. More than ten years. | high_school_chemistry | chemistry | ||
allenai/sciq_1160 | allenai/sciq | A light bulb converts electrical energy to light and what?
A. visible energy
B. thermal energy
C. kinetic energy
D. chemical energy | B. thermal energy | Most circuits have devices such as light bulbs that convert electrical energy to other forms of energy. In the case of a light bulb, electrical energy is converted to light and thermal energy. | conceptual_physics | physics | |
mmlu_aux_train_98128 | mmlu_aux_train | In an arid location, any various lifeforms will have to
A. work harder for nutriment
B. find food quite easily
C. find fast, easy nutriment
D. always eat their fill | A. work harder for nutriment | high_school_biology | biology | ||
aquarat_47141 | deepmind/aqua_rat | In Winchard's company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn $49,000 a year. What is the median salary for the company? | A. 43.0 B. 45.5 C. 46.0 D. 49.0 E. 50.0 | A. 43.0 | In Winchard's company 60% of the employees earn less than $50,000 a year, 50 and 51 employee will be each 43K. hence median = (43K+43k)/2=A | high_school_statistics | mathematics |
math_1393 | math_mc | Let $A = (1,0),$ $B = (4,3),$ and $C = (p,q)$ be three points on the parabola $y = -x^2 + 6x - 5,$ where $1 \le p \le 4.$ Find the largest possible area of triangle $ABC.$ | A | math_Intermediate Algebra | mathematics | ||
allenai/sciq_8463 | allenai/sciq | Phospholipids and some proteins move laterally within what?
A. nuclei
B. liquids
C. particles
D. membrane | D. membrane | college_biology | biology | ||
aquarat_23941 | deepmind/aqua_rat | If PINTU is coded as 79523 in a certain code language, how would you code DUMBO in the same language? | A. 43426 B. 14236 C. 13436 D. 14263 E. 15263 | A. 43426 | 1 2 3 4 5 6 7 8 9
a b c d e f g h i
j k l m n o p q r
s t u v w x y z
sooo...DUMBO is 43426...
ANSWER:A | formal_logic | mathematics |
mmlu_aux_train_88644 | mmlu_aux_train | Mary is an American schoolgirl. She is now in Beijing with her parents. She doesn't know Chinese, but she is trying to study and speak it. She often tries to speak Chinese to her Chinese friends. Sometimes they don't understand her, because she can't speak Chinese well. It's Saturday morning. Mary goes out. She is on h... | C. China | high_school_computer_science | computer_science | ||
allenai/sciq_2999 | allenai/sciq | What do you call the fragments of cells involved in the clotting process that are suspended in blood plasma?
A. platelets
B. ironites
C. hematocrit
D. hemoglobin | A. platelets | high_school_biology | biology | ||
math_1856 | math_mc | Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a standard television screen is $4:3$. What is the horizontal length (in inches) of a ``27-inch'' television screen?
[asy]
fill((0,0)--(8,0)--(8,6)--cycle,gray(0.7));
draw((0,0... | B | math_Prealgebra | mathematics | ||
math_2191 | math_mc | The matrix
\[\begin{pmatrix} a & \frac{15}{34} \\ c & \frac{25}{34} \end{pmatrix}\]corresponds to a projection. Enter the ordered pair $(a,c).$ | B | math_Precalculus | mathematics | ||
allenai/sciq_4197 | allenai/sciq | Changes in the color of the statue of liberty owe to oxidation-reduction reactions, or what simpler term?
A. immersion
B. oxygen
C. corrosion
D. copper | C. corrosion | Chemistry in Everyday Life Statue of Liberty: Changing Colors The Statue of Liberty is a landmark every American recognizes. The Statue of Liberty is easily identified by its height, stance, and unique blue-green color (Figure 17.16). When this statue was first delivered from France, its appearance was not green. It wa... | high_school_chemistry | chemistry | |
aquarat_62660 | deepmind/aqua_rat | If abc ≠ 3 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) | D. (1 – b – c)/(bc) | Answer is D though it took me around 4 minutes to get that. | college_mathematics | mathematics |
math_791 | math_mc | Line $l_1$ has equation $3x - 2y = 1$ and goes through $A = (-1, -2)$. Line $l_2$ has equation $y = 1$ and meets line $l_1$ at point $B$. Line $l_3$ has positive slope, goes through point $A$, and meets $l_2$ at point $C$. The area of $\triangle ABC$ is $3$. What is the slope of $l_3$? | B | math_Geometry | mathematics | ||
math_260 | math_mc | A portion of the graph of $f(x)=ax^2+bx+c$ is shown below. The distance between grid lines on the graph is $1$ unit.
What is the value of $a+b+2c$?
[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=-... | C | math_Algebra | mathematics | ||
math_1602 | math_mc | There are positive integers $x$ and $y$ that satisfy the system of equations\begin{align*} \log_{10} x + 2 \log_{10} (\text{gcd}(x,y)) &= 60\\ \log_{10} y + 2 \log_{10} (\text{lcm}(x,y)) &= 570. \end{align*}Let $m$ be the number of (not necessarily distinct) prime factors in the prime factorization of $x$, and let $n$ ... | C | math_Number Theory | mathematics | ||
allenai/sciq_3923 | allenai/sciq | What are 3 types of light?
A. infrared, visible, ultraviolet
B. complementary, incandescent, fluorescent
C. diffuse, ambient, opaque
D. solar , visible , ultraviolet | A. infrared, visible, ultraviolet | Electromagnetic waves that are commonly called light fall roughly in the middle of the electromagnetic spectrum. Light includes infrared light, visible light, and ultraviolet light. | high_school_physics | physics | |
NLP4Education_424 | NLP4Education | What are the complexities for the single-target dictionary attacks, when there are $N$ keys?
A. Preprocessing: $N$, Memory: $N$, Time: 1
B. Preprocessing: $N$, Memory: $1$, Time: $N$
C. Preprocessing: $1$, Memory: $N$, Time: $N$
D. Preprocessing: $0$, Memory: $1$, Time: $\sqrt{N}$ | A. Preprocessing: $N$, Memory: $N$, Time: 1 | computer_security | computer_science | ||
math_939 | math_mc | In the middle of a vast prairie, a firetruck is stationed at the intersection of two perpendicular straight highways. The truck travels at $50$ miles per hour along the highways and at $14$ miles per hour across the prairie. Consider the set of points that can be reached by the firetruck within six minutes. The area of... | B | math_Geometry | mathematics | ||
mmlu_aux_train_92929 | mmlu_aux_train | Vein deposits of gold and silver are often formed in areas that have experienced which geologic process?
A. igneous intrusion
B. transport by water
C. chemical weathering
D. compaction by pressure | A. igneous intrusion | college_earth_science | earth_science | ||
mmlu_aux_train_18715 | mmlu_aux_train | Podcasting is like radio broadcasting, except that it uses the Internet. Anyone with a computer and a microphone can record a show about any subject. Anyone with a computer and an MP3 player can download the podcasts and listen. Podcasting does require some technical knowledge, but not very much. Many education-relate... | B. it makes use of the Internet | high_school_computer_science | computer_science | ||
allenai/sciq_9579 | allenai/sciq | Some viruses carry a few viral enzyme molecules within their what?
A. DNA
B. capsids
C. plastids
D. hormones | B. capsids | virology | biology | ||
mmlu_aux_train_35515 | mmlu_aux_train | Recently,scientists attending a meeting in Chicago presented new studies showing how food and its production affect global warming.They offered some suggestions for how to eat in a more environmentally friendly way. For many years,scientists have warned us that our planet is getting warmer.If current trends continue,an... | A. what we eat can affect the whole planet | college_biology | biology | ||
math_275 | math_mc | The quadratic $3x^2+4x-9$ has two real roots. What is the sum of the squares of these roots? Express your answer as a common fraction in lowest terms. | A | math_Algebra | mathematics | ||
NLP4Education_245 | NLP4Education | Assume that we have a convolutional neural net with $L$ layers, $K$ nodes per layer, and where each node is connected to $k$ nodes in a previous layer. We ignore in the sequel the question of how we deal with the points at the boundary and assume that $k\ll\ll\ll K$ (much, much, much smaller). How does the complexity o... | D. $\Theta(L K k)$ | machine_learning | computer_science | ||
allenai/sciq_9275 | allenai/sciq | Roundworms are intervertebrates that belong to which phylum?
A. amoebozoa
B. nematoda
C. Gordiacea
D. annelida | B. nematoda | Roundworms are invertebrates in Phylum Nematoda. Roundworms have a pseudocoelom and complete digestive system. They are free-living heterotrophs or parasites. | high_school_biology | biology | |
allenai/sciq_11398 | allenai/sciq | What is created by the polymerization of glucose?
A. glucose
B. cellulose
C. carbonate
D. methane | B. cellulose | Zachary Wilson. Cellulose is created by the polymerization of glucose . CC BY-NC 3.0. | college_biology | biology | |
allenai/sciq_2555 | allenai/sciq | What is the process by which plants gain energy and produce sugar?
A. photosynthesis
B. glycolysis
C. respiration
D. chemosynthesis | A. photosynthesis | 13 Photosynthesis 6 CO2 + 6 H2 O → C6 H12 O6 + 6 O2 • One of most important reactions in history of life: • source of atmospheric O2 • ultimately led to aerobic respiration and eukaryotes • Responsible for bulk of glucose production • Early experiments showed that mass of plant must be derived from substances in the ai... | high_school_biology | biology | |
mmlu_aux_train_14181 | mmlu_aux_train | We gather a great deal of incidental knowledge from pets.If we look after them properly we learn what they like and dislike. We do not set out to gain this knowledge purposely, but in attending to our pets we gain it by the way. It is got without our realizing it. In keeping our dogs or cats we learn about various ... | C. human beings can gain knowledge by keeping pets | high_school_biology | biology | ||
NLP4Education_152 | NLP4Education | Given graph 1→2, 1→3, 2→3, 3→2, switching from Page Rank to Teleporting PageRank will have an influence on the value(s) of:
A. Node 1
B. Nodes 2 and 3
C. No nodes. The values will stay unchanged.
D. All the nodes | D. All the nodes | college_computer_science | computer_science | ||
math_929 | math_mc | Square $ABCD$ has sides of length 2. Set $S$ is the set of all line segments that have length 2 and whose endpoints are on adjacent sides of the square. The midpoints of the line segments in set $S$ enclose a region whose area to the nearest hundredth is $k$. Find $100k$.
| A | math_Geometry | mathematics | ||
math_73 | math_mc | Let $f(x)$ be the function defined on $-1\le x\le 1$ by the formula $$f(x)=1-\sqrt{1-x^2}.$$This is a graph of $y=f(x)$: [asy]
import graph; size(4cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-1.5,xmax=1.5,ymin=-1.5,ymax=1.5;
pen cqcqcq=rgb(0.75,0.75,0.75);
/*grid*/... | C | math_Algebra | mathematics | ||
aquarat_57283 | deepmind/aqua_rat | The probability that an electronic device produced by a company does not function properly is equal to 0.1. If 10 devices are bought, then the probability, to the nearest thousandth, that 7 devices function properly is | A. 0.057 B. 0.478 C. 0.001 D. 0 E. None | A. 0.057 | Solution
Let q being the probability a device does not function properly and p = 1 - q = 0.9 the probability that a device functions properly. Since there are only two possible results, it is a binomial distribution. The P probability that 7 out of 10 devices function properly is given by
C(10,7)*0.9 7*0.1 3 , where C(... | high_school_statistics | mathematics |
NLP4Education_576 | NLP4Education | Choose the \emph{correct} statement.
A. $\mathbb{Z}_n$ is a field $\Leftrightarrow$ $n$ is a composite number
B. $\mathbb{Z}_n$ is a field $\Leftrightarrow$ $\mathbb{Z}_n^* = \mathbb{Z}_n$
C. $\mathbb{Z}_n$ is a field $\Leftrightarrow$ $n$ is a prime
D. $\mathbb{Z}_n$ is a field $\Leftrightarrow$ $\mathbb{Z}_n^* = \emp... | C. $\mathbb{Z}_n$ is a field $\Leftrightarrow$ $n$ is a prime | abstract_algebra | mathematics | ||
mmlu_aux_train_92920 | mmlu_aux_train | Which rapid changes are caused by heat from inside Earth?
A. landslides
B. volcanoes
C. avalanches
D. floods | B. volcanoes | earth_science | earth_science | ||
math_117 | math_mc | The inverse of $f(x) = \frac{2x-1}{x+5}$ may be written in the form $f^{-1}(x)=\frac{ax+b}{cx+d}$, where $a$, $b$, $c$, and $d$ are real numbers. Find $a/c$. | A | math_Algebra | mathematics | ||
math_1619 | math_mc | A number is divisible by $9$ if the sum of its digits is divisible by $9.$ For example, the number $19\,836$ is divisible by $9$ but $19\,825$ is not.
If $D\,767\,E89$ is divisible by $9,$ where $D$ and $E$ each represent a single digit, what is the sum of all possible values of the sum $D+E?$ | D | math_Number Theory | mathematics | ||
aquarat_43868 | deepmind/aqua_rat | Bilal and Ahmed play the following game with n sticks on a table. Each must remove 1,2,3,4, or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. The one who removes the last stick (or sticks) from the table wins. If Bilal goes first, which of the following is a value of n suc... | A. 7 B. 10 C. 11 D. 12 E. 16 | D. 12 | If the number of sticks on a table is a multiple of 6, then the second player will win in any case (well if the player is smart enough).
Consider n=6, no matter how many stick will be removed by the first player (1, 2, 3 ,4 or 5), the rest (5, 4, 3, 2, or 1) can be removed by the second one.
The same for n=12: no matte... | formal_logic | mathematics |
mmlu_aux_train_83712 | mmlu_aux_train | Mary: Let's play computer games. Gina: That sounds great. Where is your computer? Mary: I don't have a computer. Do you have a computer? Gina: No, I don't. But I have a TV. Let's watch TV. Mary: No, that sounds boring. Let's play tennis. I have a tennis bat. Gina: Good. Where is it? Mary: On the sofa. Do you have a bat... | C. a tennis bat | high_school_computer_science | computer_science | ||
mmlu_aux_train_99661 | mmlu_aux_train | Desalinating water from the ocean does what to nearby fish?
A. helps them out
B. makes habitat nicer
C. gives them money
D. demolishes habitat | D. demolishes habitat | college_biology | biology | ||
mmlu_aux_train_98174 | mmlu_aux_train | If you are stuck in the desert and need your water to last you, it is best to
A. throw it away
B. hit it
C. safeguard it
D. sell it | C. safeguard it | high_school_biology | biology | ||
math_1401 | math_mc | Let $x$ and $y$ be real numbers such that
\[4x^2 + 8xy + 5y^2 = 1.\]Let $m$ and $M$ be the minimum and maximum values of $2x^2 + 3xy + 2y^2,$ respectively. Find the product $mM.$ | D | math_Intermediate Algebra | mathematics | ||
math_913 | math_mc | Two skaters, Allie and Billie, are at points $A$ and $B$, respectively, on a flat, frozen lake. The distance between $A$ and $B$ is $100$ meters. Allie leaves $A$ and skates at a speed of $8$ meters per second on a straight line that makes a $60^\circ$ angle with $AB$. At the same time Allie leaves $A$, Billie leaves $... | A | math_Geometry | mathematics | ||
allenai/sciq_2584 | allenai/sciq | What type of feeders are sea lilies and feather stars?
A. deposit feeder
B. suspension feeders
C. silt feeders
D. bottom feeder | B. suspension feeders | Explore the sea star’s body plan (http://openstaxcollege. org/l/sea_star) up close, watch one move across the sea floor, and see it devour a mussel. Brittle stars belong to the class Ophiuroidea. Unlike sea stars, which have plump arms, brittle stars have long, thin arms that are sharply demarcated from the central dis... | high_school_biology | biology | |
pythonio_245 | pythonio-mc | Program:
def floor_Min(A,B,N):
x = max(B - 1,N)
return (A*x) // B
Input:
floor_Min(11,10,9)
Output: | C | code | computer_science | ||
math_421 | math_mc | Rationalize the denominator of $\displaystyle \frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}$, and write your answer in the form \[
\frac{A\sqrt{2} + B\sqrt{3} + C\sqrt{7} + D\sqrt{E}}{F},
\]where everything is in simplest radical form and the fraction is in lowest terms, and $F$ is positive. What is $A + B + C + D + E + F$? | A | math_Algebra | mathematics | ||
math_2063 | math_mc | Express $4.\overline{054}$ as a common fraction in lowest terms. | B | math_Prealgebra | mathematics | ||
pythonio_903 | pythonio-mc | Program:
import re
def num_position(text):
for m in re.finditer("\d+", text):
return m.start()
Input:
num_position("isha has 79 chocolates in her bag")
Output: | A | code | computer_science | ||
aquarat_17527 | deepmind/aqua_rat | Which of the following reaches the largest value over the range -1 <= R <= 1? | A. (R+3)^100 B. (R+3)/(R^100) C. (R+1000) D. 97^97 E. (R/2R) | B. (R+3)/(R^100) | (R+3)/(R^100) can be equal any arbitrarily large number. Some of the other options are large, but they all have a definite maximum. (R+3)/(R^100) does not, so the correct answer is B. | college_mathematics | mathematics |
aquarat_48176 | deepmind/aqua_rat | For which of the following functions f is f(a) = f(1-a) for all a? | A. f (x) = 1 - x B. f (a) = 1 - a^2 C. f (a) = a^2 - (1 - a)^2 D. f (a) = a^2*(1 - a)^2 E. f (x) = x/(1 - x) | D. f (a) = a^2*(1 - a)^2 | I remember seeing this problem in a GMATprep test. I think choice D should be F(a)=(a^2) (1-a)^2. If that is true then substituting (1-a) for will give us the same function back and the answer choice is D, where the function is multiplicative | college_mathematics | mathematics |
mmlu_aux_train_36387 | mmlu_aux_train | Most earthquakes occur within the upper 15 miles of the earth's surface, but earthquakes can and do occur at all depths to about 460 miles. Their number decreases as the depth increases. At about 460 miles one earthquake occurs only every few years. Near the surface earthquakes may run as high as 100 in a month, but th... | C. Earthquakes are impossible at depths over 460 miles. | earth_science | earth_science | ||
pythonio_428 | pythonio-mc | Program:
from itertools import groupby
def group_element(test_list):
res = dict()
for key, val in groupby(sorted(test_list, key = lambda ele: ele[1]), key = lambda ele: ele[1]):
res[key] = [ele[0] for ele in val]
return (res)
Input:
group_element([(8, 7), (4, 9), (4, 7), (10, 9), (11, 10), (5, 9)])
Ou... | B | code | computer_science | ||
mmlu_aux_train_71335 | mmlu_aux_train | Computers can injure you. Most other injuries happen suddenly. For example, if you fall off a bike and break your arms, it happens very quickly. But computer injuries slowly. You probably know how to ride a bike safely. Now learn to use a computer safely. Your eyes Too much light can injure your eyes, so never sit too ... | B. move in the same way again and again | computer_security | computer_science | ||
allenai/sciq_94 | allenai/sciq | Transform faults are the site of massive what?
A. earthquakes
B. storms
C. tornadoes
D. vibrations | A. earthquakes | Transform faults are the site of massive earthquakes. | college_earth_science | earth_science | |
mmlu_aux_train_4922 | mmlu_aux_train | Jake's cats eat food from a can. The cats come running into the kitchen when they hear the electric can opener. Now, each time Jake's mother opens a can of corn, the cats come running. This is an example of
A. learned behavior
B. correct behavior
C. instinct
D. migration | A. learned behavior | high_school_biology | biology | ||
NLP4Education_113 | NLP4Education | In the χ2 statistics for a binary feature, we obtain P(χ2 | DF = 1) > 0.05. This means in this case, it is assumed:
A. That the class label is independent of the feature
B. That the class label depends on the feature
C. That the class label is strongly correlated with the feature
D. That the feature perfectly predicts ... | A. That the class label is independent of the feature | machine_learning | computer_science | ||
pythonio_85 | pythonio-mc | Program:
def find_Diff(arr,n):
arr.sort()
count = 0; max_count = 0; min_count = n
for i in range(0,(n-1)):
if arr[i] == arr[i + 1]:
count += 1
continue
else:
max_count = max(max_count,count)
min_count = min(min_count,count)
... | A | code | computer_science | ||
allenai/sciq_3547 | allenai/sciq | Each species has a characteristic number of what coiled structures made of dna and proteins?
A. genes
B. ribosomes
C. chromosomes
D. prokaryotes | C. chromosomes | Each species has a characteristic number of chromosomes. Chromosomes are coiled structures made of DNA and proteins called histones ( Figure below ). Chromosomes are the form of the genetic material of a cell during cell division. See the "Chromosomes" section for additional information. | high_school_biology | biology | |
allenai/sciq_5234 | allenai/sciq | What is the term for a mixture that varies in its composition?
A. heterogeneous
B. mixed composition
C. homogeneous
D. amorphous | A. heterogeneous | The rock in Figure above is an example of a heterogeneous mixture. A heterogeneous mixture varies in its composition. The black nuggets, for example, are not distributed evenly throughout the rock. | high_school_chemistry | chemistry | |
NLP4Education_300 | NLP4Education | We are given a data set $S=\left\{\left(\boldsymbol{x}_{n}, y_{n}\right)\right\}$ for a binary classification task where $\boldsymbol{x}_{n}$ in $\mathbb{R}^{D}$. We want to use a nearest neighbor classifier. In which of the following situations do we have a reasonable chance of success with this approach? [Ignore the ... | B. $n \rightarrow \infty, D$ is fixed | machine_learning | computer_science | ||
allenai/sciq_1984 | allenai/sciq | How do leaves export sugar to roots and other nonphotosynthetic parts of the plant?
A. veins
B. stems
C. chloroplasts
D. glands | A. veins | high_school_biology | biology | ||
mmlu_aux_train_95373 | mmlu_aux_train | adding a direct flame to container of acid causes a
A. dormant cycle
B. lot of nothing
C. lower temperature
D. vapor expulsion | D. vapor expulsion | high_school_chemistry | chemistry | ||
pythonio_665 | pythonio-mc | Program:
def clear_tuple(test_tup):
temp = list(test_tup)
temp.clear()
test_tup = tuple(temp)
return (test_tup)
Input:
clear_tuple((2, 1, 4 ,5 ,6))
Output: | C | code | computer_science | ||
aquarat_84228 | deepmind/aqua_rat | If x3−6x2+11x−6=0x3−6x2+11x−6=0 and x3+3x2−6x−8=0x3+3x2−6x−8=0 have one common root between them. What is the value of that root? | A. 3 B. 2 C. 6 D. 9 E. 1 | B. 2 | There are two equations,
x3−6x2+11x−6=0x3−6x2+11x−6=0 - - - (i)
x3+3x2−6x−8=0x3+3x2−6x−8=0 - - - (ii)
So both (i) and (ii) have one root in common and we know that at the root the value of both the equations is 0. Suppose that common root is x then,
x3−6x2+11x−6x3−6x2+11x−6 = x3+3x2−6x−8x3+3x2−6x−8 ⇒⇒ 9x2−17x−2=09x2−17... | college_mathematics | mathematics |
pythonio_425 | pythonio-mc | Program:
def mul_consecutive_nums(nums):
result = [b*a for a, b in zip(nums[:-1], nums[1:])]
return result
Input:
mul_consecutive_nums([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
Output: | A | code | computer_science | ||
allenai/sciq_7169 | allenai/sciq | Why do comet tails always point away from the sun instead of trailing behind the comet?
A. dust particles liquify
B. dust particles evaporate
C. dust particles attract
D. dust particles recoil | D. dust particles recoil | Figure 29.17 shows a comet with two prominent tails. What most people do not know about the tails is that they always point away from the Sun rather than trailing behind the comet (like the tail of Bo Peep’s sheep). Comet tails are composed of gases and dust evaporated from the body of the comet and ionized gas. The du... | astronomy | physics | |
math_255 | math_mc | For how many integer values of $a$ does the equation $$x^2 + ax + 8a = 0$$ have integer solutions for $x$? | B | math_Algebra | mathematics | ||
allenai/sciq_9873 | allenai/sciq | The type of eruption a volcano has depends on the type of what in its chamber?
A. core
B. cavity
C. funnel
D. magma | D. magma | The type of eruption a volcano has depends on the type of magma in its chamber. Some eruptions are explosive. Some eruptions are quiet. All eruptions are amazing!. | earth_science | earth_science | |
math_1871 | math_mc | Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. The hypotenuse of the largest triangle is 8 centimeters. What is the number of centimeters in the length of the longer leg of the smallest triangle? Express your answer as a common fraction.
[asy] pair O... | A | math_Prealgebra | mathematics | ||
math_1162 | math_mc | Let $p(x) = x^{2008} + x^{2007} + x^{2006} + \cdots + x + 1,$
and let $r(x)$ be the polynomial remainder when $p(x)$ is divided by $x^4+x^3+2x^2+x+1$. Find the remainder when $|r(2008)|$ is divided by $1000$.
| D | math_Intermediate Algebra | mathematics | ||
allenai/sciq_4117 | allenai/sciq | Transparent, translucent, or opaque are properties of matter based on an interaction with what?
A. air
B. electricity
C. light
D. gravity | C. light | Matter can be classified on the basis of its interactions with light. Matter may be transparent, translucent, or opaque. An example of each type of matter is pictured in the Figure below . | high_school_physics | physics | |
allenai/sciq_2196 | allenai/sciq | What is less dense then either solids or liquids?
A. gases
B. plasma
C. dark matter
D. ice | A. gases | Gases are less dense that either solids or liquids. | high_school_physics | physics | |
mmlu_aux_train_98116 | mmlu_aux_train | which pairs would likely be consumed by squirrel families?
A. bones and feathers
B. turkey and rocks
C. cardboard and sand
D. peanuts and crackers | D. peanuts and crackers | high_school_biology | biology | ||
mmlu_aux_train_2281 | mmlu_aux_train | Volcanic eruptions early in Earth's history are believed to be responsible for a large proportion of the matter now found in which Earth structure?
A. mantle
B. asthenosphere
C. hydrosphere
D. ozone layer | C. hydrosphere | college_earth_science | earth_science | ||
allenai/sciq_933 | allenai/sciq | Models may be physical, conceptual, or what else?
A. fundamental
B. mathematical
C. theoretical
D. experimental | B. mathematical | Models may be physical, conceptual, or mathematical. | college_physics | physics | |
NLP4Education_71 | NLP4Education | (Neural networks) Training only the first layer of a deep neural network using the logistic loss is equivalent to training a logistic regression over a transformed feature space.
A. True for all neural network architectures
B. False
C. True only for networks with linear activations
D. True if regularization is used | B. False | machine_learning | computer_science | ||
math_2136 | math_mc | The set of points $(x,y,z)$ that are equidistant to $(1,2,-5)$ and point $P$ satisfy an equation of the form
\[10x - 4y + 24z = 55.\]Find the point $P.$ | A | math_Precalculus | mathematics | ||
aquarat_90518 | deepmind/aqua_rat | A certain rectangular crate measures 8 feet by 14 feet by 16 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume? | A. 4 B. 5 C. 6 D. 8 E. 10 | C. 6 | Ans is "B".
For max volume of cylinder (pi*r^2*h) we need to max out r^2*h. We don't know what the dimensions of the crate refer to. . Therefore for max vol base should be 14x20 i.e. of radius 12/2 = 6
C | college_mathematics | mathematics |
mmlu_aux_train_40941 | mmlu_aux_train | Everyone is familiar with white fat, which serves as an energy warehouse. Many mammals also have brown fat, which has the unique ability to produce heat. Brown fat is sometimes mistaken for a type of gland , which it resembles more than white fat. It varies in color1 from dark red to tan. When the animal is exposed t... | C. UCP1. | college_biology | biology | ||
allenai/sciq_10449 | allenai/sciq | What type of earthquake creates a tsunami?
A. Tectonic
B. underwater
C. collapse
D. volcanic | B. underwater | An underwater earthquake creates a tsunami this way: the movement of the crust displaces water. The displacement forms a set of waves. The waves travel at jet speed through the ocean. Since the waves have low amplitudes and long wavelengths, they are unnoticed in deep water. As the waves reach shore they compress. They... | earth_science | earth_science | |
mmlu_aux_train_1443 | mmlu_aux_train | The crust, the mantle, and the core are structures of Earth. Which description is a feature of Earth's mantle?
A. contains fossil remains
B. consists of tectonic plates
C. is located at the center of Earth
D. has properties of both liquids and solids | D. has properties of both liquids and solids | earth_science | earth_science | ||
mmlu_aux_train_12803 | mmlu_aux_train | The oldest and hardest cow beef may be made as tender and tasty as young and choice met. "This declaration was made by the French physicist Denis Papin in book published in 1681, which described his "New Digester" or pressure cooker. It was a cast iron pot with an air-tight lid, which allowed liquids to boil at a high... | B. 200 | conceptual_physics | physics | ||
math_1369 | math_mc | Find all the solutions to
\[\sqrt[3]{15x - 1} + \sqrt[3]{13x + 1} = 4 \sqrt[3]{x}.\]Enter all the solutions, separated by commas. | B | math_Intermediate Algebra | mathematics | ||
aquarat_17802 | deepmind/aqua_rat | Factory X's bulbs work for over 5000 hours in 37% of cases, whereas factory Y's bulbs work for over 5000 hours in 75% of cases. It is known that factory X supplies 40% of the total bulbs available. What is the chance that a purchased bulb will work for longer than 5000 hours? | A. 56.4% B. 58% C. 57.4% D. 55% E. 59.8% | E. 59.8% | For X, 40% of 37% will work.
For Y, 60% of 75% will work. *60% is the rest of the bulb supply in the market.
So, the probability that a purchased bulb will work is:
0.40(0.37) = .148
0.60(0.75) = 0.45
The combined probability then is 14.8 + 45 = 59.8%
ANS E | high_school_statistics | mathematics |
pythonio_614 | pythonio-mc | Program:
def Odd_Length_Sum(arr):
Sum = 0
l = len(arr)
for i in range(l):
Sum += ((((i + 1) *(l - i) + 1) // 2) * arr[i])
return Sum
Input:
Odd_Length_Sum([1,7])
Output: | D | code | computer_science | ||
allenai/sciq_4811 | allenai/sciq | The strength of an acid depends on how many of which ions it produces when it dissolves in water?
A. hydrogen
B. carbon
C. silicon
D. helium | A. hydrogen | The strength of an acid depends on how many hydrogen ions it produces when it dissolves in water. A stronger acid produces more hydrogen ions than a weaker acid. For example, sulfuric acid (H 2 SO 4 ), which is found in car batteries, is a strong acid because nearly all of it breaks down into ions when it dissolves in ... | high_school_chemistry | chemistry | |
math_2125 | math_mc | Find the maximum value of
\[y = \tan \left( x + \frac{2 \pi}{3} \right) - \tan \left( x + \frac{\pi}{6} \right) + \cos \left( x + \frac{\pi}{6} \right)\]for $-\frac{5 \pi}{12} \le x \le -\frac{\pi}{3}.$ | A | math_Precalculus | mathematics | ||
math_1145 | math_mc | Let $a,b,c$ be positive real numbers such that $a+b+c=10$ and $ab+bc+ca=25$. Let $m=\min\{ab,bc,ca\}$. Find the largest possible value of $m$. | B | math_Intermediate Algebra | mathematics | ||
math_330 | math_mc | For all real numbers $r$ and $s$, define the mathematical operation $\#$ such that the following conditions apply: $r\ \#\ 0 = r, r\ \#\ s = s\ \#\ r$, and $(r + 1)\ \#\ s = (r\ \#\ s) + s + 1$. What is the value of $11\ \#\ 5$? | A | math_Algebra | mathematics | ||
aquarat_16635 | deepmind/aqua_rat | Set J consists of the terms {a, b, c, d, e}, where e > d > c > b > a > 3. Which of the following operations would decrease the standard deviation of Set J? | A. Multiply each term by e/d B. Divide each term by b/c C. Multiply each term by −1/2 D. Divide each term by d/e E. Multiply each term by c/e | C. Multiply each term by −1/2 | CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.
1) It depends on the separation between the successive terms of the set
2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence... | college_mathematics | mathematics |
aquarat_80650 | deepmind/aqua_rat | 10 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. The suspects are made to stand in a line and each person declares that the person next to him on his right is guilty. The rightmost person is not questioned. Which of the following possibilities are true? | A. A or V B. A or C C. A or B D. A or D E. A or J | C. A or B | There are only 2 cases. Either left one is guilty or one of the remaining 9 to his right is guilty.
So If the left most is guilty, All the statements including the guilty one are lies. A and C are correct.
Or If Any one except left most one is guilty, Then one of the statements given by the person should be true. In th... | formal_logic | mathematics |
mmlu_aux_train_97936 | mmlu_aux_train | Which of the following would occur in nature?
A. an osprey catches a fish with claws
B. a fish catches a fish with its claws
C. a dog catches a fish with its claws
D. a worm catches a fish with its claws | A. an osprey catches a fish with claws | high_school_biology | biology | ||
mmlu_aux_train_64869 | mmlu_aux_train | Scientists have tried to come up with biological explanations for the difference between boys and girls. However, none were believable enough to explain the general picture. As one scientist points out, "There are slight genetic differences between the sexes at birth which may affect the subjects boys and girls choose.... | B. avoid maths because of social reasons | high_school_statistics | mathematics | ||
mmlu_aux_train_57131 | mmlu_aux_train | It's a bicyclist's dream: a bike that can't be stolen. The Yerka, designed by three young Chilean engineering students, is the latest entry in a trend of bikes. They use their saddle seat as a lock. They can also use their handlebar as a lock. But the inventors of the Yerka have made an improvement to it. The bike's lo... | B. will be broken if it gets stolen | electrical_engineering | engineering | ||
math_1257 | math_mc | Let
\[f(x) = \frac{2x + 3}{kx - 2}.\]Find all real numbers $k$ so that $f^{-1}(x) = f(x).$ | D | math_Intermediate Algebra | mathematics | ||
allenai/sciq_1136 | allenai/sciq | Find the overall magnification of what instrument by finding the magnification of the objective, then the magnification of the eyepiece?
A. part microscope
B. compound microscope
C. Fixing microscope
D. belt microscope | B. compound microscope | Example 26.5 Microscope Magnification Calculate the magnification of an object placed 6.20 mm from a compound microscope that has a 6.00 mm focal length objective and a 50.0 mm focal length eyepiece. The objective and eyepiece are separated by 23.0 cm. Strategy and Concept This situation is similar to that shown in Fig... | high_school_biology | biology | |
math_750 | math_mc | A car travels due east at $\frac 23$ mile per minute on a long, straight road. At the same time, a circular storm, whose radius is $51$ miles, moves southeast at $\frac 12\sqrt{2}$ mile per minute. At time $t=0$, the center of the storm is $110$ miles due north of the car. At time $t=t_1$ minutes, the car enters the st... | A | math_Geometry | mathematics | ||
mmlu_aux_train_98674 | mmlu_aux_train | a fish lives in water and filters the water through its
A. tail
B. gill slats
C. eyes
D. fins | B. gill slats | high_school_biology | biology |
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