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 |
|---|---|---|---|---|---|---|---|
allenai/sciq_1780 | allenai/sciq | Pure constructive interference and pure destructive interference are distinguished by whether or not identical waves are what?
A. in equilibrium
B. in phase
C. before phase
D. after phase | B. in phase | Figure 27.11 The amplitudes of waves add. (a) Pure constructive interference is obtained when identical waves are in phase. (b) Pure destructive interference occurs when identical waves are exactly out of phase, or shifted by half a wavelength. | conceptual_physics | physics | |
mmlu_aux_train_53106 | mmlu_aux_train | "Iris scan , please," the bank's computer voice tells you . You step up and the computer reads your eye , comparing it to the stored file it has of your iris. The images had better match--otherwise you won't be able to get your money. Iris scanning and other technologies , such as fingerprint and voice scanning , have... | C. The iris scan | computer_security | computer_science | ||
aquarat_19227 | deepmind/aqua_rat | What is the value of(a,y) in (13^-20-a*13^y)=168*13^-22? | A. (1,2) B. (0,1) C. (-1,22) D. (1,-22) E. (1,-20) | D. (1,-22) | (13^-20-a*13^y)=168*13^-22
Divide the LHS and RHS by 13^-22
13^2-a*13^(y+22) =168
168 can be expressed as 13^2 - 1
13^2-a*13^(y+22) =13^2 - 1
a*13^(y+22) =1
Now look at options and substitute .. Its easy for y=-22 . 13^0=1 a also = 1
ANSWER:D | college_mathematics | mathematics |
math_2061 | math_mc | Piravena must make a trip from $A$ to $B$, then from $B$ to $C$, then from $C$ to $A$. Each of these three parts of the trip is made entirely by bus or entirely by airplane. The cities form a right-angled triangle as shown, with $C$ a distance of 3000 km from $A$ and with $B$ a distance of 3250 km from $A$. To take a... | C | math_Prealgebra | mathematics | ||
mmlu_aux_train_40304 | mmlu_aux_train | I was in my third year of teaching creative writing at a high school in New York, when one of my students, 15-year-old Mikey, gave me a note from his mother. It explained his absence from class the day before. I had seen Mikey himself writing the note at his desk. Most parental-excuse notes I received were penned by my... | D. He helped improve their writing skills. | high_school_computer_science | computer_science | ||
math_299 | math_mc | If $a$ and $b$ are integers with $a > b$, what is the smallest possible positive value of $\frac{a+b}{a-b} + \frac{a-b}{a+b}$? | A | math_Algebra | mathematics | ||
pythonio_135 | pythonio-mc | Program:
def assign_elements(test_list):
res = dict()
for key, val in test_list:
res.setdefault(val, [])
res.setdefault(key, []).append(val)
return (res)
Input:
assign_elements([(6, 4), (9, 4), (3, 8), (4, 9), (9, 5)] )
Output: | B | code | computer_science | ||
allenai/sciq_10737 | allenai/sciq | What is the term for the use of two or more lewis structures to represent the covalent bonding in a molecule?
A. frequency
B. resonance
C. reaction
D. harmony | B. resonance | Resonance is the use of two or more Lewis structures to represent the covalent bonding in a molecule. One of the valid structures is referred to as a resonance structure. It is now understood that the true structure of a molecule which displays resonance is that of an average or a hybrid of all the resonance structures... | college_chemistry | chemistry | |
math_1802 | math_mc | A group of 25 friends were discussing a large positive integer. ``It can be divided by 1,'' said the first friend. ``It can be divided by 2,'' said the second friend. ``And by 3,'' said the third friend. ``And by 4,'' added the fourth friend. This continued until everyone had made such a comment. If exactly two friends... | D | math_Number Theory | mathematics | ||
aquarat_28835 | deepmind/aqua_rat | Set S has a mean of 16 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most? | A. {2, 10} B. {9, 11} C. {16, 16} D. {10, 18} E. {7, 13} | C. {16, 16} | answer A,B,D, and E mean is not 16 therefore not accepted . C mean is 16 but S.D is more. therefore accepted
answer is C mean is 16 and S.D decreases minimum.
C | high_school_statistics | mathematics |
math_788 | math_mc | Let $ABCDEF$ be a regular hexagon. Let $G$, $H$, $I$, $J$, $K$, and $L$ be the midpoints of sides $AB$, $BC$, $CD$, $DE$, $EF$, and $AF$, respectively. The segments $\overline{AH}$, $\overline{BI}$, $\overline{CJ}$, $\overline{DK}$, $\overline{EL}$, and $\overline{FG}$ bound a smaller regular hexagon. Let the ratio of ... | D | math_Geometry | mathematics | ||
allenai/sciq_1610 | allenai/sciq | The amount of energy needed to raise the temperature of one gram of liquid water by 1°c is also known as?
A. mass
B. specific heat
C. Kelvin
D. calorie | B. specific heat | State of matter that has a fixed volume and fixed shape. | high_school_physics | physics | |
allenai/sciq_6974 | allenai/sciq | Different isotopes of an element have different mass numbers because they have different numbers of what?
A. electrons
B. protons
C. nuclei
D. neutrons | D. neutrons | An atom’s mass number is its mass in atomic mass units (amu), which is about equal to the total number of protons and neutrons in the atom. Different isotopes of an element have different mass numbers because they have different numbers of neutrons. | high_school_chemistry | chemistry | |
aquarat_3671 | deepmind/aqua_rat | Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1)
What is the largest prime number (written in binary) that is a factor of both 10010000 and 100100000 ? | A. 10 B. 11 C. 1001 D. 1011 E. 10001 | C. 1001 | Binary Divison can provide a quick answer if you are comfortable with it.
as option E is the biggest binary number we try with it first :
100010000/ 1001 =10000
1000100000/ 1001 =100000
so answer is option is C | college_mathematics | mathematics |
mmlu_aux_train_94335 | mmlu_aux_train | The reading on a barometer rises when the air
A. pressure increases.
B. pressure decreases.
C. speed increases.
D. speed decreases. | A. pressure increases. | high_school_physics | physics | ||
NLP4Education_488 | NLP4Education | Which of the following terms represents a mode of operation which transforms a block cipher into a stream cipher?
A. 3DES
B. CBC
C. ECB
D. CTR | D. CTR | computer_security | computer_science | ||
math_33 | math_mc | Expand $-(3-c)(c+2(3-c))$. What is the sum of the coefficients of the expanded form? | D | math_Algebra | mathematics | ||
pythonio_872 | pythonio-mc | Program:
def binomial_coeffi(n, k):
if (k == 0 or k == n):
return 1
return (binomial_coeffi(n - 1, k - 1)
+ binomial_coeffi(n - 1, k))
def rencontres_number(n, m):
if (n == 0 and m == 0):
return 1
if (n == 1 and m == 0):
return 0
if (m == 0):
return ((n - 1) * (rencontres_number(n - 1,... | D | code | computer_science | ||
aquarat_25489 | deepmind/aqua_rat | 36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is | A. 11 B. 12 C. 13 D. 15 E. 18 | B. 12 | if we take person a1 in the set then it will cover a36 and a2 for shaking hand.similarly if we take person a4 in the set then it will cover a5 and a3 for shaking hand and so on, so minimum 12 persons are required.
ANSWER:B | college_mathematics | mathematics |
allenai/sciq_11126 | allenai/sciq | What is the smallest particle of an element that still has the properties of that element is called?
A. atom
B. proton
C. nucleus
D. neutron | A. atom | The smallest particle of an element that still has the properties of that element is an atom. Atoms are extremely tiny. They can be observed only with an electron microscope. They are commonly represented by models, like the one Figure below . An atom has a central nucleus that is positive in charge. The nucleus is sur... | high_school_chemistry | chemistry | |
mmlu_aux_train_96657 | mmlu_aux_train | what do planets orbit?
A. asteroids
B. moons
C. burning hydrogen ball
D. they are orbitless | C. burning hydrogen ball | astronomy | physics | ||
math_298 | math_mc | What is the domain of the function $$f(t) = \frac{1}{(t-1)^2+(t+1)^2}~?$$ Express your answer in interval notation. | B | math_Algebra | mathematics | ||
aquarat_39515 | deepmind/aqua_rat | An athlete runs 200 meters race in 48sec. His speed is? | A. 20km/hr B. 15km/hr C. 30km/hr D. 25km/hr E. 40km/hr | B. 15km/hr | speed = 200/48 = 25/6 m/sec
= 25/6 * 18/5 km/hr = 15km/hr
Answer is B | high_school_physics | physics |
math_1983 | math_mc | How many ways can change be made for a quarter using standard U.S. coins? (Don't count "1 quarter" as making change for a quarter.) | B | math_Prealgebra | mathematics | ||
math_1466 | math_mc | The graph of an equation \[\sqrt{(x-3)^2 + (y+4)^2} + \sqrt{(x+5)^2 + (y-8)^2} = 20.\]is an ellipse. What is the distance between its foci? | B | math_Intermediate Algebra | mathematics | ||
allenai/sciq_3093 | allenai/sciq | What is the term for getting used to something after being consistently exposed to it?
A. habituation
B. acceptance
C. modification
D. dissociation | A. habituation | One of the simplest ways of learning that occurs in just about all animals is habituation. Habituation means learning to get used to something after being exposed to it repeatedly. It usually involves getting used to something that is frightening or annoying but not dangerous. | college_biology | biology | |
pythonio_83 | pythonio-mc | Program:
def basesnum_coresspondingnum(bases_num,index):
result = list(map(pow, bases_num, index))
return result
Input:
basesnum_coresspondingnum([10, 20, 30, 40, 50, 60, 70, 80, 90, 100],[1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
Output: | B | code | computer_science | ||
pythonio_642 | pythonio-mc | Program:
INT_BITS = 32
def left_Rotate(n,d):
return (n << d)|(n >> (INT_BITS - d))
Input:
left_Rotate(10,2)
Output: | A | code | computer_science | ||
allenai/sciq_6582 | allenai/sciq | White light is a mixture of all wavelengths of what?
A. x-rays
B. infrared radiation
C. gamma radiation
D. visible light | D. visible light | high_school_physics | physics | ||
mmlu_aux_train_93599 | mmlu_aux_train | Mark wants to make lemonade for his friends. He uses water, lemon juice, and sugar. Which of these best describes the lemonade?
A. a mixture
B. a metal
C. an element
D. a compound | A. a mixture | high_school_chemistry | chemistry | ||
math_930 | math_mc | What is the ratio of the area of a square inscribed in a semicircle with radius $r$ to the area of a square inscribed in a circle with radius $r$? Express your answer as a common fraction. | B | math_Geometry | mathematics | ||
NLP4Education_402 | NLP4Education | $\mathbb{Z}_{37}^*$ denotes ...
A. a field.
B. an additive group.
C. a multiplicative group.
D. a ring. | C. a multiplicative group. | abstract_algebra | mathematics | ||
mmlu_aux_train_99329 | mmlu_aux_train | Which is an electrical energy conductor?
A. cobalt
B. plastic
C. concrete
D. mahogany | A. cobalt | electrical_engineering | engineering | ||
math_1872 | math_mc | What is the perimeter, in cm, of quadrilateral $ABCD$ if $\overline{AB} \perp \overline{BC}$, $\overline{DC} \perp \overline{BC}$, $AB=9$ cm, $DC=4$ cm, and $BC=12$ cm? | C | math_Prealgebra | mathematics | ||
mmlu_aux_train_2277 | mmlu_aux_train | Which results in a chemical change?
A. A student smells a flower.
B. A teacher lights a candle.
C. A student colors a paper blue.
D. A teacher feels a rough cloth. | B. A teacher lights a candle. | high_school_chemistry | chemistry | ||
allenai/sciq_1501 | allenai/sciq | What unit are atomic radii typically measured in?
A. radons
B. powers
C. picometers
D. sporozoans | C. picometers | Atomic radii have been measured for elements. The units for atomic radii are picometers, equal to 10 -12 meters. As an example, the internuclear distance between the two hydrogen atoms in an H 2 molecule is measured to be 74 pm. Therefore, the atomic radius of a hydrogen atom is . | high_school_chemistry | chemistry | |
allenai/sciq_3988 | allenai/sciq | What is composed of a calcium cation and a nitrate anion?
A. calcium carbonate
B. nitrous oxide
C. calcium nitrate
D. dynamite | C. calcium nitrate | Writing a formula for a ternary ionic compound also involves the same steps as for a binary ionic compound. Write the symbol and charge of the cation followed by the symbol and charge of the anion. Use the crisscross method to ensure that the final formula is neutral. Calcium nitrate is composed of a calcium cation and... | high_school_chemistry | chemistry | |
allenai/sciq_9656 | allenai/sciq | Genetic traits are characteristics encoded in what?
A. nuclei
B. rna
C. bacteria
D. dna | D. dna | Characteristics that are encoded in DNA are called genetic traits . Different types of human traits are inherited in different ways. Some human traits have simple inheritance patterns like the traits that Gregor Mendel studied in pea plants. Other human traits have more complex inheritance patterns. | college_biology | biology | |
math_1276 | math_mc | Let $x,$ $y,$ $z$ be real numbers such that
\begin{align*}
x + y + z &= 4, \\
x^2 + y^2 + z^2 &= 6.
\end{align*}Let $m$ and $M$ be the smallest and largest possible values of $x,$ respectively. Find $m + M.$ | C | math_Intermediate Algebra | mathematics | ||
allenai/sciq_8286 | allenai/sciq | Primary batteries are single-use batteries because they cannot be what?
A. UP ticked.
B. plugged
C. recharged
D. refreshed | C. recharged | Primary Batteries Primary batteries are single-use batteries because they cannot be recharged. A common primary battery is the dry cell (Figure 17.10). The dry cell is a zinc-carbon battery. The zinc can serves as both a container and the negative electrode. The positive electrode is a rod made of carbon that is surrou... | high_school_chemistry | chemistry | |
aquarat_43623 | deepmind/aqua_rat | The probability of two events A and B are 0.20 and 0.40 respectively. The probability that both A and B occur is 0.15. The probability that neither A nor B occur is _________ | A. 0.45 B. 0.4 C. 0.5 D. 0.55 E. 0.6 | D. 0.55 | we are apply that formula..............
P(AorB)=P(A)+P(B)-P(A AND B)
=.20+.40-.15
=.45
but the probability of neither A nor B=1-.45
=0.55
ANSWER:D | high_school_statistics | mathematics |
allenai/sciq_6782 | allenai/sciq | What kind of organisms have many different types of specialized cells with particular jobs?
A. intricate
B. multicellular
C. crude
D. monocellular | B. multicellular | All living cells have certain things in common. Besides having the basic parts described above, all cells can perform the same basic functions. For example, all cells can use energy, respond to their environment, and reproduce. However, cells may also have special functions. Multicellular organisms such as you have man... | high_school_biology | biology | |
math_1511 | math_mc | Let $A,$ $B,$ and $C$ be constants such that the equation \[\frac{(x+B)(Ax+28)}{(x+C)(x+7)} = 2\]has infinitely many solutions for $x.$ For these values of $A,$ $B,$ and $C,$ it turns out that there are only finitely many values of $x$ which are not solutions to the equation. Find the sum of these values of $x.$ | A | math_Intermediate Algebra | mathematics | ||
math_1052 | math_mc | In triangle $ABC$, $AB = AC = 100$, and $BC = 56$. Circle $P$ has radius $16$ and is tangent to $\overline{AC}$ and $\overline{BC}$. Circle $Q$ is externally tangent to $P$ and is tangent to $\overline{AB}$ and $\overline{BC}$. No point of circle $Q$ lies outside of $\triangle ABC$. The radius of circle $Q$ can be expr... | C | math_Geometry | mathematics | ||
NLP4Education_282 | NLP4Education | If for the χ² statistics for a binary feature, we obtain P(χ² | DF = 1) < 0.05, this means:
A. That the class label is independent of the feature
B. No conclusion can be drawn
C. That the class labels depends on the feature
D. That the class label correlates with the feature | C. That the class labels depends on the feature | machine_learning | computer_science | ||
mmlu_aux_train_59053 | mmlu_aux_train | One evening in February 2007, a student named Paula Ceely brought her car to a stop on a remote road in Wales. She got out to open a metal gate that blocked her path. That's when she heard the whistle sounded by the driver of a train. Her Renault Clio was parked across a railway line. Seconds later, she watched the tra... | D. Her GPS device didn't tell her about the crossing. | computer_security | computer_science | ||
math_1287 | math_mc | Let $a$, $b$, $c$, $d$, and $e$ be positive integers with $a+b+c+d+e=2010$ and let $M$ be the largest of the sum $a+b$, $b+c$, $c+d$ and $d+e$. What is the smallest possible value of $M$? | A | math_Intermediate Algebra | mathematics | ||
allenai/sciq_2690 | allenai/sciq | What form do alkali metals take at room temperature?
A. compound
B. gas
C. liquid
D. solid | D. solid | Alkali metals are all solids at room temperature. | high_school_chemistry | chemistry | |
pythonio_214 | pythonio-mc | Program:
def diff_even_odd(list1):
first_even = next((el for el in list1 if el%2==0),-1)
first_odd = next((el for el in list1 if el%2!=0),-1)
return (first_even-first_odd)
Input:
diff_even_odd([1,2,3,4,5,6,7,8,9,10])
Output: | A | code | computer_science | ||
math_2161 | math_mc | In triangle $ABC$, $3 \sin A + 4 \cos B = 6$ and $4 \sin B + 3 \cos A = 1$. Find all possible values of $\angle C,$ in degrees. Enter all the possible values, separated by commas. | A | math_Precalculus | mathematics | ||
allenai/sciq_9739 | allenai/sciq | Damages and deaths are directly affected by what in an earthquake?
A. structures
B. shaking
C. natural
D. construction | D. construction | The type of construction has a tremendous effect on what happens during an earthquake. Damage and deaths are directly affected by the construction in an earthquake. For example, enormous damage was done in the 2011 Christchurch, New Zealand earthquake. However, far less was damaged in an earthquake of the same magnitud... | conceptual_physics | physics | |
NLP4Education_464 | NLP4Education | Tick the true assertion.
A. A dictionary attack requires less memory than a time-memory tradeoff.
B. Double-DES succumbs under a Meet-in-the-Middle attack.
C. AES is the ancestor of DES.
D. IDEA has the same round functions as DES. | B. Double-DES succumbs under a Meet-in-the-Middle attack. | computer_security | computer_science | ||
allenai/sciq_4996 | allenai/sciq | What type of rain dissolves and damages stone buildings and statues?
A. morning rain
B. plastic rain
C. stored rain
D. acid rain | D. acid rain | A: Acid rain dissolves and damages stone buildings and statues. The Figure below shows a statue that has been damaged by acid rain. | high_school_chemistry | chemistry | |
math_1665 | math_mc | Let $m$ be the smallest integer whose cube root is of the form $n+r$, where $n$ is a positive integer and $r$ is a positive real number less than $1/1000$. Find $n$. | D | math_Number Theory | mathematics | ||
math_1398 | math_mc | Let \[\begin{aligned} a &= \sqrt{2}+\sqrt{3}+\sqrt{6}, \\ b &= -\sqrt{2}+\sqrt{3}+\sqrt{6}, \\ c&= \sqrt{2}-\sqrt{3}+\sqrt{6}, \\ d&=-\sqrt{2}-\sqrt{3}+\sqrt{6}. \end{aligned}\]Evaluate $\left(\frac1a + \frac1b + \frac1c + \frac1d\right)^2.$ | A | math_Intermediate Algebra | mathematics | ||
mmlu_aux_train_2469 | mmlu_aux_train | What particle always has a mass of one atomic mass unit (amu) and no charge?
A. a neutron
B. a proton
C. an electron
D. an atom | A. a neutron | high_school_chemistry | chemistry | ||
pythonio_408 | pythonio-mc | Program:
def mul_list(nums1,nums2):
result = map(lambda x, y: x * y, nums1, nums2)
return list(result)
Input:
mul_list([90,120],[50,70])
Output: | B | code | computer_science | ||
mmlu_aux_train_95177 | mmlu_aux_train | ultraviolet light is found in light from where
A. the flaming ball of gas we orbit
B. giant planets in the neighborhood
C. light sources that we create
D. balls of fire lit with gas | A. the flaming ball of gas we orbit | high_school_physics | physics | ||
math_1928 | math_mc | At Beaumont High School, there are 20 players on the basketball team. All 20 players are taking at least one of biology or chemistry. (Biology and chemistry are two different science courses at the school.) If there are 8 players taking biology and 4 players are taking both sciences, how many players are taking chem... | A | math_Prealgebra | mathematics | ||
pythonio_572 | pythonio-mc | Program:
def find_Min_Diff(arr,n):
arr = sorted(arr)
diff = 10**20
for i in range(n-1):
if arr[i+1] - arr[i] < diff:
diff = arr[i+1] - arr[i]
return diff
Input:
find_Min_Diff((4,3,2,6),4)
Output: | C | code | computer_science | ||
mmlu_aux_train_2349 | mmlu_aux_train | Which fact about water is an example of a chemical property?
A. Water expands when it freezes.
B. The boiling point of water is 100ºC.
C. Water can separate into hydrogen and oxygen.
D. The density of water is greater than the density of ice. | C. Water can separate into hydrogen and oxygen. | high_school_chemistry | chemistry | ||
allenai/sciq_10561 | allenai/sciq | What system consists of structures that produce eggs, secrete female sex hormones, and ultimately enable birth of a fetus?
A. female reproductive system
B. female hormone system
C. female uterus system
D. male reproductive system | A. female reproductive system | The female reproductive system consists of structures that produce eggs and secrete female sex hormones. They also provide a site for fertilization and enable the development and birth of a fetus. | high_school_biology | biology | |
pythonio_412 | pythonio-mc | Program:
def sum_Of_Primes(n):
prime = [True] * (n + 1)
p = 2
while p * p <= n:
if prime[p] == True:
i = p * 2
while i <= n:
prime[i] = False
i += p
p += 1
sum = 0
for i in range (2,n + 1):
if(pr... | C | code | computer_science | ||
aquarat_92208 | deepmind/aqua_rat | The variables a and b are non-zero integers B. If a = 2b^3/c, what happens to c when a is halved and b is doubled? | A. c is not changed. B. c is halved. C. c is doubled. D. c is multiplied by 4. E. c is multiplied by 16. | E. c is multiplied by 16. | a =2b^3/c
c =2b^3/a
when a is halved and b is doubled
c=2(2b)^3/(a/2)
c= 16*2b^3/a
Ans. E c is multiplied by 16. | college_mathematics | mathematics |
math_304 | math_mc | Evaluate $\lfloor -4 -.5 \rfloor \cdot \lceil 4 +.5 \rceil \cdot \lfloor -3 -.5 \rfloor \cdot \lceil 3 +.5 \rceil \cdot \dots \cdot \lfloor -.5 \rfloor \cdot \lceil .5 \rceil$. | B | math_Algebra | mathematics | ||
mmlu_aux_train_90383 | mmlu_aux_train | A new camera made by a company named Netatmo has facial recognition software that can tell parents at work that their children have returned from school, or that a package has been taken to their home. It can also tell them if a stranger has entered their home. Janina Mattausch is a product marketing manager for Neta... | B. recognize the comers | computer_security | computer_science | ||
mmlu_aux_train_39982 | mmlu_aux_train | A baby born in India has been declared the world's seven billionth person by child rights group Plan International. Baby Nargis was born at 07:25 local time (01:55GMT) in Mall village in India's Uttar Pradesh state. Plan International says Nargis has been chosen symbolically as it is not possible to know where exactly ... | A. Baby Nargis is not the only child chosen as the seven billionth baby. | high_school_biology | biology | ||
allenai/sciq_10049 | allenai/sciq | What kind of tool, often based on mathematical equations or computer simulations, helps us understand complex systems?
A. models
B. panels
C. planes
D. levels | A. models | Food Chains. These two food chains represent complex systems in nature. They make the systems easier to understand. These are simple conceptual models. Models of very complex systems are often based on mathematical equations or computer simulations. | college_mathematics | mathematics | |
pythonio_718 | pythonio-mc | Program:
import heapq
def nth_super_ugly_number(n, primes):
uglies = [1]
def gen(prime):
for ugly in uglies:
yield ugly * prime
merged = heapq.merge(*map(gen, primes))
while len(uglies) < n:
ugly = next(merged)
if ugly != uglies[-1]:
uglies.appen... | A | code | computer_science | ||
math_844 | math_mc | Let $P_{1}: y=x^{2}+\frac{101}{100}$ and $P_{2}: x=y^{2}+\frac{45}{4}$ be two parabolas in the Cartesian plane. Let $\mathcal{L}$ be the common tangent line of $P_{1}$ and $P_{2}$ that has a rational slope. If $\mathcal{L}$ is written in the form $ax+by=c$ for positive integers $a,b,c$ where $\gcd(a,b,c)=1$, find $a+b+... | B | math_Geometry | mathematics | ||
aquarat_62218 | deepmind/aqua_rat | Given that G and H are events such that
G(Y)= 0.02
G(Z)=0.4
G(YnZ)=0.4
find G (Y|Z) and G(Y|Z) | A. 1/22 B. 1/20 C. 1/25 D. 1/10 E. 1/50 | B. 1/20 | Here, Y and Z are events
G(Y|Z) = G(YnZ)/G(Z) = 0.4/0.4= 1
Q(G|H) = G(YnZ)/G(Y) = 0.4/0.20 = 1/20
Answer is B | college_mathematics | mathematics |
pythonio_314 | pythonio-mc | Program:
import math
def wind_chill(v,t):
windchill = 13.12 + 0.6215*t - 11.37*math.pow(v, 0.16) + 0.3965*t*math.pow(v, 0.16)
return int(round(windchill, 0))
Input:
wind_chill(120,35)
Output: | A | code | computer_science | ||
pythonio_64 | pythonio-mc | Program:
import sys
def min_coins(coins, m, V):
if (V == 0):
return 0
res = sys.maxsize
for i in range(0, m):
if (coins[i] <= V):
sub_res = min_coins(coins, m, V-coins[i])
if (sub_res != sys.maxsize and sub_res + 1 < res):
res = sub_re... | C | code | computer_science | ||
mmlu_aux_train_21408 | mmlu_aux_train | As more people use smart phones to pay bills and store personal information, strict password security has become more important than ever. A new study shows that free - form gestures - sweeping fingers in shapes across the screen of a smart phone--can be used to unlock phones. These gestures are less likely to be obser... | A. They are improving mobile security in a way. | computer_security | computer_science | ||
aquarat_55806 | deepmind/aqua_rat | If x = a/(a – 1) and 1/(a – 1), then: | A. x is equal to y B. x is equal to y only if a < 1 C. x is greater than y D. x is greater than y only if a < 1 E. y is greater than x only if a < 1 | A. x is equal to y | x = a/(a – 1) = 1 + 1/(a – 1) = 1 + y.
Therefore, x > y
ANSWER:A | college_mathematics | mathematics |
mmlu_aux_train_95569 | mmlu_aux_train | The creation of sediment is produced by
A. the break down of other materials
B. materials joining together into one
C. solar interaction with the earth
D. chemicals compounds combining together | A. the break down of other materials | earth_science | earth_science | ||
allenai/sciq_838 | allenai/sciq | What is the study of the interaction between matter and energy called?
A. chemistry
B. geology
C. climatology
D. astronomy | A. chemistry | Chemistry is the study of matter and energy and how they interact, mainly at the level of atoms and molecules. Basic concepts in chemistry include chemicals, which are specific types of matter, and chemical reactions. In a chemical reaction, atoms or molecules of certain types of matter combine chemically to form other... | college_physics | physics | |
aquarat_18648 | deepmind/aqua_rat | A set consist of 2k-1 element. What is the number of subsets of this set which contain at most k-1 elements? | A. 2^(2k-2) B. 2^(2k) - 2 C. 2^(2k) -1 D. 2^(2k) E. 2^(2k-1) | A. 2^(2k-2) | I used k=3, so then we have
5!/2!3! + 5!/4!1! + 5!/0!5!
10 + 5 + 1 = 16
So our target is 16
Now replace in answer choices
A gives us 2^4 = 16
Hence A is the correct option
Read carefully it says at most so keep in mind that picking a small number such as 3 will help you save time since you have to list fewer outcomes
A... | college_mathematics | mathematics |
aquarat_10046 | deepmind/aqua_rat | In a certain encryption pattern, HARD is coded as 1357 and SOFT is coded as 2468, What will 21448 stand for? | A. SHAFT B. SHORT C. SHOOT D. SHART E. SHAOT | C. SHOOT | on the behlaf of order like
h =1
a=3
r=5 and so on.
so 21448 is SHOOT
ANSWER:C | coding | computer_science |
allenai/sciq_2759 | allenai/sciq | Where does most geological activity take place?
A. plate waves
B. plate buildings
C. plate medians
D. plate boundaries | D. plate boundaries | Most geological activity takes place at plate boundaries. This activity includes volcanoes, earthquakes, and mountain building. The activity occurs as plates interact. Giant slabs of lithosphere moving around can create a lot of activity! The features seen at a plate boundary are determined by the direction of plate mo... | earth_science | earth_science | |
NLP4Education_515 | NLP4Education | Compute $\phi(90)$.
A. 16
B. 24
C. 36
D. 48 | B. 24 | abstract_algebra | mathematics | ||
pythonio_301 | pythonio-mc | Program:
def adjac(ele, sub = []):
if not ele:
yield sub
else:
yield from [idx for j in range(ele[0] - 1, ele[0] + 2)
for idx in adjac(ele[1:], sub + [j])]
def get_coordinates(test_tup):
res = list(adjac(test_tup))
return (res)
Input:
get_coordinates((4, 5))
Output: | B | code | computer_science | ||
mmlu_aux_train_93757 | mmlu_aux_train | Which process in the water cycle would be accelerated by an increase in temperature?
A. runoff
B. evaporation
C. precipitation
D. condensation | B. evaporation | high_school_biology | biology | ||
pythonio_593 | pythonio-mc | Program:
def remove_length(test_str, K):
temp = test_str.split()
res = [ele for ele in temp if len(ele) != K]
res = ' '.join(res)
return (res)
Input:
remove_length('Forces of darkeness is come into the play', 4)
Output: | A | code | computer_science | ||
math_39 | math_mc | The difference between two perfect squares is 133. What is the smallest possible sum of the two perfect squares? | D | math_Algebra | mathematics | ||
math_1669 | math_mc | Find $10110_2\times10100_2\div10_2$. Express your answer in base 2. | D | math_Number Theory | mathematics | ||
math_565 | math_mc | Jeff will pick a card at random from ten cards numbered 1 through 10. The number on this card will indicate his starting point on the number line shown below. He will then spin the fair spinner shown below (which has three congruent sectors) and follow the instruction indicated by his spin. From this new point he wi... | B | math_Counting & Probability | mathematics | ||
math_1708 | math_mc | Suppose that $x$ is an integer that satisfies the following congruences: \begin{align*}
3+x &\equiv 2^2 \pmod{3^3} \\
5+x &\equiv 3^2 \pmod{5^3} \\
7+x &\equiv 5^2 \pmod{7^3}
\end{align*}What is the remainder when $x$ is divided by $105$? | C | math_Number Theory | mathematics | ||
math_2007 | math_mc | A book with 53 pages numbered 1 to 53 has its pages renumbered in reverse, from 53 to 1. For how many pages do the new page number and old page number share the same units digit? | A | math_Prealgebra | mathematics | ||
aquarat_23652 | deepmind/aqua_rat | 70,76, 74,85,90,105,105,130,130,130
The list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviatio... | A. 1 B. 2 C. 3 D. 4 E. 5 | C. 3 | How many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD.
We are given that SD=22.4, so we should find mean --> mean=100 --> there are only 3 data points below 100-22.4=77.6, namely 70 75, and 74.
Answer: C. | high_school_statistics | mathematics |
allenai/sciq_6731 | allenai/sciq | When atomic orbitals hybridize, the valence electrons occupy these?
A. newly created elements
B. newly created orbitals
C. newly developed orbits
D. expanded pathways | B. newly created orbitals | When atomic orbitals hybridize, the valence electrons occupy the newly created orbitals. The Be atom had two valence electrons, so each of the sp orbitals gets one of these electrons. Each of these electrons pairs up with the unpaired electron on a chlorine atom when a hybrid orbital and a chlorine orbital overlap duri... | college_chemistry | chemistry | |
allenai/sciq_5808 | allenai/sciq | If heat is released by the system into the surroundings, a chemical reaction or physical change is called what?
A. endothermic
B. biochemical
C. exothermic
D. static | C. exothermic | In the study of thermochemical processes, things are viewed from the point of view of the system. A chemical reaction or physical change is endothermic if heat is absorbed by the system from the surroundings. In the course of an endothermic process, the system gains heat from the surroundings and so the temperature of ... | high_school_chemistry | chemistry | |
aquarat_47956 | deepmind/aqua_rat | A computer program generates a sequence of numbers a1, a2, a3, ... such that a1=1, a2=2, and ak=a(k-1)*5 - 3 for 2 < k < n. If n = 10, find a5. | A. 115 B. 137 C. 141 D. 151 E. 157 | E. 157 | a1=1
a2=2
a3=2*5-3=7
a4=7*5-3=35-3=32
a5=32*5-3=160-3=157
157 | college_mathematics | mathematics |
allenai/sciq_6778 | allenai/sciq | What always has the same elements in the same ratio?
A. cell
B. component
C. compound
D. mitochondria | C. compound | A compound always consists of the same elements in the same ratio. If the same elements combine in different ratios, they form different compounds. | high_school_chemistry | chemistry | |
allenai/sciq_6121 | allenai/sciq | Heat, electricity, or light might provide what necessary input to the process of decomposition?
A. source
B. energy
C. material
D. food | B. energy | Most decomposition reactions require an input of energy in the form of heat, light, or electricity. | high_school_physics | physics | |
mmlu_aux_train_13590 | mmlu_aux_train | Angry Birds has become a worldwide gaming mega hit but how did this game come into existence? Rovio is the name of the company that created angry birds, however, it's not the first game they developed. Surprisingly they have been creating games for several years but had just never broken through into the mainstream the... | B. have to be controlled to kill all of the pigs before your birds run out | coding | computer_science | ||
aquarat_10969 | deepmind/aqua_rat | Set J consists of the terms {a, b, c, d, e}, where e > d > c > b > a > 1.5. 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 D. Divide each term by a/e E. Multiply each term by c/e | D. Divide each term by a/e | 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... | high_school_statistics | mathematics |
allenai/sciq_3504 | allenai/sciq | What is the primary gas produced from burning of wood?
A. toxic dioxide
B. carbon dioxide
C. liquid dioxide
D. Hydrogen Dioxide | B. carbon dioxide | When wood burns, it changes to ashes, carbon dioxide, water vapor, and other gases. You can see ashes in the wood fire pictured here. The gases are invisible. | high_school_chemistry | chemistry | |
math_570 | math_mc | How many non-congruent squares can be drawn, such that their vertices are lattice points on the 5 by 5 grid of lattice points shown? [asy]
dot((0,0));dot((1,0));dot((2,0));dot((3,0));dot((4,0));
dot((0,1));dot((1,1));dot((2,1));dot((3,1));dot((4,1));
dot((0,2));dot((1,2));dot((2,2));dot((3,2));dot((4,2));
dot((0,3));do... | C | math_Counting & Probability | mathematics | ||
mmlu_aux_train_48060 | mmlu_aux_train | Everyday rubbish could provide a valuable source of energy thanks to a clever new invention. Smelly methane gas expelled from landfill sites containing tones of rotting household waste could be used to produce a valuable energy resource. In Europe alone land fill tips produce 94 billion cubic meters of methane per year... | B. a new way to make use of rubbish | college_chemistry | chemistry |
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