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 |
|---|---|---|---|---|---|---|---|
aquarat_95612 | deepmind/aqua_rat | what is the remainder of 18!/23? | A. 1 B. 2 C. 3 D. 4 E. 5 | A. 1 | Let rem[18!/23]=r
Wilson's Theorem says rem[(p-2)!/p]=1
rem[21!/23]=1
rem[21*20*19*18!/23]=1
rem[(-2)(-3)(-4)*r/23]=1
rem[-24r/23]=1
24r=-23K+1 ... k=-1
r=23+1/24
r=1
ANSWER:A | college_mathematics | mathematics |
allenai/sciq_2842 | allenai/sciq | Coral and the algae living inside of them have what type of relationship, since the algae relies on the coral to stay close to the water's surface?
A. competitive
B. symbiotic
C. parasitic
D. peculiar | B. symbiotic | Corals form large colonies in shallow tropical water. They are confined to shallow water because they have a symbiotic relationship with algae that live inside of them. The algae need sunlight for photosynthesis, so they must stay relatively close to the surface of the water to get enough light. Corals exist only as po... | high_school_biology | biology | |
mmlu_aux_train_94028 | mmlu_aux_train | What season is the Northern Hemisphere experiencing when it is tilted directly toward the Sun?
A. fall
B. winter
C. spring
D. summer | D. summer | astronomy | physics | ||
allenai/sciq_10807 | allenai/sciq | While spermatogenesis produces four haploid sperm cells, oogenesis produces one mature what?
A. egg
B. ovum
C. semen
D. datum | B. ovum | Spermatogenesis produces four haploid sperm cells, while oogenesis produces one mature ovum. | high_school_biology | biology | |
pythonio_395 | pythonio-mc | Program:
from collections import OrderedDict
def remove_duplicate(string):
result = ' '.join(OrderedDict((w,w) for w in string.split()).keys())
return result
Input:
remove_duplicate("Python Exercises Practice Solution Practice")
Output: | D | code | computer_science | ||
NLP4Education_196 | NLP4Education | Decision trees...
A. are only applicable to regression tasks.
B. can be used for both classification and regression.
C. always require neural networks to function.
D. must have multiple leaves per node. | B. can be used for both classification and regression. | machine_learning | computer_science | ||
allenai/sciq_10595 | allenai/sciq | What are formed by atoms gaining electrons?
A. oxides
B. cations
C. anions
D. ions | C. anions | Figure 7.10 Cations are formed when atoms lose electrons, represented by fewer Lewis dots, whereas anions are formed by atoms gaining electrons. The total number of electrons does not change. | high_school_chemistry | chemistry | |
math_355 | math_mc | If $f(3)=1$ and $f(2x)=2f(x)$ for all $x$, find $f^{-1}(64)$. | B | math_Algebra | mathematics | ||
aquarat_29470 | deepmind/aqua_rat | If x,y ,and z are positive real numbers such that x+y-z = 62, y-z+x =82 , and z-x+y = 100, then find the x+y+z value? | A. 80 B. 91 C. 62 D. 74 E. 82 | E. 82 | x+y-z = 62, ------1)
y-z+x =82 , ------2)
z-x+y = 100------3)
from (1)&(2)
2z=20
z=10
from (2)&(3)
2y = 182
y=91
then x=62-81= -19
x+y+z = 82
correct option is E | college_mathematics | mathematics |
aquarat_90514 | deepmind/aqua_rat | Score Interval Number of Scores
50-59 2
60-69 10
70-79 16
80-89 27
90-99 17
The table shows a distribution of test scores. Which score interval contains the median of the 72 scores? | A. a) 60-69 B. b) 70-79 C. c) 80-89 D. d) 90-99 E. e) Cannot determine. | C. c) 80-89 | 36th person
80-89 C | high_school_statistics | mathematics |
NLP4Education_164 | NLP4Education | Which of the following is correct regarding prediction models?
A. Training error being lower than test error always means underfitting.
B. Complex models are more prone to overfitting, especially with limited data.
C. Simple models always have lower bias compared to complex models.
D. Training error always equals test ... | B. Complex models are more prone to overfitting, especially with limited data. | machine_learning | computer_science | ||
math_867 | math_mc | The number of inches in the perimeter of an equilateral triangle equals the number of square inches in the area of its circumscribed circle. What is the radius, in inches, of the circle? Express your answer in terms of pi and in simplest radical form. | B | math_Geometry | mathematics | ||
allenai/sciq_1529 | allenai/sciq | What is denoted by the number above the chemical symbol of each element in a modern periodic table?
A. electron count
B. metallic number
C. atomic weight
D. atomic number | D. atomic number | In the modern periodic table, each element is represented by its chemical symbol. The number above each symbol is its atomic number. Atomic numbers increase from left to right and from top to bottom in the table. | high_school_chemistry | chemistry | |
pythonio_198 | pythonio-mc | Program:
def big_diff(nums):
diff= max(nums)-min(nums)
return diff
Input:
big_diff([1,2,3,4])
Output: | A | code | computer_science | ||
allenai/sciq_10573 | allenai/sciq | What is a layer of saturated porous rock?
A. a quarry
B. an overhang
C. an aquifer
D. a shear | C. an aquifer | An aquifer is a layer of saturated porous rock. It lies below the water table. An impermeable layer, such as clay, is below the aquifer. | college_earth_science | earth_science | |
math_520 | math_mc | 23 people attend a party. Each person shakes hands with at least two other people. What is the minimum possible number of handshakes? | C | math_Counting & Probability | mathematics | ||
aquarat_68424 | deepmind/aqua_rat | Letters of alphabets no from 1 to 26 are consecutively with 1 assigned to A and 26 to Z. By 27th letter we mean A, 28th B. In general 26m+n, m and n negative intezers is same as the letters numbered n.
Let P = 6, strange country military general sends this secret message according ot the following codification scheme. ... | A. DFHASDO B. HDFAHLOU C. LDOIHYAD D. GHLKZOIR E. LODIHFAD | D. GHLKZOIR | A should be coded as 1+6 = G (it occurred for first time)
B should be coded as 2+6 = H (it occurred for first time)
B Should be coded as 2 + 36 = 38 - 26 = 12 = L (it occurred for second time)
Option D is correct | abstract_algebra | mathematics |
mmlu_aux_train_83656 | mmlu_aux_train | Peter: Let's play computer games! Barry: Sorry, I don't like computer games, and I don't have a computer. Peter: Well, do you have a volleyball? Barry: Yes. Peter: Then let's play volleyball. Barry: Oh, volleyball is difficult. Peter: OK, let's watch TV. Barry: That sounds boring. Hmm, let's play soccer! Do you have a ... | A. Peter. | high_school_computer_science | computer_science | ||
mmlu_aux_train_96011 | mmlu_aux_train | What will become magnetic in an electromagnet if the battery becomes active?
A. A construction nail
B. A plastic nail
C. A nail box
D. A wooden nail | A. A construction nail | conceptual_physics | physics | ||
math_1985 | math_mc | The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse? | D | math_Prealgebra | mathematics | ||
aquarat_20740 | deepmind/aqua_rat | The end of a blade on an airplane propeller is 10 feet from the center. If the propeller spins at the rate of 1,320 revolutions per second, how many miles will the tip of the blade travel in one minute? (1 mile = 5,280 feet) | A. 200π B. 240π C. 300π D. 480π E. 1,200π | C. 300π | Distance traveled in 1 revolution = 2πr= 2π10/5280
Revolutions in one second= 1320
Revolutions in 60 seconds (one minute)= 1320*60
Total distance traveled= total revolutions *distance traveled in one revolution
1320*60 *2π10/5280= 300π
C is the answer | college_mathematics | mathematics |
allenai/sciq_11227 | allenai/sciq | What is a thick, dark brown or black liquid found in rock layers of the earth's crust?
A. coal
B. fossil fuel
C. oil
D. propane | C. oil | Oil is a thick, dark brown or black liquid. It is found in rock layers of Earth's crust. Oil is currently the most commonly used source of energy in the world. | college_earth_science | earth_science | |
mmlu_aux_train_96037 | mmlu_aux_train | A bird eating a lizard is an example of what type of relationship?
A. symbiotic
B. producer
C. parasitic
D. predatory | D. predatory | high_school_biology | biology | ||
mmlu_aux_train_69631 | mmlu_aux_train | On April 20th,2013, a big earthquake hit Ya'an, Sichuan. Nearly 200 people died. Many people were hurt. Why do earthquakes happen? The surface of the earth has many pieces. These pieces are always moving. When two pieces move past each other, there is an earthquake. Scientists are working hard to find out more about e... | B. on April 20th, 2013 | earth_science | earth_science | ||
NLP4Education_209 | NLP4Education | Consider a learning algorithm that has the property that it depends only very weakly on the input data. E.g., this could be SGD where we choose a very small step size and only run for very few iterations. To go to the extreme, you can imagine a learning algorithm that always outputs the same model irrespective of the t... | C. Such a learning algorithm typically has a large bias. | machine_learning | computer_science | ||
math_2078 | math_mc | Find the ordered pair $(a,b)$ of integers such that
\[\sqrt{9 - 8 \sin 50^\circ} = a + b \csc 50^\circ.\] | A | math_Precalculus | mathematics | ||
allenai/sciq_5477 | allenai/sciq | Dependent on the frequency of sound waves, what term described how high or low a sound seems to a listener?
A. pitch
B. wavelength
C. direction
D. curve | A. pitch | How high or low a sound seems to a listener is its pitch . Pitch, in turn, depends on the frequency of sound waves. Wave frequency is the number of waves that pass a fixed point in a given amount of time. High-pitched sounds, like the sounds of the piccolo in the Figure below , have high-frequency waves. Low-pitched so... | conceptual_physics | physics | |
mmlu_aux_train_6301 | mmlu_aux_train | There are robots all around us,Some do very complicated jobs like flying airplanes and driving subway trains. And some do a simple job. When an automatic washing machine is switched on, water pours in. The machine waits until the water is hot before washing the clothes. It does this by "feedback". Information about wha... | D. robots are all around us | high_school_computer_science | computer_science | ||
aquarat_20355 | deepmind/aqua_rat | Statements: Government has spoiled many top ranking financial institutions by appointing bureaucrats as Directors of these institutions. Assumptions: 1) Government should appoint Directors of the financial institutes taking into consideration the expertise of the person in the area of finance. 2) The Director of the fi... | A. Only conclusion I follows B. Only conclusion II follows C. Either I or II follows D. Neither I nor II follows E. Both I and II follow | E. Both I and II follow | According to the statement, Government has spoiled financial institutions by appointing bureaucrats as Directors. This means that only those persons should be appointed as Directors who are experts in finance and are acquainted with the financial work of the institute. So, both I and II follow.
E | formal_logic | mathematics |
allenai/sciq_1805 | allenai/sciq | Balanced chemical reactions are balanced in what?
A. atoms
B. molecular bonds
C. terms of moles
D. electrical charge | C. terms of moles | Balanced chemical reactions are balanced in terms of moles. | high_school_chemistry | chemistry | |
aquarat_23869 | deepmind/aqua_rat | By how much does the larger root of the equation 2z^2+5z = 12 exceed the smaller root? | A. 5/2 B. 10/3 C. 7/2 D. 14/3 E. 11/2 | E. 11/2 | For 2z^2+5z = 12 Roots are [-5 + sqrt(25 + 96)]/4 OR [-5 - sqrt(25 + 96)]/4
= 1.5 OR -4
Hence larger root 1.5 is 1.5 - (-4) = 5.5 = 11/2 greater than smaller root (-4).
Hence option (E). | college_mathematics | mathematics |
mmlu_aux_train_28254 | mmlu_aux_train | Around 200 million years ago, the earth was 18 degrees warmer than it is now. That might be a bit hot for humans, but it was just right for the giant dinosaurs that wandered about the earth during the Mesozoic era. A new study found that planteating dinosaurs may have contributed to the warming of the earthby releas... | C. they released a lot of methane | college_biology | biology | ||
mmlu_aux_train_2356 | mmlu_aux_train | What unit do scientists use to measure the distance between stars?
A. light-year
B. angstrom unit
C. astronomical unit
D. apparent magnitude | A. light-year | astronomy | physics | ||
mmlu_aux_train_93360 | mmlu_aux_train | A negatively-charged ion has
A. a heavier nucleus.
B. a greater atomic mass.
C. more electrons than protons.
D. more electrons than neutrons. | C. more electrons than protons. | high_school_chemistry | chemistry | ||
mmlu_aux_train_30149 | mmlu_aux_train | A study of older men in The Netherlands, known for its delicious chocolate, showed those who ate the same amount of one-third of a chocolate bar every day had lower blood pressure and a reduced risk of death. The researchers say, however, it's too early to conclude that it was the chocolate that led to better health. T... | D. there had been other similar studies before the Dutch study | college_biology | biology | ||
math_552 | math_mc | When a certain biased coin is flipped five times, the probability of getting heads exactly once is not equal to $0$ and is the same as that of getting heads exactly twice. Let $\frac ij$, in lowest terms, be the probability that the coin comes up heads in exactly $3$ out of $5$ flips. Find $i+j$.
| A | math_Counting & Probability | mathematics | ||
aquarat_30828 | deepmind/aqua_rat | Given that f(x) = x×f(x - 1) for any natural number x. If f(x + 2) = 20*f(x), then what is the value of x? | A. 5 B. 6 C. 7 D. 8 E. 98 | B. 6 | Given:f(x) = x××f(x - 1) ....(a)
and f(x + 2) = 20××f(x) ....(b)
Substitute x = x + 1 in (a)
Then, f(x + 1) = (x + 1)××f(x) .........(c)
Substitute x = x + 2 in (a)
Then, f(x + 2) = (x + 2)××f(x + 1) ......(d)
From (b), 20××f(x) = f(x + 2) = (x + 2)××f(x + 1)= (x + 2)(x + 1)××f(x)
⇒⇒ 20××f(x) = (x + 2) (x + 1)××(f(x)
C... | college_mathematics | mathematics |
aquarat_15944 | deepmind/aqua_rat | Suppose son name is 120,his brother name is 150 and his mother name is 180.find out his father's name??? | A. 190 B. 210 C. 230 D. 240 E. 250 | C. 230 | since difference between all name is =30
so father's name will be 180+30=210.
ANSWER:C | formal_logic | mathematics |
aquarat_87593 | deepmind/aqua_rat | Let f(x) = ax2 - b|x|, where a and b are constant. Then at x =0, f(x) is | A. maximized whenever a>0, b>0 B. maximized whenever a>0, b<0 C. minimized whenever a>0, b>0 D. minimized whenever a>0, b<0 E. None of these | D. minimized whenever a>0, b<0 | Explanation :
When a > 0, b < 0, ax2 and –b |x| are non negative for all x.
i.e. ax2 – b|x| ≥ 0.
∴ ax2 – b |x| is minimum at x = 0 when a > 0, b < 0.
Answer : D | college_mathematics | mathematics |
mmlu_aux_train_93338 | mmlu_aux_train | Copper is used in house wiring because it is
A. magnetic.
B. an insulator.
C. an electrical conductor.
D. hard to bend into new shapes. | C. an electrical conductor. | high_school_physics | physics | ||
allenai/sciq_9359 | allenai/sciq | Breaking a window with a baseball is an example of what kind of change in matter?
A. chemical
B. unusual
C. physical
D. sudden | C. physical | You hit a baseball out of the park and head for first base. You’re excited. The score is tied, and now your team has a chance of getting a winning home run. Then you hear a crash. Oh no! The baseball hit a window in a neighboring house. The glass has a big hole in it, surrounded by a web of cracks (see Figure below ). ... | high_school_chemistry | chemistry | |
pythonio_87 | 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 | ||
aquarat_1625 | deepmind/aqua_rat | A train with a length of 100 meters, is traveling at a speed of 72 km/hr. The train enters a tunnel 2.3 km long. How many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges? | A. 2.0 B. 2.5 C. 3.0 D. 3.5 E. 4.0 | A. 2.0 | 72 km/hr = 1.2 km/min
The total distance is 2.4 km.
2.4 / 1.2 = 2 minutes
The answer is A. | high_school_physics | physics |
math_1345 | math_mc | Let $x$ be a real number, $x > 1.$ Compute
\[\sum_{n = 0}^\infty \frac{1}{x^{2^n} - x^{-2^n}}.\] | B | math_Intermediate Algebra | mathematics | ||
pythonio_434 | pythonio-mc | Program:
def extract_unique(test_dict):
res = list(sorted({ele for val in test_dict.values() for ele in val}))
return res
Input:
extract_unique({'F' : [11, 13, 14, 17],'A' : [12, 11, 15, 18],'N' : [19, 21, 15, 36],'G' : [37, 36, 35]})
Output: | D | code | computer_science | ||
allenai/sciq_9750 | allenai/sciq | What is the role of the sodium ion in the neutralization reaction of sodium flouride?
A. team ion
B. circuit ion
C. spectator ion
D. reflection ion | C. spectator ion | Since sodium fluoride is soluble, the sodium ion is a spectator ion in the neutralization reaction. The fluoride ion is capable of reacting, to a small extent, with water, accepting a proton. | high_school_chemistry | chemistry | |
aquarat_48113 | deepmind/aqua_rat | If a certain sample of data has a mean of 10.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean? | A. (5.0; 16.5) B. (8.5; 21.0) C. (14.0; 26.5) D. (16.5; 26.0) E. (21.0; 26.5) | A. (5.0; 16.5) | 2.5 standard deviation equals to 2.5*2=5;
2.5 standard deviations from the mean, so5 points, from the mean is the range from {mean-5} to {mean+5}, so from 5 to 15:
The correct answer choice must cover all this range: only answer choice A does this.
Answer:A. | high_school_statistics | mathematics |
mmlu_aux_train_20527 | mmlu_aux_train | As the mobile phones so widely appear in our daily life, someone said it would be cool if you didn't have a mobile phone nowadays. It might be true to some extent, but as for an adult, a mobile means contact. It connects your work, relatives, friends, etc. It should do great deeds for us. Months ago, my uncle gave his ... | C. mobile phones are too popular among people now | high_school_computer_science | computer_science | ||
mmlu_aux_train_99510 | mmlu_aux_train | to determine how firm a certain mineral may be a person can:
A. measure the weight of it
B. attempt to leave a mark on it
C. crush it to see the inside
D. see if it can bounce | B. attempt to leave a mark on it | high_school_chemistry | chemistry | ||
mmlu_aux_train_89918 | mmlu_aux_train | John is 14 years old. He is a student of Grade Eight. He was a very active and happy boy two years ago. But everything changed after he started to play computer games. He never plays basketball or football with his friends any more. And when he sits in the classroom, he can't listen to the teachers. He sleeps in class.... | C. active and happy | high_school_computer_science | computer_science | ||
aquarat_36104 | deepmind/aqua_rat | Amy's grade was 90th percentile of the 80 grades for her class. Of the 100 grades from another class, 19 were higher than Amy's, and the rest were lower. If no other grade was the same as Amy's grade, then Amy's grade was what percentile of the grades of the two classes of two classes combined? | A. 72nd B. 80th C. 81st D. 85th E. 92nd | D. 85th | Being in 90% percentile out of 80 grades means Amy was 73rd (from the least grade) in the class (as long as nobody had Amy's grades), she outscored 72.
In another class her grade would rank her 82 (from the least grade out of 101, 100+Amy), 81 had the grades lower than Amy.
So in combined classes she outscored 72+81=15... | high_school_statistics | mathematics |
allenai/sciq_6761 | allenai/sciq | Overharvesting is a serious threat particularly to which species?
A. amphibious species
B. terrestrial species
C. aerial species
D. aquatic species | D. aquatic species | Overharvesting Overharvesting is a serious threat to many species, but particularly to aquatic species. There are many examples of regulated fisheries (including hunting of marine mammals and harvesting of crustaceans and other species) monitored by fisheries. | college_biology | biology | |
math_729 | math_mc | [asy] draw((0,0)--(1,sqrt(3)),black+linewidth(.75),EndArrow); draw((0,0)--(1,-sqrt(3)),black+linewidth(.75),EndArrow); draw((0,0)--(1,0),dashed+black+linewidth(.75)); dot((1,0)); MP("P",(1,0),E); [/asy]
Let $S$ be the set of points on the rays forming the sides of a $120^{\circ}$ angle, and let $P$ be a fixed point ins... | A | math_Geometry | mathematics | ||
math_1729 | math_mc | Let $a_{10} = 10$, and for each positive integer $n >10$ let $a_n = 100a_{n - 1} + n$. Find the least positive $n > 10$ such that $a_n$ is a multiple of $99$.
| C | math_Number Theory | mathematics | ||
mmlu_aux_train_4818 | mmlu_aux_train | During science class, students combined 1 kg of iron filings with 1 kg of sand to create a mixture. Which of the following methods would be best for separating the iron filings from the sand?
A. Stir the mixture into hot water to dissolve the sand.
B. Strain the mixture through a paper filter to collect the sand.
C. D... | C. Drag a magnet through the mixture to attract the iron filings. | high_school_chemistry | chemistry | ||
NLP4Education_203 | NLP4Education | Your friend Charlie was training a neural net, and observed something very curious. During training, the same network, with the same exact weights, doesn't always give the same prediction for a given example. What can cause this behavior?
A. L2 regularization
B. Batch normalization
C. Convolutional layers
D. Residual l... | B. Batch normalization | machine_learning | computer_science | ||
allenai/sciq_11422 | allenai/sciq | What do we call the amount of time a substance is stored in a reservoir?
A. residence time
B. latency
C. storage time
D. presence time | A. residence time | A substance is stored in a reservoir. The amount of time it stays in that reservoir is its residence time. | college_physics | physics | |
math_286 | math_mc | If $x$ and $y$ are positive integers such that $5x+3y=100$, what is the greatest possible value of $xy$? | A | math_Algebra | mathematics | ||
pythonio_713 | pythonio-mc | Program:
def get_inv_count(arr, n):
inv_count = 0
for i in range(n):
for j in range(i + 1, n):
if (arr[i] > arr[j]):
inv_count += 1
return inv_count
Input:
get_inv_count([1, 20, 6, 4, 5], 5)
Output: | B | code | computer_science | ||
aquarat_11388 | deepmind/aqua_rat | The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ? | A. 165 B. 185 C. 198 D. 221 E. 240 | B. 185 | 185
Answer is B | high_school_statistics | mathematics |
allenai/sciq_2957 | allenai/sciq | Which part of an earthquake is in the ground where the ground breaks?
A. the tectonic plate
B. the focus
C. the fault
D. the epicenter | B. the focus | The focus of an earthquake is in the ground where the ground breaks. The epicenter is the point at the surface just above the focus. | conceptual_physics | physics | |
mmlu_aux_train_11918 | mmlu_aux_train | Interactive Home-security Systems Tarik Celebi, who lives in San Francisco suburb, takes his home-security system with him to work, to dinner, just about anywhere.By his cell phone, he "arms" his home-security alarm from his car before he leaves for work.During his workday, he gets e-mail alerts every time his front do... | D. Observe through video. | computer_security | computer_science | ||
allenai/sciq_3397 | allenai/sciq | What is the ratio of charge on a capacitor to potential difference across it called?
A. electromagnetism
B. velocity
C. capacitance
D. resonance | C. capacitance | When a capacitor is placed in a circuit, current does not actually travel across it. Rather, equal and opposite charge begins to build up on opposite sides of the capacitor --- mimicking a current --- until the electric field in the capacitor creates a potential difference across it that balances the voltage drop acros... | electrical_engineering | engineering | |
pythonio_837 | pythonio-mc | Program:
def previous_palindrome(num):
for x in range(num-1,0,-1):
if str(x) == str(x)[::-1]:
return x
Input:
previous_palindrome(99)
Output: | D | code | computer_science | ||
math_1436 | math_mc | Let $P(x) = (x-1)(x-2)(x-3)$. For how many polynomials $Q(x)$ does there exist a polynomial $R(x)$ of degree 3 such that $P\left(Q(x)\right) = P(x)\cdot R(x)$? | C | math_Intermediate Algebra | mathematics | ||
aquarat_70649 | deepmind/aqua_rat | There is a 50% chance that Alice will visit China this year, while there is a 20% chance that she will visit Brazil this year. What is the probability that Alice will visit either China or Brazil this year, but NOT both? | A. 50% B. 45% C. 40% D. 35% E. 30% | A. 50% | P(China but not Brazil)=0.5*0.8=0.4
P(Brazil but not China)=0.2*0.5=0.1
P(China or Brazil but not both)=0.4+0.1=0.5
The answer is A. | high_school_statistics | mathematics |
aquarat_65277 | deepmind/aqua_rat | In a soccer bet,we play 4 teams.first team odd 1.29,second 5.23,third 3.25,fourth 2.05.we place the bet with 5.00 euros.
how much money we expect to win? | A. 219.5 B. 224.75 C. 235.01 D. 266.74 E. 669.0 | B. 224.75 | in the case we won the bet,we have:
1.29* 5.23* 3.25* 2.0*5.00=219.50
we will win 224.75
so correct answer is B | high_school_statistics | mathematics |
math_2039 | math_mc | A pentagon is drawn by placing an isosceles right triangle on top of a square as pictured. What percent of the area of the pentagon is the area of the right triangle?
[asy]
size(50);
draw((0,0)--(0,-1)--(1,-1)--(1,0)--(0,0)--(.5,.5)--(1,0));
[/asy] | A | math_Prealgebra | mathematics | ||
math_1507 | math_mc | The four positive integers $a,$ $b,$ $c,$ $d$ satisfy
\[a \times b \times c \times d = 10!.\]Find the smallest possible value of $a + b + c + d.$ | A | math_Intermediate Algebra | mathematics | ||
NLP4Education_745 | NLP4Education | Consider a $(k+1,k)$ block code that to a binary sequence $x_1,\dots,x_k$ associates the codeword $x_1,\dots,x_k,x_{k+1}$, where $x_{k+1}= x_1+\ldots+x_k$ mod $2$. This code can detect all the errors of odd weight.
A. True, the code detects all errors of odd weight
B. False, the code cannot detect any errors
C. True, t... | A. True, the code detects all errors of odd weight | college_mathematics | mathematics | ||
allenai/sciq_9744 | allenai/sciq | Functional groups are groups of atoms that occur within molecules and confer specific chemical properties to those molecules. they are found along the “carbon backbone” of what?
A. inorganic molecules
B. micromolecules
C. macromolecules
D. functional molecules | C. macromolecules | Functional Groups Functional groups are groups of atoms that occur within molecules and confer specific chemical properties to those molecules. They are found along the “carbon backbone” of macromolecules. This carbon backbone is formed by chains and/or rings of carbon atoms with the occasional substitution of an eleme... | college_chemistry | chemistry | |
pythonio_965 | pythonio-mc | Program:
def min_sum_path(A):
memo = [None] * len(A)
n = len(A) - 1
for i in range(len(A[n])):
memo[i] = A[n][i]
for i in range(len(A) - 2, -1,-1):
for j in range( len(A[i])):
memo[j] = A[i][j] + min(memo[j],
memo[j + 1])
return memo[0]
Input:
min_sum_path([[ 3 ], [6, 4 ], [5, 2, 7... | C | code | computer_science | ||
NLP4Education_154 | NLP4Education | Which of the following is true regarding the random forest classification algorithm?
A. It is not suitable for parallelization.
B. It uses only a subset of features for learning in each weak learner.
C. A prediction is made by randomly selecting the output of one weak learner.
D. It always generates a single, easily in... | B. It uses only a subset of features for learning in each weak learner. | machine_learning | computer_science | ||
math_2162 | math_mc | If $\mathbf{a}$ and $\mathbf{b}$ are two unit vectors, with an angle of $\frac{\pi}{3}$ between them, then compute the volume of the parallelepiped generated by $\mathbf{a},$ $\mathbf{b} + \mathbf{b} \times \mathbf{a},$ and $\mathbf{b}.$ | A | math_Precalculus | mathematics | ||
mmlu_aux_train_93651 | mmlu_aux_train | When liquid water freezes, it forms ice. What is the physical state of an ice cube?
A. gas
B. solid
C. liquid
D. plasma | B. solid | high_school_physics | physics | ||
pythonio_376 | pythonio-mc | Program:
def average_Even(n) :
if (n% 2!= 0) :
return ("Invalid Input")
return -1
sm = 0
count = 0
while (n>= 2) :
count = count+1
sm = sm+n
n = n-2
return sm // count
Input:
average_Even(100)
Output: | A | code | computer_science | ||
mmlu_aux_train_1803 | mmlu_aux_train | Which geologic process most likely led to the uplifting of the Rocky Mountains?
A. glaciation
B. flooding
C. faulting
D. erosion | C. faulting | college_science | earth_science | ||
allenai/sciq_5643 | allenai/sciq | When a sperm penetrates the egg, it triggers the egg to complete what?
A. lesions
B. mutations
C. meiosis
D. fertilization | C. meiosis | When a sperm penetrates the egg, it triggers the egg to complete meiosis. The sperm also undergoes changes. Its tail falls off, and its nucleus fuses with the nucleus of the egg. The resulting cell, called a zygote, contains all the chromosomes needed for a new human organism. Half the chromosomes come from the egg and... | high_school_biology | biology | |
mmlu_aux_train_95944 | mmlu_aux_train | A television may turn on at the push of a button because
A. the circuit has shorted out
B. the television is pretty short
C. the path of electricity is completed
D. the button was plastic | C. the path of electricity is completed | conceptual_physics | physics | ||
aquarat_9786 | deepmind/aqua_rat | Set A = {1, 2, 3, 4, 5, 6, e}
Which of the following possible values for e would cause Set A to have the smallest standard deviation? | A. 1 B. 2.5 C. 3 D. 3.5 E. 7 | D. 3.5 | I agree. The mean of the set e 1,2,3,4,5,6 is 3.5 . Now if we add one extra number to the set, in order for the standard deviation to be minimum, that number must be as close as possible to the original set (1,2,3,4,5,6). Therefore we have to choose the number closest to 3,5 from the options we have, leaving D as the b... | college_mathematics | mathematics |
pythonio_317 | pythonio-mc | Program:
def sample_nam(sample_names):
sample_names=list(filter(lambda el:el[0].isupper() and el[1:].islower(),sample_names))
return len(''.join(sample_names))
Input:
sample_nam(['sally', 'Dylan', 'rebecca', 'Diana', 'Joanne', 'keith'])
Output: | B | code | computer_science | ||
allenai/sciq_1922 | allenai/sciq | The structure of the gas carbon dioxide consists of one atom of carbon and two atoms of what?
A. sulfur
B. Helium
C. oxygen
D. methane | C. oxygen | Another example is carbon dioxide. This gas is produced from a variety of reactions, often by the burning of materials. The structure of the gas consists of one atom of carbon and two atoms of oxygen. Carbon dioxide production is of interest in many areas, from the amount we breather out to the amount of the gas produc... | high_school_chemistry | chemistry | |
allenai/sciq_7226 | allenai/sciq | Pairs of fish that do not practice broadcast what may exhibit courtship behavior?
A. feeding
B. spawning
C. migration
D. inheritance | B. spawning | Vinegar is primarily an aqueous solution of acetic acid. Commercial vinegar typically contains 5.0 g of acetic acid in 95.0 g of water. What is the concentration of commercial vinegar? If only 3.1% of the acetic acid −. | high_school_biology | biology | |
aquarat_63503 | deepmind/aqua_rat | The end of a blade on an airplane propeller is 15 feet from the center. If the propeller spins at the rate of 1,320 revolutions per second, how many miles will the tip of the blade travel in one minute? (1 mile = 5,280 feet) | A. 200π B. 240π C. 300π D. 450π E. 1,200π | D. 450π | Distance traveled in 1 revolution = 2πr= 2π15/5280
Revolutions in one second= 1320
Revolutions in 60 seconds (one minute)= 1320*60
Total distance traveled= total revolutions *distance traveled in one revolution
1320*60 *2π15/5280= 450π
D is the answer | conceptual_physics | physics |
mmlu_aux_train_4543 | mmlu_aux_train | Scientists estimate that Maryland contains more than 850 million tons of coal. Coal is most commonly used to produce ___.
A. electricity
B. medicine
C. metals
D. water | A. electricity | high_school_chemistry | chemistry | ||
mmlu_aux_train_98137 | mmlu_aux_train | the central object of our solar system is also
A. the smallest object in the solar system
B. the coldest heavenly body
C. the farthest star from us
D. the closest star from us | D. the closest star from us | astronomy | physics | ||
aquarat_67723 | deepmind/aqua_rat | Find the probability that the sum of n numbers is divisible by n,assuming n is very large no. | A. 1 B. 1/2 C. 3/4 D. None of these E. Can't be determined. | B. 1/2 | sum of n numbers is n(n+1)/2
case 1)when n is odd take 3
Sum is 3*4/3 it is divisible by 3
we can conclude that n=odd sum of n numbers is divisible by n
case2) when n is even take 4
Sum is 4*5/2=>10 10/4 rem is 2 so not divisible
we can conclude that n=even sum of n numbers is not divisible by n
Total of total 2 cases ... | college_mathematics | mathematics |
aquarat_24123 | deepmind/aqua_rat | If a certain sample of data has a mean of 22.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean? | A. 12.0 B. 14.0 C. 17.0 D. 23.5 E. 26.5 | B. 14.0 | Value ismore than 2.5SDfrom the mean means that the distance between the mean and the value must be more than 2.5*SD=7.5. So the value must be either less than 22-7.5=14.5or more than 22+7.5=29.5.
Answer:B. | high_school_statistics | mathematics |
NLP4Education_809 | NLP4Education | Suppose we have the following function \(f: [0, 2] \to [-\pi, \pi]\).
\[
f(x) =
\begin{cases}
x^2 & \text{ for } 0\leq x < 1 \\
2-(x-2)^2 & \text{ for } 1 \leq x \leq 2
\end{cases}
\]
Which of the following best describes the function \(f\)?
A. \(f\) is not injective and not surjective.
B. \(f\) is injective bu... | B. \(f\) is injective but not surjective. | college_mathematics | mathematics | ||
mmlu_aux_train_6132 | mmlu_aux_train | Too much TV-watching can harm children's ability to learn and even reduce their chances of getting a college degree, new studies suggest in the latest effort to examine the effects of television on children. One of the studies looked at nearly 400 northern California third-graders. Those with TVs in their bedrooms scor... | A. have watched a lot of TV | high_school_statistics | mathematics | ||
mmlu_aux_train_39290 | mmlu_aux_train | Alexander von Humboldt was born in 1769 in Berlin, Germany. As a young boy, he wanted to learn about the world. Humboldt followed his dream. In 1799, he traveled with a friend to Central and South America. On their trip, Humboldt and his friend saw and did many things. They sailed down the Amazon River. They watched do... | A. explorer | high_school_biology | biology | ||
aquarat_34973 | deepmind/aqua_rat | What is the largest power of 3 contained in 200! | A. 88 B. 48 C. 66 D. 97 E. 39 | D. 97 | In real basic terms, we're asked to find all of the '3s' in 200!
We can figure out that 200/3 = 66, so we know that there are at least 66 '3s' in 200! While that answer is among the 5 choices, it seems a bit too 'easy', so let's do a bit more work and list out the first few numbers that we know have a '3' in them:
3 = ... | college_mathematics | mathematics |
pythonio_500 | pythonio-mc | Program:
def sum_list(lst1,lst2):
res_list = [lst1[i] + lst2[i] for i in range(len(lst1))]
return res_list
Input:
sum_list([15,20,30],[15,45,75])
Output: | C | code | computer_science | ||
math_885 | math_mc | In $\triangle ABC$, $AB= 425$, $BC=450$, and $AC=510$. An interior point $P$ is then drawn, and segments are drawn through $P$ parallel to the sides of the triangle. If these three segments are of an equal length $d$, find $d$.
| D | math_Geometry | mathematics | ||
allenai/sciq_11353 | allenai/sciq | What type of coal is formed at lower temperatures?
A. limestones
B. clean
C. calcareous
D. bituminous | D. bituminous | Coal has different grades. Bituminous coal forms at lower temperatures. It contains a lot of sulfur. When it is burned, it causes a lot of pollution. Anthracite coal forms under higher temperatures. This drives off the sulfur, and the coal burns more cleanly. | high_school_chemistry | chemistry | |
mmlu_aux_train_55760 | mmlu_aux_train | It's a safe bet that a robot made your car and made your computer. Pretty soon, they could be making your bed and breakfast too. Increasingly, engineers are saying that robots are going to move out of research departments and into your home. Companies including General Electric are working on designs for small rob... | D. Great demand from the buyers. | high_school_computer_science | computer_science | ||
math_162 | math_mc | The complete graph of $y=f(x)$, which consists of five line segments, is shown in red below. (On this graph, the distance between grid lines is $1$.)
What is the sum of the $x$-coordinates of all points where $f(x) = 1.8$?
[asy]
size(150);
real ticklen=3;
real tickspace=2;
real ticklength=0.1cm;
real axisarrowsi... | C | math_Algebra | mathematics | ||
math_1484 | math_mc | Compute
\[\sum_{n = 1}^\infty \frac{2n + 1}{n(n + 1)(n + 2)}.\] | A | math_Intermediate Algebra | mathematics | ||
math_288 | math_mc | $\sqrt{53+20\sqrt{7}}$ can be written in the form $a+b\sqrt{c}$, where $a,$ $b,$ and $c$ are integers and $c$ has no factors which is a perfect square of any positive integer other than 1. Find $a+b+c$. | B | math_Algebra | mathematics | ||
mmlu_aux_train_6503 | mmlu_aux_train | When Nick Pasqua hits his bedroom after school, he's tired. The 14-year-old high school freshman from New Rochele, New York, plays computer video games online for a couple of hours, pausing only to instant-message his friends, check his blog or download a new song to his IPOD. When his cell phone vibrates , he scans th... | B. 87 percent of kids in the USwho use the Internet | high_school_computer_science | computer_science |
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