question_id
int64 2
5k
| category
stringclasses 12
values | difficulty
stringclasses 3
values | question
stringlengths 10
89
| correct_answer
stringclasses 370
values | option_a
stringclasses 545
values | option_b
stringclasses 544
values | option_c
stringclasses 546
values | option_d
stringclasses 550
values | explanation
stringclasses 12
values |
|---|---|---|---|---|---|---|---|---|---|
4,673 |
combinatorics
|
easy
|
How many ways can 5 people stand in a line?
|
120
|
10
|
120
|
24
|
25
|
Permutations and combinations
|
3,915 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
Depends on values
|
Cannot determine
|
True
|
False
|
Logical reasoning and boolean operations
|
2,431 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
2x sin(x²)
|
cos(2x)
|
2x cos(x²)
|
cos(x²)
|
Calculus differentiation and integration
|
197 |
arithmetic
|
medium
|
What is 15% of 287?
|
43
|
53
|
48
|
43
|
38
|
Standard arithmetic calculation
|
3,332 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4
|
4.5
|
3
|
3.5
|
Probability calculation and expected value
|
3,592 |
number_theory
|
medium
|
How many factors does 24 have?
|
8
|
8
|
6
|
7
|
9
|
Number theory and modular arithmetic
|
1,813 |
fractions
|
medium
|
Divide 1 ÷ 5/7
|
7/5
|
8/5
|
5/7
|
7/6
|
7/5
|
Fraction arithmetic and simplification
|
2,204 |
calculus
|
easy
|
Evaluate ∫x^2 dx
|
x^3/3 + C
|
x^3/3 + C
|
2x^1 + C
|
x^2 + C
|
x^4/4 + C
|
Calculus differentiation and integration
|
469 |
algebra
|
easy
|
What is 7x when x = 5?
|
35
|
40
|
35
|
32
|
37
|
Algebraic manipulation and solving
|
4,093 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
Depends on other variables
|
Cannot determine
|
True
|
False
|
Logical reasoning and boolean operations
|
496 |
algebra
|
easy
|
Solve for x: x + 6 = 13
|
7
|
10
|
5
|
7
|
8
|
Algebraic manipulation and solving
|
4,965 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
120
|
24
|
60
|
48
|
Permutations and combinations
|
3,539 |
number_theory
|
medium
|
How many factors does 36 have?
|
9
|
10
|
7
|
9
|
8
|
Number theory and modular arithmetic
|
4,720 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
8
|
4
|
6
|
5
|
Permutations and combinations
|
1,537 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.54
|
2.94
|
2.24
|
1.74
|
Statistical measure calculation
|
2,744 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
√2
|
√3
|
1
|
0
|
Trigonometric functions and identities
|
601 |
algebra
|
medium
|
Find x: x² = 25
|
5
|
5
|
6
|
8
|
3
|
Algebraic manipulation and solving
|
3,600 |
number_theory
|
medium
|
Find LCM of 15 and 20
|
60
|
60
|
75
|
50
|
65
|
Number theory and modular arithmetic
|
1,312 |
statistics
|
easy
|
Find the median of 19 2 14 18 5
|
14
|
14
|
12
|
15
|
16
|
Statistical measure calculation
|
2,322 |
calculus
|
medium
|
What is d/dx(4x^3 - 2x + 1)?
|
12x^2 - 2
|
12x^2 - 2
|
12x^2 - 1
|
4x^2 - 2
|
12x^3 - 2
|
Calculus differentiation and integration
|
3,045 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
8
|
7
|
5
|
6
|
Probability calculation and expected value
|
2,980 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
5
|
6
|
7
|
8
|
Probability calculation and expected value
|
1,083 |
geometry
|
medium
|
Find the area of a circle with radius 4 (use π ≈ 3.14)
|
50.27
|
52.07
|
47.77
|
50.27
|
53.47
|
Geometric calculation and spatial reasoning
|
673 |
algebra
|
medium
|
Solve: 4x - 13 = 20
|
8
|
8
|
6
|
11
|
9
|
Algebraic manipulation and solving
|
3,298 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3
|
3.5
|
4.5
|
4
|
Probability calculation and expected value
|
3,189 |
probability
|
medium
|
Probability of drawing an ace from a standard deck
|
1/13
|
1/13
|
1/14
|
1/15
|
1/12
|
Probability calculation and expected value
|
530 |
algebra
|
easy
|
What is 6x when x = 8?
|
48
|
45
|
50
|
53
|
48
|
Algebraic manipulation and solving
|
805 |
algebra
|
hard
|
Solve: x² + -10x + 16 = 0
|
x = 8 or x = 2
|
x = 7 or x = 3
|
x = 8 or x = 2
|
x = -8 or x = -2
|
x = 9 or x = 1
|
Algebraic manipulation and solving
|
492 |
algebra
|
easy
|
What is 5x when x = 6?
|
30
|
32
|
27
|
30
|
35
|
Algebraic manipulation and solving
|
4,977 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
48
|
60
|
120
|
24
|
Permutations and combinations
|
1,639 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
1.74
|
2.24
|
2.54
|
2.94
|
Statistical measure calculation
|
306 |
arithmetic
|
hard
|
Calculate (4^4 × 2) ÷ 3
|
170
|
165
|
173
|
170
|
178
|
Standard arithmetic calculation
|
4,290 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 6]
|
[2, 7]
|
[4, 7]
|
[3, 7]
|
Vector operations and matrix calculations
|
1,331 |
statistics
|
easy
|
Find the median of 12 17 17 15 13 10 2
|
13
|
14
|
15
|
11
|
13
|
Statistical measure calculation
|
1,878 |
fractions
|
medium
|
Calculate 5/3 × 1/3
|
5/9
|
5/10
|
9/5
|
5/9
|
6/9
|
Fraction arithmetic and simplification
|
558 |
algebra
|
medium
|
Solve: 3x - 12 = 20
|
10
|
13
|
8
|
10
|
11
|
Algebraic manipulation and solving
|
3,009 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
5
|
8
|
7
|
6
|
Probability calculation and expected value
|
2,678 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
√3
|
0
|
√2
|
1
|
Trigonometric functions and identities
|
1,961 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
2/2
|
1/3
|
1/2
|
0/2
|
Fraction arithmetic and simplification
|
1,894 |
fractions
|
medium
|
Calculate 2/5 × 1/2
|
1/5
|
1/5
|
2/5
|
5/1
|
1/6
|
Fraction arithmetic and simplification
|
4,727 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
50
|
60
|
125
|
75
|
Permutations and combinations
|
1,720 |
fractions
|
easy
|
Simplify 24/32
|
3/4
|
3/4
|
12/16
|
23/31
|
25/33
|
Fraction arithmetic and simplification
|
1,480 |
statistics
|
medium
|
What is the mode of 13 13 3 7 9 17 13?
|
13
|
14
|
16
|
13
|
11
|
Statistical measure calculation
|
4,717 |
combinatorics
|
easy
|
How many ways can 4 people stand in a line?
|
24
|
16
|
6
|
24
|
8
|
Permutations and combinations
|
4,291 |
linear_algebra
|
easy
|
Calculate 2 × [2, 3]
|
[4, 6]
|
[4, 6]
|
[3, 6]
|
[4, 5]
|
[5, 6]
|
Vector operations and matrix calculations
|
366 |
arithmetic
|
hard
|
Calculate (3^4 × 3) ÷ 7
|
34
|
37
|
42
|
29
|
34
|
Standard arithmetic calculation
|
2,767 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
√3
|
1
|
√2
|
0
|
Trigonometric functions and identities
|
3,657 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
4
|
3
|
2
|
1
|
Number theory and modular arithmetic
|
3,871 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
True
|
False
|
Cannot determine
|
Depends on context
|
Logical reasoning and boolean operations
|
4,510 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
6
|
3
|
5
|
4
|
Vector operations and matrix calculations
|
3,568 |
number_theory
|
medium
|
How many factors does 30 have?
|
8
|
8
|
7
|
6
|
9
|
Number theory and modular arithmetic
|
2,191 |
calculus
|
easy
|
Evaluate ∫x^4 dx
|
x^5/5 + C
|
x^4 + C
|
4x^3 + C
|
x^5/5 + C
|
x^6/6 + C
|
Calculus differentiation and integration
|
3,964 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
Depends on values
|
True
|
False
|
Cannot determine
|
Logical reasoning and boolean operations
|
3,007 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
8
|
6
|
5
|
7
|
Probability calculation and expected value
|
3,460 |
number_theory
|
easy
|
Is 23 a prime number?
|
Yes
|
Only if x>0
|
Cannot determine
|
No
|
Yes
|
Number theory and modular arithmetic
|
2,823 |
trigonometry
|
hard
|
Solve sin(x) = 1/2 for 0° ≤ x ≤ 360°
|
x = 30° or 150°
|
x = 30° or 60°
|
x = 30° or 150°
|
x = 60° or 120°
|
x = 45° or 135°
|
Trigonometric functions and identities
|
2,711 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
0
|
2
|
sin(2x)
|
1
|
Trigonometric functions and identities
|
4,917 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
48
|
60
|
24
|
120
|
Permutations and combinations
|
4,170 |
linear_algebra
|
easy
|
Calculate 3 × [2, 3]
|
[6, 9]
|
[6, 8]
|
[7, 9]
|
[5, 9]
|
[6, 9]
|
Vector operations and matrix calculations
|
4,363 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
10
|
11
|
9
|
8
|
Vector operations and matrix calculations
|
3,651 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
3
|
4
|
2
|
1
|
Number theory and modular arithmetic
|
669 |
algebra
|
medium
|
Solve: 5x - 13 = 15
|
5
|
5
|
8
|
3
|
6
|
Algebraic manipulation and solving
|
3,954 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Cannot determine
|
Q is true
|
P is false
|
Q is false
|
Logical reasoning and boolean operations
|
540 |
algebra
|
easy
|
What is 2x when x = 5?
|
10
|
10
|
12
|
15
|
7
|
Algebraic manipulation and solving
|
1,198 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 3 and 4
|
5
|
6
|
5
|
4
|
3
|
Geometric calculation and spatial reasoning
|
4,221 |
linear_algebra
|
easy
|
Calculate 2 × [2, 3]
|
[4, 6]
|
[4, 6]
|
[4, 5]
|
[3, 6]
|
[5, 6]
|
Vector operations and matrix calculations
|
3,283 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4
|
3.5
|
4.5
|
3
|
Probability calculation and expected value
|
511 |
algebra
|
easy
|
What is 8x when x = 8?
|
64
|
66
|
64
|
61
|
69
|
Algebraic manipulation and solving
|
4,607 |
combinatorics
|
easy
|
How many ways can 5 people stand in a line?
|
120
|
120
|
25
|
10
|
24
|
Permutations and combinations
|
1,392 |
statistics
|
medium
|
What is the mode of 14 14 15 18 7 14 18?
|
14
|
17
|
12
|
15
|
14
|
Statistical measure calculation
|
3,826 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
animal
|
mammal
|
pet
|
cat
|
Logical reasoning and boolean operations
|
2,461 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(2x)
|
cos(x²)
|
2x cos(x²)
|
2x sin(x²)
|
Calculus differentiation and integration
|
2,076 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/2
|
2/2
|
1/3
|
0/2
|
Fraction arithmetic and simplification
|
2,923 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
5
|
6
|
7
|
8
|
Probability calculation and expected value
|
2,205 |
calculus
|
easy
|
Evaluate ∫x^4 dx
|
x^5/5 + C
|
x^6/6 + C
|
4x^3 + C
|
x^4 + C
|
x^5/5 + C
|
Calculus differentiation and integration
|
642 |
algebra
|
medium
|
Find x: x² = 81
|
9
|
9
|
7
|
10
|
12
|
Algebraic manipulation and solving
|
3,357 |
number_theory
|
easy
|
What is the GCD of 15 and 25?
|
5
|
5
|
6
|
3
|
4
|
Number theory and modular arithmetic
|
2,569 |
trigonometry
|
easy
|
What is sin(45°)?
|
0.71
|
-1
|
0.71
|
0
|
1
|
Trigonometric functions and identities
|
2,151 |
calculus
|
easy
|
What is the derivative of x²?
|
2x
|
2x
|
x
|
x²
|
2x²
|
Calculus differentiation and integration
|
3,563 |
number_theory
|
medium
|
Find LCM of 15 and 20
|
60
|
65
|
60
|
50
|
75
|
Number theory and modular arithmetic
|
4,990 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
120
|
48
|
60
|
24
|
Permutations and combinations
|
2,031 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
2/2
|
0/2
|
1/3
|
1/2
|
Fraction arithmetic and simplification
|
3,082 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/35
|
1/30
|
1/36
|
1/32
|
Probability calculation and expected value
|
4,383 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
10
|
8
|
9
|
11
|
Vector operations and matrix calculations
|
60 |
arithmetic
|
easy
|
Calculate 68 - 51
|
17
|
18
|
16
|
17
|
19
|
Standard arithmetic calculation
|
51 |
arithmetic
|
easy
|
What is 35 + 67?
|
102
|
102
|
100
|
105
|
103
|
Standard arithmetic calculation
|
3,010 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
5
|
8
|
7
|
6
|
Probability calculation and expected value
|
359 |
arithmetic
|
hard
|
Calculate (3^3 × 3) ÷ 8
|
10
|
18
|
10
|
13
|
5
|
Standard arithmetic calculation
|
158 |
arithmetic
|
medium
|
What is 30% of 283?
|
84
|
79
|
94
|
89
|
84
|
Standard arithmetic calculation
|
3,238 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4.5
|
4
|
3.5
|
3
|
Probability calculation and expected value
|
2,593 |
trigonometry
|
easy
|
Calculate tan(0°)
|
0
|
-1
|
1
|
undefined
|
0
|
Trigonometric functions and identities
|
2,570 |
trigonometry
|
easy
|
Find cos(60°)
|
1/2
|
1/2
|
-1
|
0
|
1
|
Trigonometric functions and identities
|
2,164 |
calculus
|
easy
|
Evaluate ∫x^2 dx
|
x^3/3 + C
|
2x^1 + C
|
x^4/4 + C
|
x^3/3 + C
|
x^2 + C
|
Calculus differentiation and integration
|
3,203 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3.5
|
3
|
4
|
4.5
|
Probability calculation and expected value
|
3,254 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3
|
4.5
|
3.5
|
4
|
Probability calculation and expected value
|
4,995 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
24
|
60
|
48
|
120
|
Permutations and combinations
|
372 |
arithmetic
|
hard
|
Calculate (5^3 × 2) ÷ 7
|
35
|
30
|
38
|
43
|
35
|
Standard arithmetic calculation
|
3,379 |
number_theory
|
easy
|
Is 31 a prime number?
|
Yes
|
Cannot determine
|
Yes
|
No
|
Only if x>0
|
Number theory and modular arithmetic
|
4,256 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[2, 7]
|
[3, 7]
|
[4, 7]
|
[3, 6]
|
Vector operations and matrix calculations
|
568 |
algebra
|
medium
|
Find x: x² = 16
|
4
|
5
|
4
|
2
|
7
|
Algebraic manipulation and solving
|
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