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 |
|---|---|---|---|---|---|---|---|---|---|
4,499 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
5
|
4
|
3
|
6
|
Vector operations and matrix calculations
|
4,579 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
4
|
6
|
5
|
3
|
Vector operations and matrix calculations
|
831 |
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
|
4,934 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
60
|
120
|
48
|
24
|
Permutations and combinations
|
121 |
arithmetic
|
easy
|
Find 12 × 5
|
60
|
65
|
57
|
62
|
60
|
Standard arithmetic calculation
|
2,085 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
0/2
|
1/3
|
1/2
|
2/2
|
Fraction arithmetic and simplification
|
1,877 |
fractions
|
medium
|
Calculate 1/3 × 1
|
1/3
|
2/3
|
3/1
|
1/4
|
1/3
|
Fraction arithmetic and simplification
|
4,549 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
5
|
4
|
6
|
3
|
Vector operations and matrix calculations
|
756 |
algebra
|
hard
|
Solve: x² + -14x + 48 = 0
|
x = 8 or x = 6
|
x = 7 or x = 7
|
x = 8 or x = 6
|
x = -8 or x = -6
|
x = 9 or x = 5
|
Algebraic manipulation and solving
|
1,463 |
statistics
|
medium
|
What is the mode of 13 2 13 2 20 16 13?
|
13
|
13
|
14
|
11
|
16
|
Statistical measure calculation
|
4,205 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[2, 7]
|
[3, 6]
|
[3, 7]
|
[4, 7]
|
Vector operations and matrix calculations
|
4,137 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
False
|
Depends on other variables
|
True
|
Cannot determine
|
Logical reasoning and boolean operations
|
1,356 |
statistics
|
easy
|
What is the mean of 11 16 13 16 9?
|
13
|
11
|
14
|
13
|
15
|
Statistical measure calculation
|
3,345 |
number_theory
|
easy
|
Is 29 a prime number?
|
Yes
|
Cannot determine
|
Yes
|
Only if x>0
|
No
|
Number theory and modular arithmetic
|
4,862 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
125
|
50
|
60
|
75
|
Permutations and combinations
|
1,413 |
statistics
|
medium
|
Calculate the range of 18 11 6 2 19 20
|
18
|
18
|
16
|
21
|
19
|
Statistical measure calculation
|
2,463 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(2x)
|
2x cos(x²)
|
cos(x²)
|
2x sin(x²)
|
Calculus differentiation and integration
|
4,418 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
10
|
11
|
9
|
8
|
Vector operations and matrix calculations
|
2,319 |
calculus
|
medium
|
What is d/dx(4x^4 - 2x + 1)?
|
16x^3 - 2
|
16x^4 - 2
|
16x^3 - 1
|
16x^3 - 2
|
4x^3 - 2
|
Calculus differentiation and integration
|
804 |
algebra
|
hard
|
Solve: x² + -10x + 24 = 0
|
x = 6 or x = 4
|
x = 5 or x = 5
|
x = 6 or x = 4
|
x = -6 or x = -4
|
x = 7 or x = 3
|
Algebraic manipulation and solving
|
2,491 |
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
|
629 |
algebra
|
medium
|
Solve: 3x - 15 = 12
|
9
|
7
|
12
|
9
|
10
|
Algebraic manipulation and solving
|
1,666 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.24
|
1.74
|
2.54
|
2.94
|
Statistical measure calculation
|
3,325 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4
|
4.5
|
3.5
|
3
|
Probability calculation and expected value
|
2,698 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
√2
|
1
|
√3
|
0
|
Trigonometric functions and identities
|
2,115 |
calculus
|
easy
|
Evaluate ∫x^2 dx
|
x^3/3 + C
|
x^4/4 + C
|
x^3/3 + C
|
2x^1 + C
|
x^2 + C
|
Calculus differentiation and integration
|
3,671 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
4
|
1
|
2
|
3
|
Number theory and modular arithmetic
|
4,907 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
120
|
60
|
24
|
48
|
Permutations and combinations
|
92 |
arithmetic
|
easy
|
Calculate 54 - 16
|
38
|
38
|
40
|
37
|
39
|
Standard arithmetic calculation
|
3,046 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
2/3
|
1/3
|
1/2
|
1/4
|
Probability calculation and expected value
|
2,211 |
calculus
|
easy
|
Evaluate ∫x^4 dx
|
x^5/5 + C
|
x^5/5 + C
|
x^4 + C
|
4x^3 + C
|
x^6/6 + C
|
Calculus differentiation and integration
|
4,144 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
True
|
Cannot determine
|
False
|
Depends on other variables
|
Logical reasoning and boolean operations
|
926 |
geometry
|
easy
|
What is the area of a rectangle with length 8 and width 5?
|
40
|
40
|
35
|
43
|
48
|
Geometric calculation and spatial reasoning
|
3,488 |
number_theory
|
medium
|
How many factors does 36 have?
|
9
|
8
|
10
|
9
|
7
|
Number theory and modular arithmetic
|
2,214 |
calculus
|
easy
|
Find d/dx(x^5)
|
5x^4
|
x^4
|
5x^5
|
5x^4
|
x^5
|
Calculus differentiation and integration
|
2,802 |
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
|
921 |
geometry
|
easy
|
What is the area of a rectangle with length 8 and width 7?
|
56
|
51
|
59
|
64
|
56
|
Geometric calculation and spatial reasoning
|
2,843 |
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
|
3,235 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4.5
|
3.5
|
3
|
4
|
Probability calculation and expected value
|
524 |
algebra
|
easy
|
What is 5x when x = 3?
|
15
|
15
|
17
|
20
|
12
|
Algebraic manipulation and solving
|
1,731 |
fractions
|
easy
|
Simplify 28/28
|
1/1
|
14/14
|
29/29
|
27/27
|
1/1
|
Fraction arithmetic and simplification
|
1,062 |
geometry
|
medium
|
Find the area of a circle with radius 8 (use π ≈ 3.14)
|
201.06
|
198.56
|
201.06
|
202.86
|
204.26
|
Geometric calculation and spatial reasoning
|
77 |
arithmetic
|
easy
|
What is 10 + 96?
|
106
|
106
|
109
|
104
|
107
|
Standard arithmetic calculation
|
1,380 |
statistics
|
easy
|
What is the mean of 10 5 4 9 18 8?
|
9
|
9
|
11
|
7
|
10
|
Statistical measure calculation
|
2,577 |
trigonometry
|
easy
|
Calculate tan(0°)
|
0
|
undefined
|
-1
|
1
|
0
|
Trigonometric functions and identities
|
2,959 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
2/3
|
1/4
|
1/3
|
1/2
|
Probability calculation and expected value
|
3,088 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/35
|
1/36
|
1/30
|
1/32
|
Probability calculation and expected value
|
1,228 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 8 and 15
|
17
|
17
|
15
|
16
|
18
|
Geometric calculation and spatial reasoning
|
4,684 |
combinatorics
|
easy
|
How many ways can 4 people stand in a line?
|
24
|
16
|
24
|
6
|
8
|
Permutations and combinations
|
3,641 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
3
|
4
|
1
|
Number theory and modular arithmetic
|
3,386 |
number_theory
|
easy
|
What is the GCD of 8 and 12?
|
4
|
5
|
2
|
3
|
4
|
Number theory and modular arithmetic
|
2,327 |
calculus
|
medium
|
What is d/dx(4x^4 - 2x + 1)?
|
16x^3 - 2
|
4x^3 - 2
|
16x^4 - 2
|
16x^3 - 1
|
16x^3 - 2
|
Calculus differentiation and integration
|
4,251 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[2, 7]
|
[3, 6]
|
[4, 7]
|
[3, 7]
|
Vector operations and matrix calculations
|
4,090 |
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
|
4,237 |
linear_algebra
|
easy
|
Calculate 3 × [2, 3]
|
[6, 9]
|
[5, 9]
|
[6, 8]
|
[7, 9]
|
[6, 9]
|
Vector operations and matrix calculations
|
4,050 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
True
|
Depends on other variables
|
Cannot determine
|
False
|
Logical reasoning and boolean operations
|
2,905 |
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
|
2,530 |
trigonometry
|
easy
|
Find cos(60°)
|
1/2
|
-1
|
1
|
1/2
|
0
|
Trigonometric functions and identities
|
1,223 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 9 and 12
|
15
|
15
|
16
|
14
|
13
|
Geometric calculation and spatial reasoning
|
3,867 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
True
|
Depends on context
|
False
|
Cannot determine
|
Logical reasoning and boolean operations
|
3,647 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
1
|
3
|
4
|
2
|
Number theory and modular arithmetic
|
806 |
algebra
|
hard
|
Solve: x² + -9x + 20 = 0
|
x = 5 or x = 4
|
x = 4 or x = 5
|
x = 5 or x = 4
|
x = -5 or x = -4
|
x = 6 or x = 3
|
Algebraic manipulation and solving
|
1,462 |
statistics
|
medium
|
Calculate the range of 16 20 5 20 20 6 15 12
|
15
|
15
|
13
|
18
|
16
|
Statistical measure calculation
|
537 |
algebra
|
easy
|
Solve for x: x + 14 = 25
|
11
|
14
|
12
|
11
|
9
|
Algebraic manipulation and solving
|
4,092 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
False
|
True
|
Depends on other variables
|
Cannot determine
|
Logical reasoning and boolean operations
|
4,561 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
3
|
5
|
4
|
6
|
Vector operations and matrix calculations
|
3,273 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4.5
|
3
|
3.5
|
4
|
Probability calculation and expected value
|
760 |
algebra
|
hard
|
Solve: x² + -9x + 14 = 0
|
x = 7 or x = 2
|
x = 6 or x = 3
|
x = 7 or x = 2
|
x = -7 or x = -2
|
x = 8 or x = 1
|
Algebraic manipulation and solving
|
2,975 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
7
|
8
|
6
|
5
|
Probability calculation and expected value
|
4,996 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
24
|
60
|
120
|
48
|
Permutations and combinations
|
3,097 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/32
|
1/30
|
1/36
|
1/35
|
Probability calculation and expected value
|
1,200 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 3 and 4
|
5
|
3
|
6
|
4
|
5
|
Geometric calculation and spatial reasoning
|
275 |
arithmetic
|
medium
|
What is 15% of 86?
|
12
|
22
|
17
|
12
|
7
|
Standard arithmetic calculation
|
4,380 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
11
|
8
|
10
|
Vector operations and matrix calculations
|
2,674 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
0
|
2
|
sin(2x)
|
1
|
Trigonometric functions and identities
|
3,738 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
3
|
4
|
1
|
Number theory and modular arithmetic
|
554 |
algebra
|
easy
|
What is 5x when x = 7?
|
35
|
35
|
37
|
40
|
32
|
Algebraic manipulation and solving
|
3,408 |
number_theory
|
easy
|
What is the GCD of 8 and 12?
|
4
|
3
|
2
|
4
|
5
|
Number theory and modular arithmetic
|
2,539 |
trigonometry
|
easy
|
Find cos(30°)
|
√3/2
|
1
|
0
|
√3/2
|
-1
|
Trigonometric functions and identities
|
245 |
arithmetic
|
medium
|
What is 8²?
|
64
|
72
|
54
|
79
|
64
|
Standard arithmetic calculation
|
1,990 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
0/2
|
1/3
|
1/2
|
2/2
|
Fraction arithmetic and simplification
|
4,605 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
4
|
8
|
5
|
6
|
Permutations and combinations
|
3,680 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
1
|
3
|
4
|
2
|
Number theory and modular arithmetic
|
3,129 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/35
|
1/32
|
1/36
|
1/30
|
Probability calculation and expected value
|
608 |
algebra
|
medium
|
Solve: 4x - 8 = 17
|
6
|
4
|
7
|
9
|
6
|
Algebraic manipulation and solving
|
4,207 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 6]
|
[4, 7]
|
[2, 7]
|
[3, 7]
|
Vector operations and matrix calculations
|
2,185 |
calculus
|
easy
|
Find d/dx(x^3)
|
3x^2
|
3x^3
|
x^2
|
3x^2
|
x^3
|
Calculus differentiation and integration
|
2,010 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/2
|
0/2
|
1/3
|
2/2
|
Fraction arithmetic and simplification
|
2,770 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
sin(2x)
|
0
|
2
|
Trigonometric functions and identities
|
4,085 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
Cannot determine
|
False
|
Depends on other variables
|
True
|
Logical reasoning and boolean operations
|
2,348 |
calculus
|
medium
|
What is d/dx(2x^4 - 5x + 1)?
|
8x^3 - 5
|
2x^3 - 5
|
8x^3 - 5
|
8x^3 - 1
|
8x^4 - 5
|
Calculus differentiation and integration
|
4,655 |
combinatorics
|
easy
|
How many ways can 4 people stand in a line?
|
24
|
16
|
8
|
6
|
24
|
Permutations and combinations
|
2,145 |
calculus
|
easy
|
What is the derivative of x²?
|
2x
|
x²
|
2x²
|
x
|
2x
|
Calculus differentiation and integration
|
2,016 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/3
|
2/2
|
1/2
|
0/2
|
Fraction arithmetic and simplification
|
1,934 |
fractions
|
medium
|
Calculate 2/5 × 1/3
|
2/15
|
15/2
|
3/15
|
2/16
|
2/15
|
Fraction arithmetic and simplification
|
4,076 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
False
|
True
|
Depends on other variables
|
Cannot determine
|
Logical reasoning and boolean operations
|
4,428 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
11
|
10
|
9
|
8
|
Vector operations and matrix calculations
|
4,647 |
combinatorics
|
easy
|
How many ways can 5 people stand in a line?
|
120
|
24
|
25
|
120
|
10
|
Permutations and combinations
|
2,338 |
calculus
|
medium
|
What is d/dx(2x^3 - 8x + 1)?
|
6x^2 - 8
|
6x^2 - 8
|
6x^2 - 1
|
6x^3 - 8
|
2x^2 - 8
|
Calculus differentiation and integration
|
3,414 |
number_theory
|
easy
|
What is the GCD of 8 and 12?
|
4
|
2
|
4
|
3
|
5
|
Number theory and modular arithmetic
|
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