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 |
|---|---|---|---|---|---|---|---|---|---|
2,481 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
2x cos(x²)
|
cos(2x)
|
cos(x²)
|
2x sin(x²)
|
Calculus differentiation and integration
|
2,394 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(2x)
|
2x sin(x²)
|
cos(x²)
|
2x cos(x²)
|
Calculus differentiation and integration
|
1,350 |
statistics
|
easy
|
What is the mean of 18 13 3 17?
|
12.8
|
12.8
|
14.8
|
13.8
|
10.8
|
Statistical measure calculation
|
1,002 |
geometry
|
medium
|
Find the area of a circle with radius 8 (use π ≈ 3.14)
|
201.06
|
202.86
|
201.06
|
198.56
|
204.26
|
Geometric calculation and spatial reasoning
|
4,823 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
50
|
125
|
75
|
60
|
Permutations and combinations
|
4,113 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
Cannot determine
|
False
|
True
|
Depends on other variables
|
Logical reasoning and boolean operations
|
3,447 |
number_theory
|
easy
|
What is the GCD of 15 and 25?
|
5
|
3
|
5
|
6
|
4
|
Number theory and modular arithmetic
|
851 |
geometry
|
easy
|
What is the area of a rectangle with length 12 and width 7?
|
84
|
79
|
84
|
92
|
87
|
Geometric calculation and spatial reasoning
|
1,038 |
geometry
|
medium
|
Find the area of a circle with radius 4 (use π ≈ 3.14)
|
50.27
|
53.47
|
47.77
|
52.07
|
50.27
|
Geometric calculation and spatial reasoning
|
4,506 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
6
|
3
|
5
|
4
|
Vector operations and matrix calculations
|
3,546 |
number_theory
|
medium
|
Find LCM of 12 and 16
|
48
|
63
|
38
|
53
|
48
|
Number theory and modular arithmetic
|
3,435 |
number_theory
|
easy
|
Is 17 a prime number?
|
Yes
|
Only if x>0
|
No
|
Yes
|
Cannot determine
|
Number theory and modular arithmetic
|
4,266 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 6]
|
[4, 7]
|
[2, 7]
|
[3, 7]
|
Vector operations and matrix calculations
|
2,831 |
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
|
4,900 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
24
|
120
|
48
|
60
|
Permutations and combinations
|
3,988 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
Depends on values
|
False
|
True
|
Cannot determine
|
Logical reasoning and boolean operations
|
2,787 |
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
|
2,130 |
calculus
|
easy
|
Find ∫x dx
|
x²/2 + C
|
x³/3 + C
|
x + C
|
x²
|
x²/2 + C
|
Calculus differentiation and integration
|
3,876 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
cat
|
mammal
|
pet
|
animal
|
Logical reasoning and boolean operations
|
1,018 |
geometry
|
medium
|
What is the volume of a cube with side length 8?
|
512
|
492
|
527
|
547
|
512
|
Geometric calculation and spatial reasoning
|
799 |
algebra
|
hard
|
Solve: x² + -11x + 24 = 0
|
x = 8 or x = 3
|
x = 7 or x = 4
|
x = 8 or x = 3
|
x = -8 or x = -3
|
x = 9 or x = 2
|
Algebraic manipulation and solving
|
4,361 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
11
|
8
|
10
|
Vector operations and matrix calculations
|
1,021 |
geometry
|
medium
|
Find the area of a circle with radius 7 (use π ≈ 3.14)
|
153.94
|
153.94
|
151.44
|
155.74
|
157.14
|
Geometric calculation and spatial reasoning
|
733 |
algebra
|
hard
|
Solve: x² + -15x + 56 = 0
|
x = 8 or x = 7
|
x = 7 or x = 8
|
x = 8 or x = 7
|
x = -8 or x = -7
|
x = 9 or x = 6
|
Algebraic manipulation and solving
|
2,669 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
2
|
sin(2x)
|
0
|
Trigonometric functions and identities
|
1,778 |
fractions
|
easy
|
What is 1/4 + 1/3?
|
7/12
|
7/12
|
8/12
|
6/12
|
7/13
|
Fraction arithmetic and simplification
|
1,932 |
fractions
|
medium
|
Calculate 5/6 × 1/3
|
5/18
|
18/5
|
5/18
|
6/18
|
5/19
|
Fraction arithmetic and simplification
|
465 |
algebra
|
easy
|
Solve for x: x + 6 = 18
|
12
|
15
|
10
|
12
|
13
|
Algebraic manipulation and solving
|
3,974 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
False
|
Depends on values
|
True
|
Cannot determine
|
Logical reasoning and boolean operations
|
2,199 |
calculus
|
easy
|
Evaluate ∫x^3 dx
|
x^4/4 + C
|
3x^2 + C
|
x^4/4 + C
|
x^3 + C
|
x^5/5 + C
|
Calculus differentiation and integration
|
2,773 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
1
|
0
|
√2
|
√3
|
Trigonometric functions and identities
|
321 |
arithmetic
|
hard
|
Calculate (3^3 × 3) ÷ 7
|
11
|
14
|
6
|
19
|
11
|
Standard arithmetic calculation
|
4,952 |
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
|
2,149 |
calculus
|
easy
|
Evaluate ∫x^2 dx
|
x^3/3 + C
|
x^4/4 + C
|
x^3/3 + C
|
x^2 + C
|
2x^1 + C
|
Calculus differentiation and integration
|
4,005 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
P is false
|
Q is true
|
Cannot determine
|
Q is false
|
Logical reasoning and boolean operations
|
3,452 |
number_theory
|
easy
|
What is the GCD of 12 and 18?
|
6
|
6
|
4
|
7
|
5
|
Number theory and modular arithmetic
|
2,125 |
calculus
|
easy
|
Find d/dx(x^5)
|
5x^4
|
x^5
|
x^4
|
5x^5
|
5x^4
|
Calculus differentiation and integration
|
4,142 |
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
|
1,668 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
1.74
|
2.94
|
2.24
|
2.54
|
Statistical measure calculation
|
474 |
algebra
|
easy
|
Solve for x: x + 13 = 22
|
9
|
12
|
7
|
9
|
10
|
Algebraic manipulation and solving
|
4,946 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
120
|
48
|
24
|
60
|
Permutations and combinations
|
2,988 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
6
|
8
|
5
|
7
|
Probability calculation and expected value
|
4,300 |
linear_algebra
|
easy
|
Calculate 3 × [2, 3]
|
[6, 9]
|
[7, 9]
|
[6, 9]
|
[5, 9]
|
[6, 8]
|
Vector operations and matrix calculations
|
4,042 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
Depends on other variables
|
True
|
Cannot determine
|
False
|
Logical reasoning and boolean operations
|
4,098 |
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
|
2,763 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
2
|
0
|
sin(2x)
|
Trigonometric functions and identities
|
522 |
algebra
|
easy
|
Solve for x: x + 11 = 18
|
7
|
5
|
10
|
7
|
8
|
Algebraic manipulation and solving
|
1,742 |
fractions
|
easy
|
What is 1/4 + 1/4?
|
1/2
|
1/2
|
1/3
|
2/2
|
0/2
|
Fraction arithmetic and simplification
|
1,980 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
0/2
|
2/2
|
1/3
|
1/2
|
Fraction arithmetic and simplification
|
3,206 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3
|
3.5
|
4
|
4.5
|
Probability calculation and expected value
|
2,803 |
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
|
3,669 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
1
|
3
|
4
|
2
|
Number theory and modular arithmetic
|
4,175 |
linear_algebra
|
easy
|
Calculate 4 × [2, 3]
|
[8, 12]
|
[8, 11]
|
[8, 12]
|
[7, 12]
|
[9, 12]
|
Vector operations and matrix calculations
|
4,346 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
11
|
10
|
8
|
9
|
Vector operations and matrix calculations
|
3,299 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3
|
4.5
|
4
|
3.5
|
Probability calculation and expected value
|
4,100 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
Depends on other variables
|
False
|
Cannot determine
|
True
|
Logical reasoning and boolean operations
|
2,703 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
√2
|
√3
|
0
|
1
|
Trigonometric functions and identities
|
4,095 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
Depends on other variables
|
True
|
False
|
Cannot determine
|
Logical reasoning and boolean operations
|
1,385 |
statistics
|
easy
|
Find the median of 14 9 5 18 12 12 17 18
|
13
|
13
|
15
|
11
|
14
|
Statistical measure calculation
|
834 |
algebra
|
hard
|
Solve: x² + -12x + 32 = 0
|
x = 8 or x = 4
|
x = 7 or x = 5
|
x = 8 or x = 4
|
x = -8 or x = -4
|
x = 9 or x = 3
|
Algebraic manipulation and solving
|
1,680 |
fractions
|
easy
|
What is 1/3 + 1/4?
|
7/12
|
7/12
|
6/12
|
7/13
|
8/12
|
Fraction arithmetic and simplification
|
1,069 |
geometry
|
medium
|
Find the area of a circle with radius 6 (use π ≈ 3.14)
|
113.1
|
116.3
|
114.9
|
110.6
|
113.1
|
Geometric calculation and spatial reasoning
|
1,738 |
fractions
|
easy
|
Simplify 12/9
|
4/3
|
6/4
|
13/10
|
11/8
|
4/3
|
Fraction arithmetic and simplification
|
3,726 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
4
|
1
|
3
|
2
|
Number theory and modular arithmetic
|
1,012 |
geometry
|
medium
|
Find the area of a circle with radius 3 (use π ≈ 3.14)
|
28.27
|
28.27
|
30.07
|
31.47
|
25.77
|
Geometric calculation and spatial reasoning
|
4,474 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
3
|
4
|
5
|
6
|
Vector operations and matrix calculations
|
4,866 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
24
|
120
|
48
|
60
|
Permutations and combinations
|
1,327 |
statistics
|
easy
|
What is the mean of 16 9 19 12 17 16?
|
14.8
|
12.8
|
16.8
|
15.8
|
14.8
|
Statistical measure calculation
|
67 |
arithmetic
|
easy
|
Find 5 × 9
|
45
|
50
|
47
|
42
|
45
|
Standard arithmetic calculation
|
3,886 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Cannot determine
|
Depends on context
|
False
|
True
|
Logical reasoning and boolean operations
|
4,373 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
11
|
10
|
8
|
9
|
Vector operations and matrix calculations
|
3,504 |
number_theory
|
medium
|
Find LCM of 9 and 15
|
45
|
50
|
45
|
60
|
35
|
Number theory and modular arithmetic
|
989 |
geometry
|
medium
|
Find the area of a circle with radius 6 (use π ≈ 3.14)
|
113.1
|
116.3
|
110.6
|
113.1
|
114.9
|
Geometric calculation and spatial reasoning
|
88 |
arithmetic
|
easy
|
What is 28 + 53?
|
81
|
82
|
84
|
81
|
79
|
Standard arithmetic calculation
|
1,400 |
statistics
|
medium
|
What is the mode of 12 14 6 12 10 12 3?
|
12
|
12
|
15
|
13
|
10
|
Statistical measure calculation
|
3,976 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
True
|
False
|
Cannot determine
|
Depends on values
|
Logical reasoning and boolean operations
|
1,146 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 5 and 12
|
13
|
12
|
13
|
14
|
11
|
Geometric calculation and spatial reasoning
|
3,891 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Cannot determine
|
True
|
Depends on context
|
False
|
Logical reasoning and boolean operations
|
3,854 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
False
|
Cannot determine
|
Depends on context
|
True
|
Logical reasoning and boolean operations
|
3,741 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
1
|
3
|
2
|
4
|
Number theory and modular arithmetic
|
1,316 |
statistics
|
easy
|
Find the median of 12 13 15 17
|
14
|
15
|
16
|
14
|
12
|
Statistical measure calculation
|
2,443 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
2x sin(x²)
|
cos(2x)
|
cos(x²)
|
2x cos(x²)
|
Calculus differentiation and integration
|
4,511 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
5
|
6
|
4
|
3
|
Vector operations and matrix calculations
|
4,308 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
8
|
9
|
11
|
10
|
Vector operations and matrix calculations
|
2,445 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(x²)
|
cos(2x)
|
2x sin(x²)
|
2x cos(x²)
|
Calculus differentiation and integration
|
3,892 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Q is false
|
Q is true
|
Cannot determine
|
P is false
|
Logical reasoning and boolean operations
|
4,795 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
75
|
125
|
60
|
50
|
Permutations and combinations
|
870 |
geometry
|
easy
|
What is the area of a rectangle with length 12 and width 8?
|
96
|
99
|
104
|
91
|
96
|
Geometric calculation and spatial reasoning
|
2,686 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
1
|
√3
|
√2
|
0
|
Trigonometric functions and identities
|
3,252 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3
|
3.5
|
4
|
4.5
|
Probability calculation and expected value
|
1,831 |
fractions
|
medium
|
Calculate 3/5 × 1/2
|
3/10
|
3/11
|
10/3
|
3/10
|
4/10
|
Fraction arithmetic and simplification
|
1,619 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.54
|
1.74
|
2.94
|
2.24
|
Statistical measure calculation
|
1,395 |
statistics
|
medium
|
Calculate the range of 19 4 3 5
|
16
|
17
|
16
|
19
|
14
|
Statistical measure calculation
|
2,051 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/2
|
0/2
|
1/3
|
2/2
|
Fraction arithmetic and simplification
|
3,322 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3.5
|
4.5
|
3
|
4
|
Probability calculation and expected value
|
3,555 |
number_theory
|
medium
|
Find LCM of 9 and 15
|
45
|
35
|
50
|
60
|
45
|
Number theory and modular arithmetic
|
4,107 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
False
|
True
|
Cannot determine
|
Depends on other variables
|
Logical reasoning and boolean operations
|
4,815 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
60
|
125
|
75
|
50
|
Permutations and combinations
|
3,768 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Cannot determine
|
True
|
Depends on context
|
False
|
Logical reasoning and boolean operations
|
1,247 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 7 and 24
|
25
|
23
|
24
|
25
|
26
|
Geometric calculation and spatial reasoning
|
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