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 |
|---|---|---|---|---|---|---|---|---|---|
2,197 |
calculus
|
easy
|
Evaluate ∫x^2 dx
|
x^3/3 + C
|
2x^1 + C
|
x^3/3 + C
|
x^2 + C
|
x^4/4 + C
|
Calculus differentiation and integration
|
434 |
algebra
|
easy
|
Solve for x: x + 5 = 12
|
7
|
8
|
10
|
7
|
5
|
Algebraic manipulation and solving
|
4,086 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
False
|
Cannot determine
|
Depends on other variables
|
True
|
Logical reasoning and boolean operations
|
896 |
geometry
|
easy
|
How many sides does a hexagon have?
|
6
|
6
|
7
|
5
|
8
|
Geometric calculation and spatial reasoning
|
3,754 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
True
|
Cannot determine
|
Depends on context
|
False
|
Logical reasoning and boolean operations
|
1,056 |
geometry
|
medium
|
What is the volume of a cube with side length 6?
|
216
|
251
|
231
|
216
|
196
|
Geometric calculation and spatial reasoning
|
2,986 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
6
|
7
|
5
|
8
|
Probability calculation and expected value
|
2,791 |
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
|
4,681 |
combinatorics
|
easy
|
How many ways can 6 people stand in a line?
|
720
|
720
|
12
|
120
|
36
|
Permutations and combinations
|
1,974 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/2
|
0/2
|
1/3
|
2/2
|
Fraction arithmetic and simplification
|
4,583 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
5
|
4
|
6
|
3
|
Vector operations and matrix calculations
|
4,730 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
50
|
60
|
75
|
125
|
Permutations and combinations
|
643 |
algebra
|
medium
|
Solve: 4x - 10 = 10
|
5
|
5
|
8
|
3
|
6
|
Algebraic manipulation and solving
|
2,375 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(x²)
|
cos(2x)
|
2x cos(x²)
|
2x sin(x²)
|
Calculus differentiation and integration
|
4,312 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
8
|
10
|
11
|
Vector operations and matrix calculations
|
3,797 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
False
|
Cannot determine
|
True
|
Depends on context
|
Logical reasoning and boolean operations
|
4,592 |
combinatorics
|
easy
|
How many ways can 5 people stand in a line?
|
120
|
24
|
10
|
25
|
120
|
Permutations and combinations
|
563 |
algebra
|
medium
|
Find x: x² = 25
|
5
|
5
|
6
|
8
|
3
|
Algebraic manipulation and solving
|
284 |
arithmetic
|
hard
|
Calculate (6^4 × 2) ÷ 5
|
518
|
526
|
518
|
513
|
521
|
Standard arithmetic calculation
|
3,686 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
1
|
2
|
4
|
3
|
Number theory and modular arithmetic
|
3,367 |
number_theory
|
easy
|
Is 19 a prime number?
|
Yes
|
Yes
|
No
|
Cannot determine
|
Only if x>0
|
Number theory and modular arithmetic
|
4,236 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 7]
|
[2, 7]
|
[4, 7]
|
[3, 6]
|
Vector operations and matrix calculations
|
4,183 |
linear_algebra
|
easy
|
Calculate 2 × [2, 3]
|
[4, 6]
|
[3, 6]
|
[4, 5]
|
[4, 6]
|
[5, 6]
|
Vector operations and matrix calculations
|
4,793 |
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
|
1,688 |
fractions
|
easy
|
Simplify 24/36
|
2/3
|
23/35
|
2/3
|
12/18
|
25/37
|
Fraction arithmetic and simplification
|
4,369 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
11
|
10
|
9
|
8
|
Vector operations and matrix calculations
|
4,535 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
4
|
6
|
5
|
3
|
Vector operations and matrix calculations
|
730 |
algebra
|
hard
|
Solve: x² + -4x + 4 = 0
|
x = 2 or x = 2
|
x = 1 or x = 3
|
x = 2 or x = 2
|
x = -2 or x = -2
|
x = 3 or x = 1
|
Algebraic manipulation and solving
|
1,919 |
fractions
|
medium
|
Divide 5/3 ÷ 1/2
|
10/3
|
10/3
|
10/4
|
11/3
|
3/10
|
Fraction arithmetic and simplification
|
1,686 |
fractions
|
easy
|
What is 1/3 + 1/3?
|
2/3
|
2/3
|
1/3
|
3/3
|
2/4
|
Fraction arithmetic and simplification
|
3,759 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
animal
|
pet
|
cat
|
mammal
|
Logical reasoning and boolean operations
|
2,091 |
calculus
|
easy
|
Find d/dx(x^3)
|
3x^2
|
x^2
|
x^3
|
3x^3
|
3x^2
|
Calculus differentiation and integration
|
3,933 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Cannot determine
|
Q is false
|
Q is true
|
P is false
|
Logical reasoning and boolean operations
|
1,450 |
statistics
|
medium
|
Calculate the range of 12 15 16 13 5 4 14 15
|
12
|
15
|
10
|
12
|
13
|
Statistical measure calculation
|
1,797 |
fractions
|
easy
|
Simplify 12/54
|
2/9
|
11/53
|
13/55
|
2/9
|
6/27
|
Fraction arithmetic and simplification
|
4,010 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Cannot determine
|
Q is true
|
Q is false
|
P is false
|
Logical reasoning and boolean operations
|
4,034 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
True
|
Depends on other variables
|
False
|
Cannot determine
|
Logical reasoning and boolean operations
|
3,083 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/36
|
1/32
|
1/30
|
1/35
|
Probability calculation and expected value
|
80 |
arithmetic
|
easy
|
What is 83 + 46?
|
129
|
127
|
130
|
129
|
132
|
Standard arithmetic calculation
|
42 |
arithmetic
|
easy
|
Calculate 99 - 38
|
61
|
63
|
62
|
61
|
60
|
Standard arithmetic calculation
|
3,077 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/32
|
1/36
|
1/35
|
1/30
|
Probability calculation and expected value
|
1,872 |
fractions
|
medium
|
Calculate 1/2 × 5/8
|
5/16
|
5/17
|
6/16
|
5/16
|
16/5
|
Fraction arithmetic and simplification
|
4,780 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
125
|
75
|
60
|
50
|
Permutations and combinations
|
688 |
algebra
|
medium
|
Solve: 5x - 13 = 10
|
4
|
4
|
7
|
2
|
5
|
Algebraic manipulation and solving
|
2,682 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
sin(2x)
|
2
|
0
|
1
|
Trigonometric functions and identities
|
775 |
algebra
|
hard
|
Solve: x² + -8x + 15 = 0
|
x = 3 or x = 5
|
x = 2 or x = 6
|
x = 3 or x = 5
|
x = -3 or x = -5
|
x = 4 or x = 4
|
Algebraic manipulation and solving
|
2,500 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(2x)
|
2x cos(x²)
|
2x sin(x²)
|
cos(x²)
|
Calculus differentiation and integration
|
4,052 |
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
|
4,733 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
60
|
50
|
75
|
125
|
Permutations and combinations
|
1,192 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 5 and 12
|
13
|
13
|
11
|
14
|
12
|
Geometric calculation and spatial reasoning
|
1,390 |
statistics
|
easy
|
Find the median of 19 4 5 9
|
7
|
7
|
8
|
9
|
5
|
Statistical measure calculation
|
2,945 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
5
|
7
|
8
|
6
|
Probability calculation and expected value
|
4,531 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
3
|
5
|
4
|
6
|
Vector operations and matrix calculations
|
3,190 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/35
|
1/32
|
1/30
|
1/36
|
Probability calculation and expected value
|
4,598 |
combinatorics
|
easy
|
How many ways can 5 people stand in a line?
|
120
|
120
|
24
|
25
|
10
|
Permutations and combinations
|
737 |
algebra
|
hard
|
Solve: x² + -7x + 12 = 0
|
x = 4 or x = 3
|
x = 3 or x = 4
|
x = 4 or x = 3
|
x = -4 or x = -3
|
x = 5 or x = 2
|
Algebraic manipulation and solving
|
3,653 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
4
|
2
|
1
|
3
|
Number theory and modular arithmetic
|
3,385 |
number_theory
|
easy
|
What is the GCD of 14 and 21?
|
7
|
8
|
7
|
5
|
6
|
Number theory and modular arithmetic
|
440 |
algebra
|
easy
|
What is 2x when x = 7?
|
14
|
16
|
19
|
14
|
11
|
Algebraic manipulation and solving
|
3,116 |
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
|
4,754 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
125
|
60
|
50
|
75
|
Permutations and combinations
|
3,785 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
False
|
Depends on context
|
Cannot determine
|
True
|
Logical reasoning and boolean operations
|
2,118 |
calculus
|
easy
|
Evaluate ∫x^3 dx
|
x^4/4 + C
|
x^4/4 + C
|
x^5/5 + C
|
x^3 + C
|
3x^2 + C
|
Calculus differentiation and integration
|
1,509 |
statistics
|
medium
|
Calculate the range of 7 17 16 10 8 12
|
10
|
8
|
13
|
11
|
10
|
Statistical measure calculation
|
4,307 |
linear_algebra
|
easy
|
Calculate 3 × [2, 3]
|
[6, 9]
|
[7, 9]
|
[6, 9]
|
[6, 8]
|
[5, 9]
|
Vector operations and matrix calculations
|
3,855 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
False
|
Depends on context
|
Cannot determine
|
True
|
Logical reasoning and boolean operations
|
1,941 |
fractions
|
medium
|
Calculate 2/7 × 2/5
|
4/35
|
5/35
|
4/36
|
4/35
|
35/4
|
Fraction arithmetic and simplification
|
3,622 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
3
|
4
|
1
|
Number theory and modular arithmetic
|
308 |
arithmetic
|
hard
|
Calculate (4^4 × 4) ÷ 9
|
113
|
116
|
121
|
113
|
108
|
Standard arithmetic calculation
|
1,320 |
statistics
|
easy
|
Find the median of 4 9 7 14 7
|
7
|
7
|
5
|
8
|
9
|
Statistical measure calculation
|
695 |
algebra
|
medium
|
Solve: 2x - 11 = 16
|
13
|
11
|
13
|
16
|
14
|
Algebraic manipulation and solving
|
4,545 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
4
|
5
|
3
|
6
|
Vector operations and matrix calculations
|
678 |
algebra
|
medium
|
Find x: x² = 36
|
6
|
9
|
6
|
7
|
4
|
Algebraic manipulation and solving
|
2,771 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
1
|
0
|
√3
|
√2
|
Trigonometric functions and identities
|
4,833 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
50
|
60
|
75
|
125
|
Permutations and combinations
|
570 |
algebra
|
medium
|
Find x: x² = 100
|
10
|
10
|
8
|
13
|
11
|
Algebraic manipulation and solving
|
672 |
algebra
|
medium
|
Solve: 5x - 8 = 22
|
6
|
9
|
6
|
4
|
7
|
Algebraic manipulation and solving
|
717 |
algebra
|
hard
|
Solve: x² + -12x + 35 = 0
|
x = 7 or x = 5
|
x = 6 or x = 6
|
x = 7 or x = 5
|
x = -7 or x = -5
|
x = 8 or x = 4
|
Algebraic manipulation and solving
|
4,820 |
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
|
1,710 |
fractions
|
easy
|
What is 1/3 + 1/3?
|
2/3
|
1/3
|
3/3
|
2/4
|
2/3
|
Fraction arithmetic and simplification
|
1,866 |
fractions
|
medium
|
Calculate 1/2 × 1/3
|
1/6
|
1/7
|
2/6
|
6/1
|
1/6
|
Fraction arithmetic and simplification
|
3,306 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4
|
3.5
|
3
|
4.5
|
Probability calculation and expected value
|
1,082 |
geometry
|
medium
|
Find the area of a circle with radius 3 (use π ≈ 3.14)
|
28.27
|
25.77
|
28.27
|
30.07
|
31.47
|
Geometric calculation and spatial reasoning
|
920 |
geometry
|
easy
|
What is the area of a rectangle with length 11 and width 9?
|
99
|
99
|
107
|
102
|
94
|
Geometric calculation and spatial reasoning
|
4,463 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
6
|
4
|
5
|
3
|
Vector operations and matrix calculations
|
1,061 |
geometry
|
medium
|
What is the volume of a cube with side length 6?
|
216
|
251
|
216
|
196
|
231
|
Geometric calculation and spatial reasoning
|
3,508 |
number_theory
|
medium
|
How many factors does 30 have?
|
8
|
9
|
7
|
8
|
6
|
Number theory and modular arithmetic
|
4,984 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
60
|
48
|
120
|
24
|
Permutations and combinations
|
1,751 |
fractions
|
easy
|
Simplify 48/24
|
2/1
|
49/25
|
24/12
|
47/23
|
2/1
|
Fraction arithmetic and simplification
|
1,031 |
geometry
|
medium
|
What is the volume of a cube with side length 6?
|
216
|
251
|
196
|
231
|
216
|
Geometric calculation and spatial reasoning
|
1,233 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 8 and 15
|
17
|
17
|
18
|
16
|
15
|
Geometric calculation and spatial reasoning
|
1,140 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 3 and 4
|
5
|
4
|
5
|
6
|
3
|
Geometric calculation and spatial reasoning
|
1,244 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 5 and 12
|
13
|
14
|
11
|
12
|
13
|
Geometric calculation and spatial reasoning
|
1,047 |
geometry
|
medium
|
Find the area of a circle with radius 4 (use π ≈ 3.14)
|
50.27
|
47.77
|
53.47
|
50.27
|
52.07
|
Geometric calculation and spatial reasoning
|
7 |
arithmetic
|
easy
|
Calculate 66 - 10
|
56
|
56
|
57
|
55
|
58
|
Standard arithmetic calculation
|
3,403 |
number_theory
|
easy
|
Is 29 a prime number?
|
Yes
|
No
|
Cannot determine
|
Only if x>0
|
Yes
|
Number theory and modular arithmetic
|
2,454 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
2x cos(x²)
|
2x sin(x²)
|
cos(2x)
|
cos(x²)
|
Calculus differentiation and integration
|
123 |
arithmetic
|
easy
|
Find 9 × 5
|
45
|
45
|
42
|
47
|
50
|
Standard arithmetic calculation
|
2,735 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
2
|
sin(2x)
|
0
|
Trigonometric functions and identities
|
1,129 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 8 and 15
|
17
|
17
|
16
|
15
|
18
|
Geometric calculation and spatial reasoning
|
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