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 |
|---|---|---|---|---|---|---|---|---|---|
2,012 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/2
|
1/3
|
0/2
|
2/2
|
Fraction arithmetic and simplification
|
2,920 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
6
|
5
|
8
|
7
|
Probability calculation and expected value
|
293 |
arithmetic
|
hard
|
Calculate (6^4 × 2) ÷ 5
|
518
|
513
|
518
|
521
|
526
|
Standard arithmetic calculation
|
4,009 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
False
|
True
|
Depends on values
|
Cannot determine
|
Logical reasoning and boolean operations
|
1,060 |
geometry
|
medium
|
What is the volume of a cube with side length 5?
|
125
|
125
|
140
|
160
|
105
|
Geometric calculation and spatial reasoning
|
2,307 |
calculus
|
medium
|
What is d/dx(2x^2 - 6x + 1)?
|
4x^1 - 6
|
4x^1 - 1
|
4x^1 - 6
|
4x^2 - 6
|
2x^1 - 6
|
Calculus differentiation and integration
|
2,648 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
0
|
2
|
sin(2x)
|
Trigonometric functions and identities
|
3,314 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4
|
3
|
3.5
|
4.5
|
Probability calculation and expected value
|
2,089 |
calculus
|
easy
|
Find d/dx(x^5)
|
5x^4
|
x^4
|
5x^5
|
x^5
|
5x^4
|
Calculus differentiation and integration
|
1,266 |
statistics
|
easy
|
What is the mean of 19 14 20 14 17 11 13 6?
|
14.2
|
14.2
|
12.2
|
15.2
|
16.2
|
Statistical measure calculation
|
4,429 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
11
|
9
|
10
|
8
|
Vector operations and matrix calculations
|
2,025 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/3
|
1/2
|
0/2
|
2/2
|
Fraction arithmetic and simplification
|
3,342 |
number_theory
|
easy
|
What is the GCD of 15 and 25?
|
5
|
6
|
3
|
4
|
5
|
Number theory and modular arithmetic
|
2,795 |
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
|
4,704 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
5
|
6
|
4
|
8
|
Permutations and combinations
|
4,895 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
48
|
120
|
24
|
60
|
Permutations and combinations
|
188 |
arithmetic
|
medium
|
Calculate 266 ÷ 14
|
19
|
19
|
20
|
17
|
22
|
Standard arithmetic calculation
|
2,407 |
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
|
4,794 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
125
|
60
|
75
|
50
|
Permutations and combinations
|
2,324 |
calculus
|
medium
|
What is d/dx(2x^2 - 7x + 1)?
|
4x^1 - 7
|
4x^1 - 1
|
4x^1 - 7
|
4x^2 - 7
|
2x^1 - 7
|
Calculus differentiation and integration
|
635 |
algebra
|
medium
|
Solve: 6x - 12 = 18
|
5
|
5
|
3
|
6
|
8
|
Algebraic manipulation and solving
|
4,066 |
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
|
False
|
True
|
Logical reasoning and boolean operations
|
4,039 |
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
|
4,031 |
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
|
948 |
geometry
|
easy
|
What is the area of a rectangle with length 12 and width 6?
|
72
|
75
|
72
|
80
|
67
|
Geometric calculation and spatial reasoning
|
2,901 |
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
|
2,928 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
2/3
|
1/4
|
1/2
|
1/3
|
Probability calculation and expected value
|
1,847 |
fractions
|
medium
|
Divide 5/8 ÷ 2/7
|
35/16
|
36/16
|
35/17
|
16/35
|
35/16
|
Fraction arithmetic and simplification
|
955 |
geometry
|
easy
|
How many sides does a hexagon have?
|
6
|
8
|
6
|
7
|
5
|
Geometric calculation and spatial reasoning
|
4,492 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
4
|
3
|
6
|
5
|
Vector operations and matrix calculations
|
4,319 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
11
|
8
|
10
|
9
|
Vector operations and matrix calculations
|
3,609 |
number_theory
|
medium
|
Find LCM of 12 and 16
|
48
|
63
|
48
|
53
|
38
|
Number theory and modular arithmetic
|
4,026 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
Depends on values
|
True
|
Cannot determine
|
False
|
Logical reasoning and boolean operations
|
1,857 |
fractions
|
medium
|
Calculate 1 × 2/5
|
2/5
|
3/5
|
5/2
|
2/5
|
2/6
|
Fraction arithmetic and simplification
|
2,724 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
√2
|
0
|
1
|
√3
|
Trigonometric functions and identities
|
209 |
arithmetic
|
medium
|
What is 11²?
|
121
|
136
|
121
|
129
|
111
|
Standard arithmetic calculation
|
3,963 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Cannot determine
|
P is false
|
Q is true
|
Q is false
|
Logical reasoning and boolean operations
|
3,000 |
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
|
4,367 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
11
|
10
|
8
|
Vector operations and matrix calculations
|
517 |
algebra
|
easy
|
What is 2x when x = 3?
|
6
|
3
|
11
|
6
|
8
|
Algebraic manipulation and solving
|
518 |
algebra
|
easy
|
Solve for x: x + 7 = 17
|
10
|
13
|
11
|
10
|
8
|
Algebraic manipulation and solving
|
4,568 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
5
|
3
|
6
|
4
|
Vector operations and matrix calculations
|
3,673 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
4
|
1
|
3
|
2
|
Number theory and modular arithmetic
|
3,612 |
number_theory
|
medium
|
How many factors does 30 have?
|
8
|
9
|
8
|
7
|
6
|
Number theory and modular arithmetic
|
3,324 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3.5
|
4
|
3
|
4.5
|
Probability calculation and expected value
|
1,289 |
statistics
|
easy
|
Find the median of 5 9 3 6 20
|
6
|
8
|
7
|
6
|
4
|
Statistical measure calculation
|
4,147 |
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
|
447 |
algebra
|
easy
|
Solve for x: x + 11 = 23
|
12
|
12
|
15
|
13
|
10
|
Algebraic manipulation and solving
|
4,899 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
60
|
24
|
48
|
120
|
Permutations and combinations
|
2,120 |
calculus
|
easy
|
What is the derivative of x²?
|
2x
|
2x²
|
x
|
2x
|
x²
|
Calculus differentiation and integration
|
495 |
algebra
|
easy
|
What is 8x when x = 5?
|
40
|
37
|
42
|
45
|
40
|
Algebraic manipulation and solving
|
3,049 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
7
|
5
|
8
|
6
|
Probability calculation and expected value
|
4,819 |
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
|
2,231 |
calculus
|
medium
|
What is d/dx(3x^2 - 1x + 1)?
|
6x^1 - 1
|
6x^1 - 1
|
3x^1 - 1
|
6x^1 - 1
|
6x^2 - 1
|
Calculus differentiation and integration
|
4,752 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
75
|
50
|
125
|
60
|
Permutations and combinations
|
4,602 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
5
|
8
|
4
|
6
|
Permutations and combinations
|
2,622 |
trigonometry
|
easy
|
What is sin(60°)?
|
0.87
|
0
|
0.87
|
1
|
-1
|
Trigonometric functions and identities
|
709 |
algebra
|
hard
|
Solve: x² + -8x + 12 = 0
|
x = 2 or x = 6
|
x = 1 or x = 7
|
x = 2 or x = 6
|
x = -2 or x = -6
|
x = 3 or x = 5
|
Algebraic manipulation and solving
|
4,491 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
5
|
3
|
4
|
6
|
Vector operations and matrix calculations
|
136 |
arithmetic
|
easy
|
Find 12 × 6
|
72
|
72
|
74
|
77
|
69
|
Standard arithmetic calculation
|
3,197 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/30
|
1/36
|
1/32
|
1/35
|
Probability calculation and expected value
|
3,034 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
8
|
7
|
5
|
6
|
Probability calculation and expected value
|
569 |
algebra
|
medium
|
Solve: 5x - 12 = 15
|
5
|
8
|
5
|
3
|
6
|
Algebraic manipulation and solving
|
3,516 |
number_theory
|
medium
|
Find LCM of 15 and 20
|
60
|
65
|
50
|
75
|
60
|
Number theory and modular arithmetic
|
2,101 |
calculus
|
easy
|
What is the derivative of x²?
|
2x
|
x²
|
2x²
|
x
|
2x
|
Calculus differentiation and integration
|
4,218 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[4, 7]
|
[3, 7]
|
[3, 6]
|
[2, 7]
|
Vector operations and matrix calculations
|
1,333 |
statistics
|
easy
|
Find the median of 5 11 13 8 14 7 18
|
11
|
11
|
12
|
9
|
13
|
Statistical measure calculation
|
2,315 |
calculus
|
medium
|
What is d/dx(5x^3 - 2x + 1)?
|
15x^2 - 2
|
15x^2 - 1
|
15x^2 - 2
|
5x^2 - 2
|
15x^3 - 2
|
Calculus differentiation and integration
|
250 |
arithmetic
|
medium
|
What is 25% of 240?
|
60
|
65
|
60
|
70
|
55
|
Standard arithmetic calculation
|
4,588 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
5
|
6
|
4
|
8
|
Permutations and combinations
|
1,461 |
statistics
|
medium
|
Calculate the range of 6 9 10 7 10 5
|
5
|
6
|
8
|
5
|
3
|
Statistical measure calculation
|
3,617 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
3
|
4
|
1
|
Number theory and modular arithmetic
|
2,592 |
trigonometry
|
easy
|
What is sin(30°)?
|
0.5
|
-1
|
0.5
|
1
|
0
|
Trigonometric functions and identities
|
4,204 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[4, 7]
|
[3, 7]
|
[2, 7]
|
[3, 6]
|
Vector operations and matrix calculations
|
3,412 |
number_theory
|
easy
|
What is the GCD of 8 and 12?
|
4
|
5
|
2
|
4
|
3
|
Number theory and modular arithmetic
|
4,756 |
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
|
4,432 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
8
|
9
|
11
|
10
|
Vector operations and matrix calculations
|
911 |
geometry
|
easy
|
What is the area of a rectangle with length 9 and width 9?
|
81
|
81
|
89
|
76
|
84
|
Geometric calculation and spatial reasoning
|
1,288 |
statistics
|
easy
|
What is the mean of 11 5 11 19 14 19 5 15?
|
12.4
|
13.4
|
10.4
|
12.4
|
14.4
|
Statistical measure calculation
|
4,529 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
5
|
6
|
4
|
3
|
Vector operations and matrix calculations
|
2,632 |
trigonometry
|
easy
|
What is sin(0°)?
|
0
|
0
|
0
|
1
|
-1
|
Trigonometric functions and identities
|
3,646 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
4
|
1
|
3
|
2
|
Number theory and modular arithmetic
|
1,020 |
geometry
|
medium
|
What is the volume of a cube with side length 9?
|
729
|
709
|
764
|
729
|
744
|
Geometric calculation and spatial reasoning
|
1,951 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
2/2
|
1/2
|
0/2
|
1/3
|
Fraction arithmetic and simplification
|
3,372 |
number_theory
|
easy
|
Is 19 a prime number?
|
Yes
|
Yes
|
No
|
Cannot determine
|
Only if x>0
|
Number theory and modular arithmetic
|
3,966 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Q is true
|
P is false
|
Q is false
|
Cannot determine
|
Logical reasoning and boolean operations
|
3,426 |
number_theory
|
easy
|
What is the GCD of 15 and 25?
|
5
|
4
|
5
|
6
|
3
|
Number theory and modular arithmetic
|
4,625 |
combinatorics
|
easy
|
How many ways can 5 people stand in a line?
|
120
|
10
|
24
|
25
|
120
|
Permutations and combinations
|
3,038 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
2/3
|
1/4
|
1/2
|
1/3
|
Probability calculation and expected value
|
4,225 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 6]
|
[2, 7]
|
[4, 7]
|
[3, 7]
|
Vector operations and matrix calculations
|
397 |
arithmetic
|
hard
|
Calculate (3^3 × 4) ÷ 6
|
18
|
13
|
21
|
18
|
26
|
Standard arithmetic calculation
|
2,521 |
trigonometry
|
easy
|
Find cos(30°)
|
√3/2
|
-1
|
1
|
0
|
√3/2
|
Trigonometric functions and identities
|
4,264 |
linear_algebra
|
easy
|
Calculate 4 × [2, 3]
|
[8, 12]
|
[8, 12]
|
[8, 11]
|
[7, 12]
|
[9, 12]
|
Vector operations and matrix calculations
|
2,827 |
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
|
741 |
algebra
|
hard
|
Solve: x² + -9x + 18 = 0
|
x = 6 or x = 3
|
x = 5 or x = 4
|
x = 6 or x = 3
|
x = -6 or x = -3
|
x = 7 or x = 2
|
Algebraic manipulation and solving
|
3,278 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3.5
|
4.5
|
3
|
4
|
Probability calculation and expected value
|
2,540 |
trigonometry
|
easy
|
What is sin(45°)?
|
0.71
|
1
|
-1
|
0
|
0.71
|
Trigonometric functions and identities
|
2,807 |
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
|
1,780 |
fractions
|
easy
|
Simplify 4/12
|
1/3
|
5/13
|
2/6
|
3/11
|
1/3
|
Fraction arithmetic and simplification
|
4,110 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
Depends on other variables
|
False
|
True
|
Cannot determine
|
Logical reasoning and boolean operations
|
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