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 |
|---|---|---|---|---|---|---|---|---|---|
4,355 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
8
|
10
|
11
|
Vector operations and matrix calculations
|
1,623 |
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
|
3,143 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/32
|
1/35
|
1/36
|
1/30
|
Probability calculation and expected value
|
3,650 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
1
|
4
|
3
|
Number theory and modular arithmetic
|
4,871 |
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
|
4,527 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
4
|
5
|
3
|
6
|
Vector operations and matrix calculations
|
3,940 |
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
|
49 |
arithmetic
|
easy
|
Find 7 × 11
|
77
|
79
|
74
|
77
|
82
|
Standard arithmetic calculation
|
999 |
geometry
|
medium
|
Find the area of a circle with radius 4 (use π ≈ 3.14)
|
50.27
|
50.27
|
52.07
|
53.47
|
47.77
|
Geometric calculation and spatial reasoning
|
81 |
arithmetic
|
easy
|
What is 69 + 65?
|
134
|
132
|
134
|
137
|
135
|
Standard arithmetic calculation
|
937 |
geometry
|
easy
|
How many sides does a heptagon have?
|
7
|
7
|
9
|
8
|
6
|
Geometric calculation and spatial reasoning
|
3,619 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
3
|
4
|
1
|
Number theory and modular arithmetic
|
3,540 |
number_theory
|
medium
|
How many factors does 30 have?
|
8
|
7
|
9
|
6
|
8
|
Number theory and modular arithmetic
|
4,745 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
60
|
75
|
50
|
125
|
Permutations and combinations
|
4,601 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
6
|
8
|
5
|
4
|
Permutations and combinations
|
14 |
arithmetic
|
easy
|
Calculate 57 - 45
|
12
|
13
|
11
|
14
|
12
|
Standard arithmetic calculation
|
1,066 |
geometry
|
medium
|
What is the volume of a cube with side length 9?
|
729
|
744
|
764
|
709
|
729
|
Geometric calculation and spatial reasoning
|
3,849 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Depends on context
|
False
|
True
|
Cannot determine
|
Logical reasoning and boolean operations
|
1,384 |
statistics
|
easy
|
Find the median of 3 2 17 17
|
10
|
10
|
12
|
11
|
8
|
Statistical measure calculation
|
4,624 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
8
|
5
|
4
|
6
|
Permutations and combinations
|
1,712 |
fractions
|
easy
|
What is 1/2 + 1/6?
|
2/3
|
1/3
|
3/3
|
2/4
|
2/3
|
Fraction arithmetic and simplification
|
1,477 |
statistics
|
medium
|
Calculate the range of 3 8 8 9 13 9 13
|
10
|
8
|
10
|
11
|
13
|
Statistical measure calculation
|
2,762 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
√2
|
0
|
1
|
√3
|
Trigonometric functions and identities
|
639 |
algebra
|
medium
|
Find x: x² = 25
|
5
|
8
|
3
|
6
|
5
|
Algebraic manipulation and solving
|
516 |
algebra
|
easy
|
What is 8x when x = 4?
|
32
|
34
|
37
|
32
|
29
|
Algebraic manipulation and solving
|
2,550 |
trigonometry
|
easy
|
What is sin(0°)?
|
0
|
0
|
-1
|
0
|
1
|
Trigonometric functions and identities
|
312 |
arithmetic
|
hard
|
Calculate (6^4 × 2) ÷ 3
|
864
|
859
|
867
|
872
|
864
|
Standard arithmetic calculation
|
1,032 |
geometry
|
medium
|
Find the area of a circle with radius 7 (use π ≈ 3.14)
|
153.94
|
151.44
|
157.14
|
153.94
|
155.74
|
Geometric calculation and spatial reasoning
|
63 |
arithmetic
|
easy
|
Calculate 54 - 46
|
8
|
10
|
8
|
7
|
9
|
Standard arithmetic calculation
|
3,776 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Depends on context
|
Cannot determine
|
True
|
False
|
Logical reasoning and boolean operations
|
1,756 |
fractions
|
easy
|
Simplify 4/8
|
1/2
|
5/9
|
3/7
|
2/4
|
1/2
|
Fraction arithmetic and simplification
|
1,586 |
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
|
3,163 |
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
|
895 |
geometry
|
easy
|
What is the area of a rectangle with length 11 and width 8?
|
88
|
83
|
88
|
91
|
96
|
Geometric calculation and spatial reasoning
|
1,155 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 5 and 12
|
13
|
14
|
13
|
11
|
12
|
Geometric calculation and spatial reasoning
|
2,162 |
calculus
|
easy
|
Evaluate ∫x^2 dx
|
x^3/3 + C
|
x^4/4 + C
|
2x^1 + C
|
x^2 + C
|
x^3/3 + C
|
Calculus differentiation and integration
|
2,812 |
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
|
4,859 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
50
|
125
|
60
|
75
|
Permutations and combinations
|
3,310 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4.5
|
3
|
4
|
3.5
|
Probability calculation and expected value
|
3,594 |
number_theory
|
medium
|
Find LCM of 12 and 16
|
48
|
63
|
48
|
53
|
38
|
Number theory and modular arithmetic
|
2,391 |
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
|
396 |
arithmetic
|
hard
|
Calculate (5^3 × 2) ÷ 8
|
31
|
26
|
34
|
39
|
31
|
Standard arithmetic calculation
|
736 |
algebra
|
hard
|
Solve: x² + -10x + 16 = 0
|
x = 2 or x = 8
|
x = 1 or x = 9
|
x = 2 or x = 8
|
x = -2 or x = -8
|
x = 3 or x = 7
|
Algebraic manipulation and solving
|
647 |
algebra
|
medium
|
Solve: 3x - 12 = 25
|
12
|
13
|
15
|
12
|
10
|
Algebraic manipulation and solving
|
3,469 |
number_theory
|
easy
|
Is 19 a prime number?
|
Yes
|
No
|
Cannot determine
|
Only if x>0
|
Yes
|
Number theory and modular arithmetic
|
2,506 |
trigonometry
|
easy
|
What is sin(180°)?
|
0
|
0
|
1
|
-1
|
0
|
Trigonometric functions and identities
|
4,446 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
8
|
10
|
9
|
11
|
Vector operations and matrix calculations
|
2,294 |
calculus
|
medium
|
What is d/dx(4x^4 - 5x + 1)?
|
16x^3 - 5
|
4x^3 - 5
|
16x^3 - 1
|
16x^4 - 5
|
16x^3 - 5
|
Calculus differentiation and integration
|
4,192 |
linear_algebra
|
easy
|
Calculate 3 × [2, 3]
|
[6, 9]
|
[6, 8]
|
[6, 9]
|
[5, 9]
|
[7, 9]
|
Vector operations and matrix calculations
|
3,749 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
4
|
1
|
3
|
2
|
Number theory and modular arithmetic
|
1,673 |
fractions
|
easy
|
Simplify 20/20
|
1/1
|
21/21
|
1/1
|
10/10
|
19/19
|
Fraction arithmetic and simplification
|
4,931 |
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
|
1,181 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 8 and 15
|
17
|
16
|
15
|
17
|
18
|
Geometric calculation and spatial reasoning
|
4,649 |
combinatorics
|
easy
|
How many ways can 4 people stand in a line?
|
24
|
16
|
8
|
24
|
6
|
Permutations and combinations
|
699 |
algebra
|
hard
|
Solve: x² + -11x + 30 = 0
|
x = 6 or x = 5
|
x = 5 or x = 6
|
x = 6 or x = 5
|
x = -6 or x = -5
|
x = 7 or x = 4
|
Algebraic manipulation and solving
|
4,441 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
11
|
8
|
10
|
Vector operations and matrix calculations
|
3,161 |
probability
|
medium
|
Probability of drawing an ace from a standard deck
|
1/13
|
1/15
|
1/14
|
1/13
|
1/12
|
Probability calculation and expected value
|
3,852 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
False
|
True
|
Cannot determine
|
Depends on context
|
Logical reasoning and boolean operations
|
656 |
algebra
|
medium
|
Find x: x² = 36
|
6
|
6
|
9
|
4
|
7
|
Algebraic manipulation and solving
|
3,244 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4
|
4.5
|
3
|
3.5
|
Probability calculation and expected value
|
2,634 |
trigonometry
|
easy
|
What is tan(45°)?
|
1
|
√3
|
√2
|
1
|
0
|
Trigonometric functions and identities
|
3,806 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
pet
|
mammal
|
animal
|
cat
|
Logical reasoning and boolean operations
|
3,291 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
3.5
|
4.5
|
3
|
4
|
Probability calculation and expected value
|
1,386 |
statistics
|
easy
|
Find the median of 12 15 2 19 10 5
|
11
|
12
|
13
|
9
|
11
|
Statistical measure calculation
|
2,158 |
calculus
|
easy
|
Find d/dx(x^4)
|
4x^3
|
x^3
|
4x^4
|
4x^3
|
x^4
|
Calculus differentiation and integration
|
2,296 |
calculus
|
medium
|
What is d/dx(2x^3 - 5x + 1)?
|
6x^2 - 5
|
6x^2 - 5
|
6x^3 - 5
|
6x^2 - 1
|
2x^2 - 5
|
Calculus differentiation and integration
|
3,053 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
1/3
|
2/3
|
1/2
|
1/4
|
Probability calculation and expected value
|
127 |
arithmetic
|
easy
|
Find 11 × 12
|
132
|
134
|
132
|
129
|
137
|
Standard arithmetic calculation
|
3,735 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
3
|
1
|
2
|
4
|
Number theory and modular arithmetic
|
3,573 |
number_theory
|
medium
|
Find LCM of 15 and 20
|
60
|
50
|
75
|
65
|
60
|
Number theory and modular arithmetic
|
2,738 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
√3
|
0
|
√2
|
1
|
Trigonometric functions and identities
|
1,913 |
fractions
|
medium
|
Calculate 3/5 × 1/3
|
1/5
|
1/5
|
2/5
|
5/1
|
1/6
|
Fraction arithmetic and simplification
|
280 |
arithmetic
|
hard
|
Calculate (5^3 × 4) ÷ 5
|
100
|
108
|
100
|
103
|
95
|
Standard arithmetic calculation
|
3,434 |
number_theory
|
easy
|
Is 13 a prime number?
|
Yes
|
No
|
Only if x>0
|
Yes
|
Cannot determine
|
Number theory and modular arithmetic
|
2,156 |
calculus
|
easy
|
Find d/dx(x^5)
|
5x^4
|
x^5
|
x^4
|
5x^5
|
5x^4
|
Calculus differentiation and integration
|
3,169 |
probability
|
medium
|
Probability of drawing an ace from a standard deck
|
1/13
|
1/15
|
1/14
|
1/12
|
1/13
|
Probability calculation and expected value
|
3,629 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
3
|
1
|
2
|
4
|
Number theory and modular arithmetic
|
4,636 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
6
|
8
|
4
|
5
|
Permutations and combinations
|
4,569 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
4
|
5
|
6
|
3
|
Vector operations and matrix calculations
|
1,550 |
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
|
2,097 |
calculus
|
easy
|
Evaluate ∫x^4 dx
|
x^5/5 + C
|
x^6/6 + C
|
x^4 + C
|
4x^3 + C
|
x^5/5 + C
|
Calculus differentiation and integration
|
3,526 |
number_theory
|
medium
|
How many factors does 24 have?
|
8
|
7
|
8
|
6
|
9
|
Number theory and modular arithmetic
|
503 |
algebra
|
easy
|
What is 5x when x = 6?
|
30
|
30
|
35
|
27
|
32
|
Algebraic manipulation and solving
|
3,918 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
True
|
Depends on values
|
Cannot determine
|
False
|
Logical reasoning and boolean operations
|
1,104 |
geometry
|
medium
|
Find the area of a circle with radius 7 (use π ≈ 3.14)
|
153.94
|
157.14
|
153.94
|
151.44
|
155.74
|
Geometric calculation and spatial reasoning
|
964 |
geometry
|
easy
|
How many sides does a octagon have?
|
8
|
8
|
7
|
10
|
9
|
Geometric calculation and spatial reasoning
|
4,283 |
linear_algebra
|
easy
|
Calculate 3 × [2, 3]
|
[6, 9]
|
[6, 8]
|
[5, 9]
|
[7, 9]
|
[6, 9]
|
Vector operations and matrix calculations
|
1,302 |
statistics
|
easy
|
What is the mean of 6 8 16 5 17 3?
|
9.2
|
9.2
|
10.2
|
7.199999999999999
|
11.2
|
Statistical measure calculation
|
2,321 |
calculus
|
medium
|
What is d/dx(3x^2 - 3x + 1)?
|
6x^1 - 3
|
6x^1 - 3
|
6x^2 - 3
|
6x^1 - 1
|
3x^1 - 3
|
Calculus differentiation and integration
|
2,291 |
calculus
|
medium
|
What is d/dx(3x^2 - 3x + 1)?
|
6x^1 - 3
|
6x^2 - 3
|
3x^1 - 3
|
6x^1 - 1
|
6x^1 - 3
|
Calculus differentiation and integration
|
4,206 |
linear_algebra
|
easy
|
Calculate 5 × [2, 3]
|
[10, 15]
|
[10, 15]
|
[10, 14]
|
[11, 15]
|
[9, 15]
|
Vector operations and matrix calculations
|
4,930 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
48
|
24
|
120
|
60
|
Permutations and combinations
|
3,662 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
1
|
2
|
3
|
4
|
Number theory and modular arithmetic
|
4,552 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
6
|
3
|
4
|
5
|
Vector operations and matrix calculations
|
646 |
algebra
|
medium
|
Solve: 4x - 13 = 16
|
7
|
8
|
10
|
7
|
5
|
Algebraic manipulation and solving
|
2,079 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/3
|
1/2
|
2/2
|
0/2
|
Fraction arithmetic and simplification
|
2,134 |
calculus
|
easy
|
Find d/dx(x^3)
|
3x^2
|
3x^3
|
3x^2
|
x^2
|
x^3
|
Calculus differentiation and integration
|
3,537 |
number_theory
|
medium
|
How many factors does 24 have?
|
8
|
7
|
9
|
8
|
6
|
Number theory and modular arithmetic
|
449 |
algebra
|
easy
|
What is 5x when x = 8?
|
40
|
42
|
45
|
37
|
40
|
Algebraic manipulation and solving
|
1,716 |
fractions
|
easy
|
Simplify 16/12
|
4/3
|
17/13
|
8/6
|
4/3
|
15/11
|
Fraction arithmetic and simplification
|
Subsets and Splits
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