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 |
|---|---|---|---|---|---|---|---|---|---|
4,991 |
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
|
1,222 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 7 and 24
|
25
|
23
|
25
|
26
|
24
|
Geometric calculation and spatial reasoning
|
2,148 |
calculus
|
easy
|
Find d/dx(x^5)
|
5x^4
|
x^4
|
x^5
|
5x^5
|
5x^4
|
Calculus differentiation and integration
|
1,427 |
statistics
|
medium
|
Calculate the range of 5 13 19 9 13
|
14
|
12
|
17
|
15
|
14
|
Statistical measure calculation
|
781 |
algebra
|
hard
|
Solve: x² + -10x + 21 = 0
|
x = 3 or x = 7
|
x = 2 or x = 8
|
x = 3 or x = 7
|
x = -3 or x = -7
|
x = 4 or x = 6
|
Algebraic manipulation and solving
|
4,470 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
3
|
5
|
4
|
6
|
Vector operations and matrix calculations
|
4,959 |
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
|
3,397 |
number_theory
|
easy
|
Is 31 a prime number?
|
Yes
|
Yes
|
Cannot determine
|
No
|
Only if x>0
|
Number theory and modular arithmetic
|
4,847 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
60
|
75
|
125
|
50
|
Permutations and combinations
|
875 |
geometry
|
easy
|
What is the area of a rectangle with length 6 and width 6?
|
36
|
36
|
39
|
31
|
44
|
Geometric calculation and spatial reasoning
|
4,016 |
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 false
|
Q is true
|
Logical reasoning and boolean operations
|
4,321 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
10
|
11
|
8
|
Vector operations and matrix calculations
|
4,633 |
combinatorics
|
easy
|
How many ways can 6 people stand in a line?
|
720
|
36
|
720
|
120
|
12
|
Permutations and combinations
|
1,248 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 8 and 15
|
17
|
15
|
16
|
17
|
18
|
Geometric calculation and spatial reasoning
|
2,971 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
7
|
5
|
6
|
8
|
Probability calculation and expected value
|
2,541 |
trigonometry
|
easy
|
What is tan(45°)?
|
1
|
√2
|
0
|
1
|
√3
|
Trigonometric functions and identities
|
4,435 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
10
|
9
|
8
|
11
|
Vector operations and matrix calculations
|
3,870 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Cannot determine
|
Depends on context
|
True
|
False
|
Logical reasoning and boolean operations
|
4,640 |
combinatorics
|
easy
|
How many ways can 5 people stand in a line?
|
120
|
10
|
25
|
24
|
120
|
Permutations and combinations
|
216 |
arithmetic
|
medium
|
What is 15% of 355?
|
53
|
63
|
48
|
58
|
53
|
Standard arithmetic calculation
|
2,420 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(2x)
|
2x sin(x²)
|
2x cos(x²)
|
cos(x²)
|
Calculus differentiation and integration
|
663 |
algebra
|
medium
|
Find x: x² = 25
|
5
|
3
|
6
|
8
|
5
|
Algebraic manipulation and solving
|
1,366 |
statistics
|
easy
|
Find the median of 9 13 7 17
|
11
|
9
|
12
|
13
|
11
|
Statistical measure calculation
|
124 |
arithmetic
|
easy
|
What is 14 + 50?
|
64
|
64
|
65
|
62
|
67
|
Standard arithmetic calculation
|
3,599 |
number_theory
|
medium
|
Find LCM of 9 and 15
|
45
|
50
|
60
|
35
|
45
|
Number theory and modular arithmetic
|
2,487 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
2x cos(x²)
|
cos(2x)
|
2x sin(x²)
|
cos(x²)
|
Calculus differentiation and integration
|
930 |
geometry
|
easy
|
What is the area of a rectangle with length 8 and width 9?
|
72
|
67
|
72
|
75
|
80
|
Geometric calculation and spatial reasoning
|
4,486 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
4
|
3
|
6
|
5
|
Vector operations and matrix calculations
|
2,818 |
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
|
941 |
geometry
|
easy
|
What is the area of a rectangle with length 9 and width 6?
|
54
|
62
|
54
|
49
|
57
|
Geometric calculation and spatial reasoning
|
1,109 |
geometry
|
medium
|
Find the area of a circle with radius 5 (use π ≈ 3.14)
|
78.54
|
76.04
|
80.34
|
78.54
|
81.74
|
Geometric calculation and spatial reasoning
|
4,850 |
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
|
4,417 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
8
|
9
|
11
|
10
|
Vector operations and matrix calculations
|
1,260 |
statistics
|
easy
|
Find the median of 20 9 13 2 3 6 14 2
|
7.5
|
7.5
|
9.5
|
8.5
|
5.5
|
Statistical measure calculation
|
1,034 |
geometry
|
medium
|
Find the area of a circle with radius 3 (use π ≈ 3.14)
|
28.27
|
31.47
|
25.77
|
30.07
|
28.27
|
Geometric calculation and spatial reasoning
|
1,449 |
statistics
|
medium
|
What is the mode of 9 7 9 9 18 5 8?
|
9
|
9
|
7
|
12
|
10
|
Statistical measure calculation
|
2,318 |
calculus
|
medium
|
What is d/dx(2x^4 - 8x + 1)?
|
8x^3 - 8
|
8x^3 - 1
|
8x^3 - 8
|
8x^4 - 8
|
2x^3 - 8
|
Calculus differentiation and integration
|
4,512 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
6
|
5
|
3
|
4
|
Vector operations and matrix calculations
|
1,903 |
fractions
|
medium
|
Divide 2/7 ÷ 1/2
|
4/7
|
5/7
|
7/4
|
4/8
|
4/7
|
Fraction arithmetic and simplification
|
4,186 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[3, 6]
|
[2, 7]
|
[3, 7]
|
[4, 7]
|
Vector operations and matrix calculations
|
2,300 |
calculus
|
medium
|
What is d/dx(5x^4 - 3x + 1)?
|
20x^3 - 3
|
5x^3 - 3
|
20x^3 - 3
|
20x^4 - 3
|
20x^3 - 1
|
Calculus differentiation and integration
|
3,502 |
number_theory
|
medium
|
Find LCM of 12 and 16
|
48
|
48
|
63
|
53
|
38
|
Number theory and modular arithmetic
|
4,057 |
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
|
2,043 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/2
|
1/3
|
0/2
|
2/2
|
Fraction arithmetic and simplification
|
4,532 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
5
|
4
|
6
|
3
|
Vector operations and matrix calculations
|
2,737 |
trigonometry
|
medium
|
What is tan(45°)?
|
1
|
√2
|
1
|
√3
|
0
|
Trigonometric functions and identities
|
4,639 |
combinatorics
|
easy
|
How many ways can 4 people stand in a line?
|
24
|
6
|
16
|
24
|
8
|
Permutations and combinations
|
105 |
arithmetic
|
easy
|
Calculate 51 - 37
|
14
|
14
|
13
|
15
|
16
|
Standard arithmetic calculation
|
3,492 |
number_theory
|
medium
|
Find LCM of 9 and 15
|
45
|
60
|
50
|
45
|
35
|
Number theory and modular arithmetic
|
2,267 |
calculus
|
medium
|
What is d/dx(2x^3 - 3x + 1)?
|
6x^2 - 3
|
6x^3 - 3
|
2x^2 - 3
|
6x^2 - 3
|
6x^2 - 1
|
Calculus differentiation and integration
|
1,571 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.24
|
2.94
|
1.74
|
2.54
|
Statistical measure calculation
|
3,380 |
number_theory
|
easy
|
What is the GCD of 14 and 21?
|
7
|
7
|
5
|
8
|
6
|
Number theory and modular arithmetic
|
3,753 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
cat
|
pet
|
animal
|
mammal
|
Logical reasoning and boolean operations
|
4,566 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
3
|
6
|
5
|
4
|
Vector operations and matrix calculations
|
1,042 |
geometry
|
medium
|
Find the area of a circle with radius 8 (use π ≈ 3.14)
|
201.06
|
202.86
|
198.56
|
204.26
|
201.06
|
Geometric calculation and spatial reasoning
|
660 |
algebra
|
medium
|
Find x: x² = 36
|
6
|
4
|
7
|
6
|
9
|
Algebraic manipulation and solving
|
3,819 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
mammal
|
cat
|
animal
|
pet
|
Logical reasoning and boolean operations
|
892 |
geometry
|
easy
|
What is the area of a rectangle with length 11 and width 7?
|
77
|
72
|
77
|
80
|
85
|
Geometric calculation and spatial reasoning
|
1,734 |
fractions
|
easy
|
Simplify 14/6
|
7/3
|
13/5
|
15/7
|
7/3
|
7/3
|
Fraction arithmetic and simplification
|
4,779 |
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
|
2,964 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
8
|
7
|
5
|
6
|
Probability calculation and expected value
|
4,750 |
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
|
2,987 |
probability
|
easy
|
What is the probability of getting heads on a fair coin flip?
|
1/2
|
2/3
|
1/2
|
1/4
|
1/3
|
Probability calculation and expected value
|
1,399 |
statistics
|
medium
|
What is the mode of 19 8 5 15 5 6 5?
|
5
|
3
|
8
|
5
|
6
|
Statistical measure calculation
|
3,762 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Depends on context
|
False
|
Cannot determine
|
True
|
Logical reasoning and boolean operations
|
4,134 |
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
|
1,159 |
geometry
|
hard
|
Find the hypotenuse of a right triangle with legs 7 and 24
|
25
|
25
|
24
|
26
|
23
|
Geometric calculation and spatial reasoning
|
3,515 |
number_theory
|
medium
|
Find LCM of 12 and 16
|
48
|
53
|
48
|
38
|
63
|
Number theory and modular arithmetic
|
971 |
geometry
|
easy
|
How many sides does a hexagon have?
|
6
|
8
|
6
|
7
|
5
|
Geometric calculation and spatial reasoning
|
4,001 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
False
|
True
|
Depends on values
|
Cannot determine
|
Logical reasoning and boolean operations
|
2,641 |
trigonometry
|
easy
|
Calculate tan(0°)
|
0
|
1
|
undefined
|
0
|
-1
|
Trigonometric functions and identities
|
4,663 |
combinatorics
|
easy
|
How many ways to choose 2 items from 4 items?
|
6
|
6
|
8
|
4
|
5
|
Permutations and combinations
|
1,422 |
statistics
|
medium
|
Calculate the range of 5 4 11 6 6 11 9 15
|
11
|
12
|
9
|
11
|
14
|
Statistical measure calculation
|
1,285 |
statistics
|
easy
|
What is the mean of 8 10 19 18 19 13?
|
14.5
|
12.5
|
15.5
|
16.5
|
14.5
|
Statistical measure calculation
|
3,631 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
2
|
1
|
3
|
4
|
Number theory and modular arithmetic
|
3,869 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
animal
|
mammal
|
cat
|
pet
|
Logical reasoning and boolean operations
|
650 |
algebra
|
medium
|
Solve: 6x - 11 = 12
|
3
|
4
|
6
|
1
|
3
|
Algebraic manipulation and solving
|
544 |
algebra
|
easy
|
What is 8x when x = 7?
|
56
|
56
|
61
|
53
|
58
|
Algebraic manipulation and solving
|
3,739 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
3
|
4
|
1
|
2
|
Number theory and modular arithmetic
|
3,421 |
number_theory
|
easy
|
What is the GCD of 14 and 21?
|
7
|
8
|
7
|
6
|
5
|
Number theory and modular arithmetic
|
2,259 |
calculus
|
medium
|
What is d/dx(5x^2 - 6x + 1)?
|
10x^1 - 6
|
10x^2 - 6
|
10x^1 - 1
|
5x^1 - 6
|
10x^1 - 6
|
Calculus differentiation and integration
|
453 |
algebra
|
easy
|
What is 6x when x = 3?
|
18
|
20
|
15
|
18
|
23
|
Algebraic manipulation and solving
|
2,696 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
sin(2x)
|
1
|
0
|
2
|
Trigonometric functions and identities
|
4,519 |
linear_algebra
|
hard
|
Find the determinant of matrix [[2, 3], [1, 4]]
|
5
|
3
|
6
|
4
|
5
|
Vector operations and matrix calculations
|
1,904 |
fractions
|
medium
|
Calculate 3/4 × 6/7
|
9/14
|
10/14
|
14/9
|
9/14
|
9/15
|
Fraction arithmetic and simplification
|
483 |
algebra
|
easy
|
Solve for x: x + 11 = 22
|
11
|
14
|
11
|
9
|
12
|
Algebraic manipulation and solving
|
3,995 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Q is false
|
P is false
|
Q is true
|
Cannot determine
|
Logical reasoning and boolean operations
|
4,913 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
24
|
48
|
60
|
120
|
Permutations and combinations
|
3,040 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
5
|
7
|
6
|
8
|
Probability calculation and expected value
|
181 |
arithmetic
|
medium
|
What is 10²?
|
100
|
108
|
100
|
115
|
90
|
Standard arithmetic calculation
|
1,454 |
statistics
|
medium
|
Calculate the range of 20 17 2 11
|
18
|
18
|
21
|
16
|
19
|
Statistical measure calculation
|
3,167 |
probability
|
medium
|
Probability of rolling two sixes with two dice
|
1/36
|
1/32
|
1/30
|
1/35
|
1/36
|
Probability calculation and expected value
|
2,638 |
trigonometry
|
easy
|
Find cos(45°)
|
√2/2
|
0
|
1
|
√2/2
|
-1
|
Trigonometric functions and identities
|
12 |
arithmetic
|
easy
|
What is 33 + 70?
|
103
|
106
|
104
|
101
|
103
|
Standard arithmetic calculation
|
751 |
algebra
|
hard
|
Solve: x² + -7x + 12 = 0
|
x = 3 or x = 4
|
x = 2 or x = 5
|
x = 3 or x = 4
|
x = -3 or x = -4
|
x = 4 or x = 3
|
Algebraic manipulation and solving
|
2,564 |
trigonometry
|
easy
|
What is sin(0°)?
|
0
|
0
|
-1
|
1
|
0
|
Trigonometric functions and identities
|
3,695 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
3
|
4
|
1
|
2
|
Number theory and modular arithmetic
|
4,853 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
75
|
50
|
60
|
125
|
Permutations and combinations
|
4,293 |
linear_algebra
|
easy
|
Calculate 5 × [2, 3]
|
[10, 15]
|
[11, 15]
|
[10, 14]
|
[10, 15]
|
[9, 15]
|
Vector operations and matrix calculations
|
1,261 |
statistics
|
easy
|
What is the mean of 3 13 11 19?
|
11.5
|
12.5
|
9.5
|
11.5
|
13.5
|
Statistical measure calculation
|
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