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 |
|---|---|---|---|---|---|---|---|---|---|
4,938 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
24
|
60
|
120
|
48
|
Permutations and combinations
|
4,787 |
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
|
884 |
geometry
|
easy
|
How many sides does a heptagon have?
|
7
|
6
|
7
|
8
|
9
|
Geometric calculation and spatial reasoning
|
859 |
geometry
|
easy
|
How many sides does a heptagon have?
|
7
|
7
|
6
|
8
|
9
|
Geometric calculation and spatial reasoning
|
2,578 |
trigonometry
|
easy
|
Find cos(90°)
|
0
|
1
|
0
|
-1
|
0
|
Trigonometric functions and identities
|
820 |
algebra
|
hard
|
Solve: x² + -13x + 40 = 0
|
x = 8 or x = 5
|
x = 7 or x = 6
|
x = 8 or x = 5
|
x = -8 or x = -5
|
x = 9 or x = 4
|
Algebraic manipulation and solving
|
3,200 |
probability
|
hard
|
Expected value of rolling a fair six-sided die
|
3.5
|
4.5
|
3.5
|
4
|
3
|
Probability calculation and expected value
|
2,505 |
trigonometry
|
easy
|
Calculate tan(0°)
|
0
|
1
|
undefined
|
0
|
-1
|
Trigonometric functions and identities
|
3,830 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Depends on context
|
True
|
False
|
Cannot determine
|
Logical reasoning and boolean operations
|
931 |
geometry
|
easy
|
What is the area of a rectangle with length 9 and width 8?
|
72
|
80
|
75
|
67
|
72
|
Geometric calculation and spatial reasoning
|
4,008 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
False
|
Cannot determine
|
True
|
Depends on values
|
Logical reasoning and boolean operations
|
2,694 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
sin(2x)
|
0
|
1
|
2
|
Trigonometric functions and identities
|
2,647 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
0
|
1
|
sin(2x)
|
2
|
Trigonometric functions and identities
|
3,471 |
number_theory
|
easy
|
What is the GCD of 14 and 21?
|
7
|
6
|
7
|
8
|
5
|
Number theory and modular arithmetic
|
2,594 |
trigonometry
|
easy
|
What is sin(0°)?
|
0
|
1
|
-1
|
0
|
0
|
Trigonometric functions and identities
|
2,333 |
calculus
|
medium
|
What is d/dx(3x^2 - 2x + 1)?
|
6x^1 - 2
|
6x^1 - 1
|
6x^1 - 2
|
3x^1 - 2
|
6x^2 - 2
|
Calculus differentiation and integration
|
1,667 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.24
|
2.54
|
2.94
|
1.74
|
Statistical measure calculation
|
1,362 |
statistics
|
easy
|
What is the mean of 10 19 2 19 20 15 3 3?
|
11.4
|
13.4
|
9.4
|
12.4
|
11.4
|
Statistical measure calculation
|
1,589 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.24
|
1.74
|
2.54
|
2.94
|
Statistical measure calculation
|
3,359 |
number_theory
|
easy
|
What is the GCD of 8 and 12?
|
4
|
4
|
5
|
2
|
3
|
Number theory and modular arithmetic
|
2,112 |
calculus
|
easy
|
Find ∫x dx
|
x²/2 + C
|
x + C
|
x³/3 + C
|
x²/2 + C
|
x²
|
Calculus differentiation and integration
|
50 |
arithmetic
|
easy
|
Find 5 × 7
|
35
|
37
|
35
|
40
|
32
|
Standard arithmetic calculation
|
1,837 |
fractions
|
medium
|
Calculate 4/3 × 6/7
|
8/7
|
8/7
|
9/7
|
7/8
|
8/8
|
Fraction arithmetic and simplification
|
1,938 |
fractions
|
medium
|
Divide 5/3 ÷ 5/3
|
1/1
|
1/1
|
1/1
|
1/2
|
2/1
|
Fraction arithmetic and simplification
|
4,203 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[4, 7]
|
[3, 7]
|
[2, 7]
|
[3, 6]
|
Vector operations and matrix calculations
|
2,495 |
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
|
3,848 |
logic
|
easy
|
If all cats are mammals and Fluffy is a cat, then Fluffy is a:
|
mammal
|
mammal
|
pet
|
animal
|
cat
|
Logical reasoning and boolean operations
|
4,201 |
linear_algebra
|
easy
|
Calculate 2 × [2, 3]
|
[4, 6]
|
[3, 6]
|
[4, 6]
|
[4, 5]
|
[5, 6]
|
Vector operations and matrix calculations
|
130 |
arithmetic
|
easy
|
Find 11 × 6
|
66
|
66
|
63
|
71
|
68
|
Standard arithmetic calculation
|
2,292 |
calculus
|
medium
|
What is d/dx(4x^4 - 3x + 1)?
|
16x^3 - 3
|
4x^3 - 3
|
16x^3 - 1
|
16x^4 - 3
|
16x^3 - 3
|
Calculus differentiation and integration
|
3,008 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
8
|
7
|
5
|
6
|
Probability calculation and expected value
|
1,737 |
fractions
|
easy
|
What is 1/4 + 1/6?
|
5/12
|
5/12
|
6/12
|
5/13
|
4/12
|
Fraction arithmetic and simplification
|
789 |
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
|
3,951 |
logic
|
medium
|
What is NOT(True AND False)?
|
True
|
Depends on values
|
True
|
Cannot determine
|
False
|
Logical reasoning and boolean operations
|
1,253 |
statistics
|
easy
|
Find the median of 7 16 15 20 2 17
|
15.5
|
15.5
|
16.5
|
13.5
|
17.5
|
Statistical measure calculation
|
2,182 |
calculus
|
easy
|
Evaluate ∫x^4 dx
|
x^5/5 + C
|
x^6/6 + C
|
4x^3 + C
|
x^5/5 + C
|
x^4 + C
|
Calculus differentiation and integration
|
3,889 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Depends on context
|
True
|
False
|
Cannot determine
|
Logical reasoning and boolean operations
|
2,913 |
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
|
533 |
algebra
|
easy
|
What is 3x when x = 8?
|
24
|
24
|
26
|
21
|
29
|
Algebraic manipulation and solving
|
2,304 |
calculus
|
medium
|
What is d/dx(4x^4 - 8x + 1)?
|
16x^3 - 8
|
16x^4 - 8
|
4x^3 - 8
|
16x^3 - 8
|
16x^3 - 1
|
Calculus differentiation and integration
|
4,890 |
combinatorics
|
hard
|
In how many ways can 5 books be arranged on a shelf if 2 specific books must be together?
|
48
|
60
|
48
|
24
|
120
|
Permutations and combinations
|
4,837 |
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
|
71 |
arithmetic
|
easy
|
What is 96 + 46?
|
142
|
143
|
140
|
142
|
145
|
Standard arithmetic calculation
|
1,308 |
statistics
|
easy
|
Find the median of 12 9 14 5
|
10.5
|
12.5
|
11.5
|
8.5
|
10.5
|
Statistical measure calculation
|
872 |
geometry
|
easy
|
How many sides does a heptagon have?
|
7
|
8
|
6
|
7
|
9
|
Geometric calculation and spatial reasoning
|
621 |
algebra
|
medium
|
Find x: x² = 81
|
9
|
10
|
9
|
7
|
12
|
Algebraic manipulation and solving
|
4,386 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
9
|
8
|
10
|
11
|
Vector operations and matrix calculations
|
458 |
algebra
|
easy
|
What is 8x when x = 6?
|
48
|
50
|
45
|
53
|
48
|
Algebraic manipulation and solving
|
3,683 |
number_theory
|
hard
|
What is 7³ mod 11?
|
2
|
4
|
3
|
2
|
1
|
Number theory and modular arithmetic
|
2,138 |
calculus
|
easy
|
Evaluate ∫x^2 dx
|
x^3/3 + C
|
x^3/3 + C
|
x^4/4 + C
|
x^2 + C
|
2x^1 + C
|
Calculus differentiation and integration
|
1,343 |
statistics
|
easy
|
What is the mean of 2 6 17 12 19?
|
11.2
|
13.2
|
11.2
|
12.2
|
9.2
|
Statistical measure calculation
|
4,289 |
linear_algebra
|
easy
|
Calculate 2 × [2, 3]
|
[4, 6]
|
[4, 5]
|
[5, 6]
|
[3, 6]
|
[4, 6]
|
Vector operations and matrix calculations
|
2,073 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
2/2
|
1/3
|
0/2
|
1/2
|
Fraction arithmetic and simplification
|
1,328 |
statistics
|
easy
|
What is the mean of 7 16 14 13?
|
12.5
|
12.5
|
14.5
|
13.5
|
10.5
|
Statistical measure calculation
|
2,518 |
trigonometry
|
easy
|
Find cos(180°)
|
-1
|
1
|
0
|
-1
|
-1
|
Trigonometric functions and identities
|
1,629 |
statistics
|
hard
|
Find the standard deviation of 2 4 6 8 (population)
|
2.24
|
2.24
|
2.54
|
2.94
|
1.74
|
Statistical measure calculation
|
1,368 |
statistics
|
easy
|
Find the median of 9 7 10 18 16 4 6
|
9
|
9
|
10
|
7
|
11
|
Statistical measure calculation
|
2,168 |
calculus
|
easy
|
Evaluate ∫x^3 dx
|
x^4/4 + C
|
3x^2 + C
|
x^3 + C
|
x^5/5 + C
|
x^4/4 + C
|
Calculus differentiation and integration
|
2,229 |
calculus
|
medium
|
What is d/dx(3x^4 - 3x + 1)?
|
12x^3 - 3
|
12x^4 - 3
|
3x^3 - 3
|
12x^3 - 1
|
12x^3 - 3
|
Calculus differentiation and integration
|
3,971 |
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
|
4,360 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
11
|
10
|
8
|
9
|
Vector operations and matrix calculations
|
1,708 |
fractions
|
easy
|
Simplify 4/10
|
2/5
|
2/5
|
2/5
|
5/11
|
3/9
|
Fraction arithmetic and simplification
|
3,005 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
8
|
5
|
6
|
7
|
Probability calculation and expected value
|
4,782 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
50
|
75
|
60
|
125
|
Permutations and combinations
|
282 |
arithmetic
|
hard
|
Calculate (3^3 × 2) ÷ 8
|
6
|
6
|
1
|
9
|
14
|
Standard arithmetic calculation
|
3,921 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Q is true
|
Cannot determine
|
Q is false
|
P is false
|
Logical reasoning and boolean operations
|
3,569 |
number_theory
|
medium
|
How many factors does 24 have?
|
8
|
6
|
9
|
7
|
8
|
Number theory and modular arithmetic
|
4,831 |
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
|
762 |
algebra
|
hard
|
Solve: x² + -13x + 42 = 0
|
x = 7 or x = 6
|
x = 6 or x = 7
|
x = 7 or x = 6
|
x = -7 or x = -6
|
x = 8 or x = 5
|
Algebraic manipulation and solving
|
938 |
geometry
|
easy
|
What is the area of a rectangle with length 10 and width 7?
|
70
|
70
|
65
|
73
|
78
|
Geometric calculation and spatial reasoning
|
2,369 |
calculus
|
hard
|
Find the derivative of sin(x²)
|
2x cos(x²)
|
cos(2x)
|
cos(x²)
|
2x cos(x²)
|
2x sin(x²)
|
Calculus differentiation and integration
|
186 |
arithmetic
|
medium
|
What is 14²?
|
196
|
211
|
204
|
186
|
196
|
Standard arithmetic calculation
|
338 |
arithmetic
|
hard
|
Calculate (5^4 × 4) ÷ 6
|
416
|
416
|
424
|
419
|
411
|
Standard arithmetic calculation
|
467 |
algebra
|
easy
|
Solve for x: x + 5 = 16
|
11
|
12
|
11
|
9
|
14
|
Algebraic manipulation and solving
|
1,953 |
fractions
|
hard
|
Simplify (2/3 + 1/6) × 3/5
|
1/2
|
1/3
|
1/2
|
0/2
|
2/2
|
Fraction arithmetic and simplification
|
1,106 |
geometry
|
medium
|
Find the area of a circle with radius 6 (use π ≈ 3.14)
|
113.1
|
110.6
|
114.9
|
116.3
|
113.1
|
Geometric calculation and spatial reasoning
|
4,760 |
combinatorics
|
medium
|
How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
|
60
|
75
|
60
|
125
|
50
|
Permutations and combinations
|
1,300 |
statistics
|
easy
|
Find the median of 8 19 13 10
|
11.5
|
9.5
|
13.5
|
11.5
|
12.5
|
Statistical measure calculation
|
3,118 |
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
|
1,834 |
fractions
|
medium
|
Calculate 2/3 × 1/3
|
2/9
|
2/10
|
3/9
|
2/9
|
9/2
|
Fraction arithmetic and simplification
|
3,378 |
number_theory
|
easy
|
Is 17 a prime number?
|
Yes
|
Cannot determine
|
Only if x>0
|
Yes
|
No
|
Number theory and modular arithmetic
|
2,100 |
calculus
|
easy
|
Evaluate ∫x^4 dx
|
x^5/5 + C
|
x^4 + C
|
x^6/6 + C
|
x^5/5 + C
|
4x^3 + C
|
Calculus differentiation and integration
|
374 |
arithmetic
|
hard
|
Calculate (5^4 × 4) ÷ 9
|
277
|
272
|
285
|
280
|
277
|
Standard arithmetic calculation
|
4,160 |
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
|
4,721 |
combinatorics
|
easy
|
How many ways can 5 people stand in a line?
|
120
|
24
|
25
|
10
|
120
|
Permutations and combinations
|
2,904 |
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
|
3,812 |
logic
|
easy
|
True or False: 5 > 3 AND 2 < 4
|
True
|
Cannot determine
|
False
|
Depends on context
|
True
|
Logical reasoning and boolean operations
|
4,023 |
logic
|
medium
|
If P implies Q and P is true, what can we conclude about Q?
|
Q is true
|
Cannot determine
|
Q is true
|
P is false
|
Q is false
|
Logical reasoning and boolean operations
|
867 |
geometry
|
easy
|
What is the area of a rectangle with length 7 and width 4?
|
28
|
23
|
36
|
31
|
28
|
Geometric calculation and spatial reasoning
|
2,142 |
calculus
|
easy
|
Find d/dx(x^3)
|
3x^2
|
x^3
|
x^2
|
3x^3
|
3x^2
|
Calculus differentiation and integration
|
687 |
algebra
|
medium
|
Solve: 2x - 8 = 19
|
13
|
13
|
16
|
14
|
11
|
Algebraic manipulation and solving
|
4,337 |
linear_algebra
|
medium
|
What is the dot product of [3, 4] and [2, 1]?
|
10
|
8
|
11
|
10
|
9
|
Vector operations and matrix calculations
|
2,660 |
trigonometry
|
medium
|
Calculate sin²(x) + cos²(x)
|
1
|
1
|
2
|
0
|
sin(2x)
|
Trigonometric functions and identities
|
485 |
algebra
|
easy
|
What is 3x when x = 9?
|
27
|
27
|
32
|
24
|
29
|
Algebraic manipulation and solving
|
4,080 |
logic
|
hard
|
Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True
|
True
|
False
|
Cannot determine
|
True
|
Depends on other variables
|
Logical reasoning and boolean operations
|
2,963 |
probability
|
easy
|
How many outcomes when rolling a six-sided die?
|
6
|
5
|
8
|
6
|
7
|
Probability calculation and expected value
|
1,059 |
geometry
|
medium
|
What is the volume of a cube with side length 7?
|
343
|
358
|
323
|
343
|
378
|
Geometric calculation and spatial reasoning
|
1,495 |
statistics
|
medium
|
Calculate the range of 8 16 12 14 3 17 18
|
15
|
16
|
15
|
18
|
13
|
Statistical measure calculation
|
572 |
algebra
|
medium
|
Solve: 3x - 7 = 18
|
8
|
11
|
8
|
6
|
9
|
Algebraic manipulation and solving
|
4,248 |
linear_algebra
|
easy
|
Add vectors [2, 3] + [1, 4]
|
[3, 7]
|
[4, 7]
|
[2, 7]
|
[3, 7]
|
[3, 6]
|
Vector operations and matrix calculations
|
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