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 |
|---|---|---|---|---|---|---|---|---|---|
2,481 | calculus | hard | Find the derivative of sin(x²) | 2x cos(x²) | 2x cos(x²) | cos(2x) | cos(x²) | 2x sin(x²) | Calculus differentiation and integration |
2,394 | calculus | hard | Find the derivative of sin(x²) | 2x cos(x²) | cos(2x) | 2x sin(x²) | cos(x²) | 2x cos(x²) | Calculus differentiation and integration |
1,350 | statistics | easy | What is the mean of 18 13 3 17? | 12.8 | 12.8 | 14.8 | 13.8 | 10.8 | Statistical measure calculation |
1,002 | geometry | medium | Find the area of a circle with radius 8 (use π ≈ 3.14) | 201.06 | 202.86 | 201.06 | 198.56 | 204.26 | Geometric calculation and spatial reasoning |
4,823 | 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 |
4,113 | logic | hard | Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True | True | Cannot determine | False | True | Depends on other variables | Logical reasoning and boolean operations |
3,447 | number_theory | easy | What is the GCD of 15 and 25? | 5 | 3 | 5 | 6 | 4 | Number theory and modular arithmetic |
851 | geometry | easy | What is the area of a rectangle with length 12 and width 7? | 84 | 79 | 84 | 92 | 87 | Geometric calculation and spatial reasoning |
1,038 | geometry | medium | Find the area of a circle with radius 4 (use π ≈ 3.14) | 50.27 | 53.47 | 47.77 | 52.07 | 50.27 | Geometric calculation and spatial reasoning |
4,506 | linear_algebra | hard | Find the determinant of matrix [[2, 3], [1, 4]] | 5 | 6 | 3 | 5 | 4 | Vector operations and matrix calculations |
3,546 | number_theory | medium | Find LCM of 12 and 16 | 48 | 63 | 38 | 53 | 48 | Number theory and modular arithmetic |
3,435 | number_theory | easy | Is 17 a prime number? | Yes | Only if x>0 | No | Yes | Cannot determine | Number theory and modular arithmetic |
4,266 | linear_algebra | easy | Add vectors [2, 3] + [1, 4] | [3, 7] | [3, 6] | [4, 7] | [2, 7] | [3, 7] | Vector operations and matrix calculations |
2,831 | 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 |
4,900 | combinatorics | hard | In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? | 48 | 24 | 120 | 48 | 60 | Permutations and combinations |
3,988 | logic | medium | What is NOT(True AND False)? | True | Depends on values | False | True | Cannot determine | Logical reasoning and boolean operations |
2,787 | 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 |
2,130 | calculus | easy | Find ∫x dx | x²/2 + C | x³/3 + C | x + C | x² | x²/2 + C | Calculus differentiation and integration |
3,876 | logic | easy | If all cats are mammals and Fluffy is a cat, then Fluffy is a: | mammal | cat | mammal | pet | animal | Logical reasoning and boolean operations |
1,018 | geometry | medium | What is the volume of a cube with side length 8? | 512 | 492 | 527 | 547 | 512 | Geometric calculation and spatial reasoning |
799 | algebra | hard | Solve: x² + -11x + 24 = 0 | x = 8 or x = 3 | x = 7 or x = 4 | x = 8 or x = 3 | x = -8 or x = -3 | x = 9 or x = 2 | Algebraic manipulation and solving |
4,361 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 9 | 11 | 8 | 10 | Vector operations and matrix calculations |
1,021 | geometry | medium | Find the area of a circle with radius 7 (use π ≈ 3.14) | 153.94 | 153.94 | 151.44 | 155.74 | 157.14 | Geometric calculation and spatial reasoning |
733 | algebra | hard | Solve: x² + -15x + 56 = 0 | x = 8 or x = 7 | x = 7 or x = 8 | x = 8 or x = 7 | x = -8 or x = -7 | x = 9 or x = 6 | Algebraic manipulation and solving |
2,669 | trigonometry | medium | Calculate sin²(x) + cos²(x) | 1 | 1 | 2 | sin(2x) | 0 | Trigonometric functions and identities |
1,778 | fractions | easy | What is 1/4 + 1/3? | 7/12 | 7/12 | 8/12 | 6/12 | 7/13 | Fraction arithmetic and simplification |
1,932 | fractions | medium | Calculate 5/6 × 1/3 | 5/18 | 18/5 | 5/18 | 6/18 | 5/19 | Fraction arithmetic and simplification |
465 | algebra | easy | Solve for x: x + 6 = 18 | 12 | 15 | 10 | 12 | 13 | Algebraic manipulation and solving |
3,974 | logic | medium | What is NOT(True AND False)? | True | False | Depends on values | True | Cannot determine | Logical reasoning and boolean operations |
2,199 | calculus | easy | Evaluate ∫x^3 dx | x^4/4 + C | 3x^2 + C | x^4/4 + C | x^3 + C | x^5/5 + C | Calculus differentiation and integration |
2,773 | trigonometry | medium | What is tan(45°)? | 1 | 1 | 0 | √2 | √3 | Trigonometric functions and identities |
321 | arithmetic | hard | Calculate (3^3 × 3) ÷ 7 | 11 | 14 | 6 | 19 | 11 | Standard arithmetic calculation |
4,952 | combinatorics | hard | In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? | 48 | 120 | 24 | 60 | 48 | Permutations and combinations |
2,149 | calculus | easy | Evaluate ∫x^2 dx | x^3/3 + C | x^4/4 + C | x^3/3 + C | x^2 + C | 2x^1 + C | Calculus differentiation and integration |
4,005 | logic | medium | If P implies Q and P is true, what can we conclude about Q? | Q is true | P is false | Q is true | Cannot determine | Q is false | Logical reasoning and boolean operations |
3,452 | number_theory | easy | What is the GCD of 12 and 18? | 6 | 6 | 4 | 7 | 5 | Number theory and modular arithmetic |
2,125 | calculus | easy | Find d/dx(x^5) | 5x^4 | x^5 | x^4 | 5x^5 | 5x^4 | Calculus differentiation and integration |
4,142 | logic | hard | Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True | True | False | True | Depends on other variables | Cannot determine | Logical reasoning and boolean operations |
1,668 | 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 |
474 | algebra | easy | Solve for x: x + 13 = 22 | 9 | 12 | 7 | 9 | 10 | Algebraic manipulation and solving |
4,946 | combinatorics | hard | In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? | 48 | 120 | 48 | 24 | 60 | Permutations and combinations |
2,988 | probability | easy | How many outcomes when rolling a six-sided die? | 6 | 6 | 8 | 5 | 7 | Probability calculation and expected value |
4,300 | linear_algebra | easy | Calculate 3 × [2, 3] | [6, 9] | [7, 9] | [6, 9] | [5, 9] | [6, 8] | Vector operations and matrix calculations |
4,042 | logic | hard | Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True | True | Depends on other variables | True | Cannot determine | False | Logical reasoning and boolean operations |
4,098 | logic | hard | Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True | True | False | True | Depends on other variables | Cannot determine | Logical reasoning and boolean operations |
2,763 | trigonometry | medium | Calculate sin²(x) + cos²(x) | 1 | 1 | 2 | 0 | sin(2x) | Trigonometric functions and identities |
522 | algebra | easy | Solve for x: x + 11 = 18 | 7 | 5 | 10 | 7 | 8 | Algebraic manipulation and solving |
1,742 | fractions | easy | What is 1/4 + 1/4? | 1/2 | 1/2 | 1/3 | 2/2 | 0/2 | Fraction arithmetic and simplification |
1,980 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 0/2 | 2/2 | 1/3 | 1/2 | Fraction arithmetic and simplification |
3,206 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 3 | 3.5 | 4 | 4.5 | Probability calculation and expected value |
2,803 | 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 |
3,669 | number_theory | hard | What is 7³ mod 11? | 2 | 1 | 3 | 4 | 2 | Number theory and modular arithmetic |
4,175 | linear_algebra | easy | Calculate 4 × [2, 3] | [8, 12] | [8, 11] | [8, 12] | [7, 12] | [9, 12] | Vector operations and matrix calculations |
4,346 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 11 | 10 | 8 | 9 | Vector operations and matrix calculations |
3,299 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 3 | 4.5 | 4 | 3.5 | Probability calculation and expected value |
4,100 | logic | hard | Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True | True | Depends on other variables | False | Cannot determine | True | Logical reasoning and boolean operations |
2,703 | trigonometry | medium | What is tan(45°)? | 1 | √2 | √3 | 0 | 1 | Trigonometric functions and identities |
4,095 | 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 |
1,385 | statistics | easy | Find the median of 14 9 5 18 12 12 17 18 | 13 | 13 | 15 | 11 | 14 | Statistical measure calculation |
834 | algebra | hard | Solve: x² + -12x + 32 = 0 | x = 8 or x = 4 | x = 7 or x = 5 | x = 8 or x = 4 | x = -8 or x = -4 | x = 9 or x = 3 | Algebraic manipulation and solving |
1,680 | fractions | easy | What is 1/3 + 1/4? | 7/12 | 7/12 | 6/12 | 7/13 | 8/12 | Fraction arithmetic and simplification |
1,069 | geometry | medium | Find the area of a circle with radius 6 (use π ≈ 3.14) | 113.1 | 116.3 | 114.9 | 110.6 | 113.1 | Geometric calculation and spatial reasoning |
1,738 | fractions | easy | Simplify 12/9 | 4/3 | 6/4 | 13/10 | 11/8 | 4/3 | Fraction arithmetic and simplification |
3,726 | number_theory | hard | What is 7³ mod 11? | 2 | 4 | 1 | 3 | 2 | Number theory and modular arithmetic |
1,012 | geometry | medium | Find the area of a circle with radius 3 (use π ≈ 3.14) | 28.27 | 28.27 | 30.07 | 31.47 | 25.77 | Geometric calculation and spatial reasoning |
4,474 | linear_algebra | hard | Find the determinant of matrix [[2, 3], [1, 4]] | 5 | 3 | 4 | 5 | 6 | Vector operations and matrix calculations |
4,866 | combinatorics | hard | In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? | 48 | 24 | 120 | 48 | 60 | Permutations and combinations |
1,327 | statistics | easy | What is the mean of 16 9 19 12 17 16? | 14.8 | 12.8 | 16.8 | 15.8 | 14.8 | Statistical measure calculation |
67 | arithmetic | easy | Find 5 × 9 | 45 | 50 | 47 | 42 | 45 | Standard arithmetic calculation |
3,886 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | Cannot determine | Depends on context | False | True | Logical reasoning and boolean operations |
4,373 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 11 | 10 | 8 | 9 | Vector operations and matrix calculations |
3,504 | number_theory | medium | Find LCM of 9 and 15 | 45 | 50 | 45 | 60 | 35 | Number theory and modular arithmetic |
989 | geometry | medium | Find the area of a circle with radius 6 (use π ≈ 3.14) | 113.1 | 116.3 | 110.6 | 113.1 | 114.9 | Geometric calculation and spatial reasoning |
88 | arithmetic | easy | What is 28 + 53? | 81 | 82 | 84 | 81 | 79 | Standard arithmetic calculation |
1,400 | statistics | medium | What is the mode of 12 14 6 12 10 12 3? | 12 | 12 | 15 | 13 | 10 | Statistical measure calculation |
3,976 | logic | medium | What is NOT(True AND False)? | True | True | False | Cannot determine | Depends on values | Logical reasoning and boolean operations |
1,146 | geometry | hard | Find the hypotenuse of a right triangle with legs 5 and 12 | 13 | 12 | 13 | 14 | 11 | Geometric calculation and spatial reasoning |
3,891 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | Cannot determine | True | Depends on context | False | Logical reasoning and boolean operations |
3,854 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | False | Cannot determine | Depends on context | True | Logical reasoning and boolean operations |
3,741 | number_theory | hard | What is 7³ mod 11? | 2 | 1 | 3 | 2 | 4 | Number theory and modular arithmetic |
1,316 | statistics | easy | Find the median of 12 13 15 17 | 14 | 15 | 16 | 14 | 12 | Statistical measure calculation |
2,443 | 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 |
4,511 | linear_algebra | hard | Find the determinant of matrix [[2, 3], [1, 4]] | 5 | 5 | 6 | 4 | 3 | Vector operations and matrix calculations |
4,308 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 8 | 9 | 11 | 10 | Vector operations and matrix calculations |
2,445 | calculus | hard | Find the derivative of sin(x²) | 2x cos(x²) | cos(x²) | cos(2x) | 2x sin(x²) | 2x cos(x²) | Calculus differentiation and integration |
3,892 | logic | medium | If P implies Q and P is true, what can we conclude about Q? | Q is true | Q is false | Q is true | Cannot determine | P is false | Logical reasoning and boolean operations |
4,795 | 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 |
870 | geometry | easy | What is the area of a rectangle with length 12 and width 8? | 96 | 99 | 104 | 91 | 96 | Geometric calculation and spatial reasoning |
2,686 | trigonometry | medium | What is tan(45°)? | 1 | 1 | √3 | √2 | 0 | Trigonometric functions and identities |
3,252 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 3 | 3.5 | 4 | 4.5 | Probability calculation and expected value |
1,831 | fractions | medium | Calculate 3/5 × 1/2 | 3/10 | 3/11 | 10/3 | 3/10 | 4/10 | Fraction arithmetic and simplification |
1,619 | statistics | hard | Find the standard deviation of 2 4 6 8 (population) | 2.24 | 2.54 | 1.74 | 2.94 | 2.24 | Statistical measure calculation |
1,395 | statistics | medium | Calculate the range of 19 4 3 5 | 16 | 17 | 16 | 19 | 14 | Statistical measure calculation |
2,051 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 1/2 | 0/2 | 1/3 | 2/2 | Fraction arithmetic and simplification |
3,322 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 3.5 | 4.5 | 3 | 4 | Probability calculation and expected value |
3,555 | number_theory | medium | Find LCM of 9 and 15 | 45 | 35 | 50 | 60 | 45 | Number theory and modular arithmetic |
4,107 | 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 |
4,815 | 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 |
3,768 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | Cannot determine | True | Depends on context | False | Logical reasoning and boolean operations |
1,247 | geometry | hard | Find the hypotenuse of a right triangle with legs 7 and 24 | 25 | 23 | 24 | 25 | 26 | Geometric calculation and spatial reasoning |
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