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 |
|---|---|---|---|---|---|---|---|---|---|
4,120 | logic | hard | Evaluate: (A OR B) AND (NOT A OR C) when A=True, B=False, C=True | True | True | False | Depends on other variables | Cannot determine | Logical reasoning and boolean operations |
574 | algebra | medium | Solve: 5x - 8 = 24 | 6 | 9 | 6 | 7 | 4 | Algebraic manipulation and solving |
4,797 | 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 |
1,255 | statistics | easy | What is the mean of 7 10 14 18 17? | 13.2 | 11.2 | 14.2 | 13.2 | 15.2 | Statistical measure calculation |
4,659 | combinatorics | easy | How many ways to choose 2 items from 4 items? | 6 | 6 | 8 | 5 | 4 | Permutations and combinations |
2,252 | calculus | medium | What is d/dx(2x^2 - 5x + 1)? | 4x^1 - 5 | 4x^1 - 5 | 4x^1 - 1 | 4x^2 - 5 | 2x^1 - 5 | Calculus differentiation and integration |
1,163 | geometry | hard | Find the hypotenuse of a right triangle with legs 3 and 4 | 5 | 5 | 3 | 4 | 6 | Geometric calculation and spatial reasoning |
3,405 | number_theory | easy | What is the GCD of 12 and 18? | 6 | 7 | 4 | 5 | 6 | Number theory and modular arithmetic |
2,972 | probability | easy | How many outcomes when rolling a six-sided die? | 6 | 8 | 5 | 7 | 6 | Probability calculation and expected value |
3,664 | number_theory | hard | What is 7³ mod 11? | 2 | 3 | 4 | 1 | 2 | Number theory and modular arithmetic |
559 | algebra | medium | Find x: x² = 100 | 10 | 10 | 8 | 11 | 13 | Algebraic manipulation and solving |
3,865 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | True | Depends on context | Cannot determine | False | Logical reasoning and boolean operations |
3,171 | probability | medium | Probability of rolling two sixes with two dice | 1/36 | 1/30 | 1/32 | 1/35 | 1/36 | Probability calculation and expected value |
1,521 | statistics | medium | What is the mode of 13 2 2 13 13 19 5? | 13 | 13 | 11 | 14 | 16 | Statistical measure calculation |
4,405 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 9 | 8 | 10 | 11 | Vector operations and matrix calculations |
2,209 | calculus | easy | Find d/dx(x^5) | 5x^4 | x^4 | 5x^4 | x^5 | 5x^5 | Calculus differentiation and integration |
4,656 | combinatorics | easy | How many ways can 5 people stand in a line? | 120 | 24 | 25 | 120 | 10 | Permutations and combinations |
4,932 | 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 |
1,645 | statistics | hard | Find the standard deviation of 2 4 6 8 (population) | 2.24 | 2.24 | 2.94 | 2.54 | 1.74 | Statistical measure calculation |
1,205 | geometry | hard | Find the hypotenuse of a right triangle with legs 9 and 12 | 15 | 15 | 14 | 13 | 16 | Geometric calculation and spatial reasoning |
734 | algebra | hard | Solve: x² + -9x + 18 = 0 | x = 3 or x = 6 | x = 2 or x = 7 | x = 3 or x = 6 | x = -3 or x = -6 | x = 4 or x = 5 | Algebraic manipulation and solving |
4,284 | linear_algebra | easy | Calculate 4 × [2, 3] | [8, 12] | [7, 12] | [8, 12] | [9, 12] | [8, 11] | Vector operations and matrix calculations |
4,897 | 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 |
2,349 | calculus | medium | What is d/dx(3x^2 - 5x + 1)? | 6x^1 - 5 | 6x^2 - 5 | 6x^1 - 1 | 6x^1 - 5 | 3x^1 - 5 | Calculus differentiation and integration |
3,810 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | False | Cannot determine | Depends on context | True | Logical reasoning and boolean operations |
2,295 | calculus | medium | What is d/dx(4x^3 - 4x + 1)? | 12x^2 - 4 | 12x^2 - 1 | 12x^2 - 4 | 4x^2 - 4 | 12x^3 - 4 | Calculus differentiation and integration |
4,699 | combinatorics | easy | How many ways to choose 2 items from 4 items? | 6 | 4 | 8 | 5 | 6 | Permutations and combinations |
827 | algebra | hard | Solve: x² + -11x + 28 = 0 | x = 7 or x = 4 | x = 6 or x = 5 | x = 7 or x = 4 | x = -7 or x = -4 | x = 8 or x = 3 | Algebraic manipulation and solving |
588 | algebra | medium | Solve: 3x - 14 = 12 | 8 | 11 | 9 | 6 | 8 | Algebraic manipulation and solving |
3,131 | 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 |
1,758 | fractions | easy | What is 1/3 + 1/3? | 2/3 | 1/3 | 2/4 | 2/3 | 3/3 | Fraction arithmetic and simplification |
4,783 | combinatorics | medium | How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition? | 60 | 75 | 125 | 50 | 60 | Permutations and combinations |
3,486 | number_theory | medium | How many factors does 30 have? | 8 | 7 | 9 | 6 | 8 | Number theory and modular arithmetic |
455 | algebra | easy | Solve for x: x + 8 = 11 | 3 | 3 | 6 | 1 | 4 | Algebraic manipulation and solving |
4,106 | 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 |
1,898 | fractions | medium | Divide 2/7 ÷ 1/2 | 4/7 | 7/4 | 4/8 | 4/7 | 5/7 | Fraction arithmetic and simplification |
1,207 | geometry | hard | Find the hypotenuse of a right triangle with legs 3 and 4 | 5 | 6 | 3 | 4 | 5 | Geometric calculation and spatial reasoning |
1,184 | geometry | hard | Find the hypotenuse of a right triangle with legs 3 and 4 | 5 | 4 | 3 | 6 | 5 | Geometric calculation and spatial reasoning |
3,732 | number_theory | hard | What is 7³ mod 11? | 2 | 2 | 1 | 3 | 4 | Number theory and modular arithmetic |
2,418 | calculus | hard | Find the derivative of sin(x²) | 2x cos(x²) | 2x sin(x²) | 2x cos(x²) | cos(2x) | cos(x²) | Calculus differentiation and integration |
3,866 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | True | Depends on context | False | Cannot determine | Logical reasoning and boolean operations |
2,379 | calculus | hard | Find the derivative of sin(x²) | 2x cos(x²) | cos(x²) | 2x cos(x²) | cos(2x) | 2x sin(x²) | Calculus differentiation and integration |
1,679 | fractions | easy | Simplify 6/6 | 1/1 | 7/7 | 5/5 | 1/1 | 3/3 | Fraction arithmetic and simplification |
4,048 | 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 |
27 | arithmetic | easy | What is 60 + 48? | 108 | 108 | 106 | 111 | 109 | Standard arithmetic calculation |
417 | arithmetic | hard | Calculate (3^3 × 3) ÷ 5 | 16 | 11 | 24 | 16 | 19 | Standard arithmetic calculation |
3,241 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 3.5 | 3 | 4.5 | 4 | Probability calculation and expected value |
3,134 | probability | medium | Probability of rolling two sixes with two dice | 1/36 | 1/30 | 1/36 | 1/35 | 1/32 | Probability calculation and expected value |
212 | arithmetic | medium | What is 12²? | 144 | 144 | 159 | 152 | 134 | Standard arithmetic calculation |
4,480 | linear_algebra | hard | Find the determinant of matrix [[2, 3], [1, 4]] | 5 | 4 | 3 | 6 | 5 | Vector operations and matrix calculations |
2,150 | calculus | easy | Find d/dx(x^3) | 3x^2 | x^2 | 3x^3 | x^3 | 3x^2 | Calculus differentiation and integration |
3,500 | number_theory | medium | Find LCM of 12 and 16 | 48 | 48 | 53 | 63 | 38 | Number theory and modular arithmetic |
1,071 | geometry | medium | What is the volume of a cube with side length 7? | 343 | 343 | 378 | 358 | 323 | Geometric calculation and spatial reasoning |
3,145 | probability | medium | Probability of drawing an ace from a standard deck | 1/13 | 1/13 | 1/12 | 1/15 | 1/14 | Probability calculation and expected value |
3,157 | probability | medium | Probability of drawing an ace from a standard deck | 1/13 | 1/12 | 1/14 | 1/15 | 1/13 | Probability calculation and expected value |
1,856 | fractions | medium | Divide 5/7 ÷ 1/2 | 10/7 | 11/7 | 7/10 | 10/8 | 10/7 | Fraction arithmetic and simplification |
61 | arithmetic | easy | What is 54 + 77? | 131 | 134 | 132 | 129 | 131 | Standard arithmetic calculation |
1,396 | statistics | medium | Calculate the range of 16 13 18 7 9 3 10 20 | 17 | 18 | 17 | 20 | 15 | Statistical measure calculation |
3,483 | number_theory | medium | How many factors does 36 have? | 9 | 8 | 10 | 7 | 9 | Number theory and modular arithmetic |
3,217 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 4 | 4.5 | 3 | 3.5 | Probability calculation and expected value |
201 | arithmetic | medium | Calculate 204 ÷ 12 | 17 | 15 | 18 | 20 | 17 | Standard arithmetic calculation |
219 | arithmetic | medium | Calculate 234 ÷ 13 | 18 | 19 | 18 | 21 | 16 | Standard arithmetic calculation |
2,392 | 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 |
4,195 | linear_algebra | easy | Add vectors [2, 3] + [1, 4] | [3, 7] | [4, 7] | [3, 7] | [3, 6] | [2, 7] | Vector operations and matrix calculations |
2,128 | calculus | easy | Evaluate ∫x^3 dx | x^4/4 + C | 3x^2 + C | x^5/5 + C | x^4/4 + C | x^3 + C | Calculus differentiation and integration |
4,494 | linear_algebra | hard | Find the determinant of matrix [[2, 3], [1, 4]] | 5 | 6 | 3 | 4 | 5 | Vector operations and matrix calculations |
4,910 | combinatorics | hard | In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? | 48 | 120 | 60 | 48 | 24 | Permutations and combinations |
2,650 | trigonometry | medium | Calculate sin²(x) + cos²(x) | 1 | 1 | 2 | sin(2x) | 0 | Trigonometric functions and identities |
2,753 | trigonometry | medium | Calculate sin²(x) + cos²(x) | 1 | 2 | 0 | 1 | sin(2x) | Trigonometric functions and identities |
4,313 | linear_algebra | medium | What is the dot product of [3, 4] and [2, 1]? | 10 | 11 | 8 | 10 | 9 | Vector operations and matrix calculations |
1,607 | statistics | hard | Find the standard deviation of 2 4 6 8 (population) | 2.24 | 2.94 | 2.54 | 2.24 | 1.74 | Statistical measure calculation |
2,595 | trigonometry | easy | Calculate tan(0°) | 0 | 0 | -1 | undefined | 1 | Trigonometric functions and identities |
2,954 | probability | easy | What is the probability of getting heads on a fair coin flip? | 1/2 | 1/2 | 1/4 | 1/3 | 2/3 | Probability calculation and expected value |
3,351 | number_theory | easy | Is 23 a prime number? | Yes | Only if x>0 | No | Yes | Cannot determine | Number theory and modular arithmetic |
1,789 | fractions | easy | What is 1/2 + 1/3? | 5/6 | 5/7 | 4/6 | 5/6 | 6/6 | Fraction arithmetic and simplification |
585 | algebra | medium | Solve: 6x - 15 = 12 | 4 | 7 | 4 | 5 | 2 | Algebraic manipulation and solving |
3,031 | probability | easy | How many outcomes when rolling a six-sided die? | 6 | 7 | 8 | 6 | 5 | Probability calculation and expected value |
1,216 | geometry | hard | Find the hypotenuse of a right triangle with legs 3 and 4 | 5 | 6 | 4 | 3 | 5 | Geometric calculation and spatial reasoning |
1,869 | fractions | medium | Calculate 1/3 × 3/4 | 1/4 | 4/1 | 1/4 | 1/5 | 2/4 | Fraction arithmetic and simplification |
2,874 | 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 |
904 | geometry | easy | How many sides does a octagon have? | 8 | 10 | 7 | 8 | 9 | Geometric calculation and spatial reasoning |
2,081 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 2/2 | 0/2 | 1/3 | 1/2 | Fraction arithmetic and simplification |
2,778 | trigonometry | medium | What is tan(45°)? | 1 | √3 | √2 | 0 | 1 | Trigonometric functions and identities |
19 | arithmetic | easy | What is 34 + 24? | 58 | 56 | 59 | 61 | 58 | Standard arithmetic calculation |
838 | geometry | easy | How many sides does a pentagon have? | 5 | 4 | 5 | 6 | 7 | Geometric calculation and spatial reasoning |
15 | arithmetic | easy | Find 6 × 8 | 48 | 50 | 48 | 53 | 45 | Standard arithmetic calculation |
1,678 | fractions | easy | What is 1/4 + 1/3? | 7/12 | 6/12 | 7/13 | 7/12 | 8/12 | Fraction arithmetic and simplification |
1,973 | fractions | hard | Simplify (2/3 + 1/6) × 3/5 | 1/2 | 1/3 | 1/2 | 0/2 | 2/2 | Fraction arithmetic and simplification |
4,619 | combinatorics | easy | How many ways can 4 people stand in a line? | 24 | 6 | 16 | 24 | 8 | Permutations and combinations |
535 | algebra | easy | Solve for x: x + 10 = 16 | 6 | 9 | 6 | 7 | 4 | Algebraic manipulation and solving |
3,904 | logic | medium | What is NOT(True AND False)? | True | Depends on values | False | Cannot determine | True | Logical reasoning and boolean operations |
3,450 | number_theory | easy | Is 23 a prime number? | Yes | No | Cannot determine | Yes | Only if x>0 | Number theory and modular arithmetic |
2,284 | calculus | medium | What is d/dx(2x^4 - 8x + 1)? | 8x^3 - 8 | 8x^3 - 8 | 2x^3 - 8 | 8x^4 - 8 | 8x^3 - 1 | Calculus differentiation and integration |
2,693 | trigonometry | medium | Calculate sin²(x) + cos²(x) | 1 | 0 | sin(2x) | 1 | 2 | Trigonometric functions and identities |
3,413 | number_theory | easy | Is 31 a prime number? | Yes | Cannot determine | Yes | Only if x>0 | No | Number theory and modular arithmetic |
482 | algebra | easy | Solve for x: x + 7 = 15 | 8 | 9 | 8 | 11 | 6 | Algebraic manipulation and solving |
1,845 | fractions | medium | Divide 4/5 ÷ 1 | 4/5 | 5/4 | 4/6 | 4/5 | 5/5 | Fraction arithmetic and simplification |
3,846 | logic | easy | True or False: 5 > 3 AND 2 < 4 | True | False | Depends on context | True | Cannot determine | Logical reasoning and boolean operations |
3,308 | probability | hard | Expected value of rolling a fair six-sided die | 3.5 | 4.5 | 3 | 3.5 | 4 | Probability calculation and expected value |
1,249 | geometry | hard | Find the hypotenuse of a right triangle with legs 3 and 4 | 5 | 4 | 6 | 5 | 3 | Geometric calculation and spatial reasoning |
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