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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