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## List of Generators
| Id | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
## algebra
| Id | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 11 | Basic Algebra | 8x + 7 = 7 | 0 | basic_algebra |
| 12 | Logarithm | log2(32) | 5 | log |
| 17 | Integer Multiplication with 2x2 Matrix | 10 * [[10, 4], [7, 0]] = | [[100,40],[70,0]] | multiply_int_to_22_matrix |
| 20 | Midpoint of the two point | (-11,1),(20,-20)= | (4.5,-9.5) | midpoint_of_two_points |
| 21 | Factoring Quadratic | x^2+14x+49 | (x+7)(x+7) | factoring |
| 23 | Solve a System of Equations in R^2 | 5x - y = 36, 8x + 7y = 135 | x = 9, y = 9 | system_of_equations |
| 24 | Distance between 2 points | Find the distance between (4, -7) and (-17, 21) | sqrt(1225) | distance_two_points |
| 26 | Linear Equations | -16x + 18y = -282, -4x + -14y = 22 | x = 12, y = -5 | linear_equations |
| 41 | Intersection of Two Lines | Find the point of intersection of the two lines: y = 1/3x - 10 and y = -10/4x - 2 | (48/17, -154/17) | intersection_of_two_lines |
| 43 | Cross Product of 2 Vectors | [14, 0, 10] X [18, -17, 17] = | [170, -58, -238] | vector_cross |
| 45 | Simple Interest | Simple interest for a principle amount of 5365 dollars, 4% rate of interest and for a time period of 1 years is = | 214.6 | simple_interest |
| 46 | Multiplication of two matrices | Multiply<table><tr><td>5</td><td>-9</td></tr><tr><td>0</td><td>-2</td></tr><tr><td>-7</td><td>8</td></tr></table>and<table><tr><td>9</td><td>9</td><td>-9</td><td>-3</td></tr><tr><td>6</td><td>-8</td><td>-9</td><td>8</td></tr></table> | <table><tr><td>-9</td><td>117</td><td>36</td><td>-87</td></tr><tr><td>-12</td><td>16</td><td>18</td><td>-16</td></tr><tr><td>-15</td><td>-127</td><td>-9</td><td>85</td></tr></table> | matrix_multiplication |
| 50 | Quadratic Equation | Zeros of the Quadratic Equation 1x^2+15x+17=0 | [-1.24, -13.76] | quadratic_equation |
| 65 | Multiplication of 2 complex numbers | (17+15j) * (-20-10j) = | (-190-470j) | multiply_complex_numbers |
| 72 | Dot Product of 2 Vectors | [3, -14, -17] . [6, 16, -11] = | -19 | vector_dot |
| 74 | Inverse of a Matrix | Inverse of Matrix Matrix([[38, 76, 13], [27, 97, 60], [32, 17, 71]]) is: | Matrix([[5867/188789, -5175/188789, 3299/188789], [3/188789, 2282/188789, -1929/188789], [-2645/188789, 1786/188789, 1634/188789]]) | invert_matrix |
| 77 | Determinant to 2x2 Matrix | Det([[49, 17], [48, 27]]) = | 507 | int_matrix_22_determinant |
| 78 | Compound Interest | Compound interest for a principle amount of 5556 dollars, 6% rate of interest and for a time period of 9 year is = | 9386.75 | compound_interest |
| 100 | complex Quadratic Equation | Find the roots of given Quadratic Equation x^2 + 8x + 9 = 0 | simplified solution : ((-1.354, -6.646)), generalized solution : ((-8 + sqrt(28))/2*1, (-8 - sqrt(28))/2*1) | complex_quadratic |
| 105 | Combine Like terms | 9x^8 + 10x^4 + 10x^6 + 10x^2 + 7x^2 + 6x^6 + 5x^5 + 8x^4 + 10x^8 + 7x^1 | 7x^1 + 17x^2 + 18x^4 + 5x^5 + 16x^6 + 19x^8 | combine_like_terms |
| 111 | Expanding Factored Binomial | (-3x-5)(+10x+6) | -30*x^2-68*x-30 | expanding |
| 11 | Basic Algebra | 3x + 9 = 9 | 0 | basic_algebra |
| 12 | Logarithm | log3(6561) | 8 | log |
| 17 | Integer Multiplication with 2x2 Matrix | 10 * [[8, 6], [7, 3]] = | [[80,60],[70,30]] | multiply_int_to_22_matrix |
| 20 | Midpoint of the two point | (3,-15),(-17,1)= | (-7.0,-7.0) | midpoint_of_two_points |
| 21 | Factoring Quadratic | x^2-8x+7 | (x-7)(x-1) | factoring |
| 23 | Solve a System of Equations in R^2 | 9x - 9y = -72, -10x - 5y = 20 | x = -4, y = 4 | system_of_equations |
| 24 | Distance between 2 points | Find the distance between (0, -14) and (-8, -6) | sqrt(128) | distance_two_points |
| 26 | Linear Equations | -12x + -11y = 138, -1x + -14y = 247 | x = 5, y = -18 | linear_equations |
| 41 | Intersection of Two Lines | Find the point of intersection of the two lines: y = -2/4x + 8 and y = 1x - 8 | (32/3, 8/3) | intersection_of_two_lines |
| 43 | Cross Product of 2 Vectors | [7, -3, 11] X [3, -12, -16] = | [180, 145, -75] | vector_cross |
| 45 | Simple Interest | Simple interest for a principle amount of 1601 dollars, 2% rate of interest and for a time period of 5 years is = | 160.1 | simple_interest |
| 46 | Multiplication of two matrices | Multiply<table><tr><td>10</td><td>-3</td><td>-1</td></tr><tr><td>-3</td><td>-1</td><td>-7</td></tr><tr><td>-3</td><td>-9</td><td>7</td></tr><tr><td>5</td><td>8</td><td>1</td></tr></table>and<table><tr><td>9</td><td>5</td><td>8</td><td>-5</td></tr><tr><td>-1</td><td>4</td><td>3</td><td>7</td></tr><tr><td>-8</td><td>5</td><td>8</td><td>-1</td></tr></table> | <table><tr><td>101</td><td>33</td><td>63</td><td>-70</td></tr><tr><td>30</td><td>-54</td><td>-83</td><td>15</td></tr><tr><td>-74</td><td>-16</td><td>5</td><td>-55</td></tr><tr><td>29</td><td>62</td><td>72</td><td>30</td></tr></table> | matrix_multiplication |
| 50 | Quadratic Equation | Zeros of the Quadratic Equation 96x^2+123x+24=0 | [-0.24, -1.04] | quadratic_equation |
| 65 | Multiplication of 2 complex numbers | (2-12j) * -10j = | (-120-20j) | multiply_complex_numbers |
| 72 | Dot Product of 2 Vectors | [-19, -4, 13] . [-11, -2, -9] = | 100 | vector_dot |
| 74 | Inverse of a Matrix | Inverse of Matrix Matrix([[59, 45, 48], [15, 9, 31], [29, 51, 17]]) is: | Matrix([[17/370, -561/10360, -321/10360], [-23/1110, 389/31080, 1109/31080], [-3/185, 71/1295, 6/1295]]) | invert_matrix |
| 77 | Determinant to 2x2 Matrix | Det([[55, 69], [58, 66]]) = | -372 | int_matrix_22_determinant |
| 78 | Compound Interest | Compound interest for a principle amount of 7423 dollars, 9% rate of interest and for a time period of 1 year is = | 8091.07 | compound_interest |
| 100 | complex Quadratic Equation | Find the roots of given Quadratic Equation x^2 + 9x + 7 = 0 | simplified solution : ((-0.86, -8.14)), generalized solution : ((-9 + sqrt(53))/2*1, (-9 - sqrt(53))/2*1) | complex_quadratic |
| 105 | Combine Like terms | 4x^1 + 6x^7 + 4x^9 + 3x^6 + 7x^4 + 6x^9 + 3x^7 + 8x^5 + 3x^2 + 1x^5 | 4x^1 + 3x^2 + 7x^4 + 9x^5 + 3x^6 + 9x^7 + 10x^9 | combine_like_terms |
| 111 | Expanding Factored Binomial | (-5x+10)(-6x-8) | 30*x^2-20*x-80 | expanding |
## basic_math
| Id | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 0 | Addition | 27+49= | 76 | addition |
| 1 | Subtraction | 32-6= | 26 | subtraction |
| 2 | Multiplication | 36*1= | 36 | multiplication |
| 3 | Division | 450/18= | 25 | division |
| 6 | Square Root | sqrt(1)= | 1 | square_root |
| 8 | Square | 6^2= | 36 | square |
| 13 | Complex Division | 30/91= | 0.33 | complex_division |
| 16 | Fraction Division | (6/8)/(7/2) | 3/14 | divide_fractions |
| 28 | Fraction Multiplication | (8/3)*(2/8) | 2/3 | fraction_multiplication |
| 31 | Factorial | 5! = | 120 | factorial |
| 44 | Compare Fractions | Which symbol represents the comparison between 1/7 and 1/8? | > | compare_fractions |
| 47 | Cube Root | cuberoot of 875 upto 2 decimal places is: | 9.56 | cube_root |
| 53 | Exponentiation | 14^1 = | 14 | exponentiation |
| 71 | Absolute difference between two numbers | Absolute difference between numbers -98 and -100 = | 2 | absolute_difference |
| 80 | Percentage of a number | What is 34% of 29? | Required percentage = 9.86% | percentage |
| 90 | isprime | 28 | False | is_prime |
| 97 | Power of Powers | The 6^3^1 = 6^(3*1) = 6^3 | 216 | power_of_powers |
| 0 | Addition | 49+24= | 73 | addition |
| 1 | Subtraction | 90-14= | 76 | subtraction |
| 2 | Multiplication | 65*0= | 0 | multiplication |
| 3 | Division | 153/9= | 17 | division |
| 6 | Square Root | sqrt(121)= | 11 | square_root |
| 8 | Square | 13^2= | 169 | square |
| 13 | Complex Division | 99/25= | 3.96 | complex_division |
| 16 | Fraction Division | (9/5)/(1/10) | 18 | divide_fractions |
| 28 | Fraction Multiplication | (6/1)*(4/9) | 8/3 | fraction_multiplication |
| 31 | Factorial | 4! = | 24 | factorial |
| 44 | Compare Fractions | Which symbol represents the comparison between 2/3 and 1/8? | > | compare_fractions |
| 47 | Cube Root | cuberoot of 431 upto 2 decimal places is: | 7.55 | cube_root |
| 53 | Exponentiation | 16^9 = | 68719476736 | exponentiation |
| 71 | Absolute difference between two numbers | Absolute difference between numbers -48 and -85 = | 37 | absolute_difference |
| 80 | Percentage of a number | What is 26% of 50? | Required percentage = 13.00% | percentage |
| 90 | isprime | 71 | True | is_prime |
| 97 | Power of Powers | The 44^5^2 = 44^(5*2) = 44^10 | 27197360938418176 | power_of_powers |
## calculus
| Id | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 7 | Power Rule Differentiation | 2x^2 + 5x^3 + 2x^3 + 3x^10 | 4x^1 + 15x^2 + 6x^2 + 30x^9 | power_rule_differentiation |
| 48 | Power Rule Integration | 5x^2 + 5x^1 | (5/2)x^3 + (5/1)x^2 + c | power_rule_integration |
| 88 | Differentiation | differentiate w.r.t x : d(exp(x)+7*x^4)/dx | 28*x^3 + exp(x) | differentiation |
| 89 | Definite Integral of Quadratic Equation | The definite integral within limits 0 to 1 of the equation 36x^2 + 57x + 67 is = | 107.5 | definite_integral |
| 110 | Stationary Points | f(x)=10*x^2 + 3*x + 10 | (-3/20,391/40) | stationary_points |
| 7 | Power Rule Differentiation | 6x^2 + 9x^2 + 2x^8 + 3x^1 | 12x^1 + 18x^1 + 16x^7 + 3x^0 | power_rule_differentiation |
| 48 | Power Rule Integration | 9x^4 + 7x^7 + 6x^6 + 6x^4 | (9/4)x^5 + (7/7)x^8 + (6/6)x^7 + (6/4)x^5 + c | power_rule_integration |
| 88 | Differentiation | differentiate w.r.t x : d(sec(x)+4*x^3)/dx | 12*x^2 + tan(x)*sec(x) | differentiation |
| 89 | Definite Integral of Quadratic Equation | The definite integral within limits 0 to 1 of the equation 62x^2 + 2x + 78 is = | 99.6667 | definite_integral |
| 110 | Stationary Points | f(x)=8*x^2 + 7*x + 1 | (-7/16,-17/32) | stationary_points |
## computer_science
| Id | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 4 | Binary Complement 1s | 01100= | 10011 | binary_complement_1s |
| 5 | Modulo Division | 27%45= | 27 | modulo_division |
| 14 | Decimal to Binary | Binary of 30= | 11110 | decimal_to_binary |
| 15 | Binary to Decimal | 0110 | 6 | binary_to_decimal |
| 56 | Fibonacci Series | The Fibonacci Series of the first 18 numbers is ? | [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597] | fibonacci_series |
| 62 | nth Fibonacci number | What is the 49th Fibonacci number? | 7778742049 | nth_fibonacci_number |
| 64 | Binary to Hexidecimal | 1010 | 0xa | binary_to_hex |
| 73 | Binary 2's Complement | 2's complement of 11 = | 1 | binary_2s_complement |
| 79 | Decimal to Hexadecimal | Binary of 541= | 0x21d | decimal_to_hexadeci |
| 84 | Converts decimal to octal | The decimal number 1868 in Octal is: | 0o3514 | decimal_to_octal |
| 91 | Binary Coded Decimal to Integer | Integer of Binary Coded Decimal 9 is = | 37220 | bcd_to_decimal |
| 103 | Decimal to Binary Coded Decimal | BCD of Decimal Number 9722 is = | 251510 | decimal_to_bcd |
| 4 | Binary Complement 1s | 10010001= | 01101110 | binary_complement_1s |
| 5 | Modulo Division | 85%29= | 27 | modulo_division |
| 14 | Decimal to Binary | Binary of 17= | 10001 | decimal_to_binary |
| 15 | Binary to Decimal | 0 | 0 | binary_to_decimal |
| 56 | Fibonacci Series | The Fibonacci Series of the first 20 numbers is ? | [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181] | fibonacci_series |
| 62 | nth Fibonacci number | What is the 48th Fibonacci number? | 4807526976 | nth_fibonacci_number |
| 64 | Binary to Hexidecimal | 00 | 0x0 | binary_to_hex |
| 73 | Binary 2's Complement | 2's complement of = | | binary_2s_complement |
| 79 | Decimal to Hexadecimal | Binary of 280= | 0x118 | decimal_to_hexadeci |
| 84 | Converts decimal to octal | The decimal number 1994 in Octal is: | 0o3712 | decimal_to_octal |
| 91 | Binary Coded Decimal to Integer | Integer of Binary Coded Decimal 7 is = | 29299 | bcd_to_decimal |
| 103 | Decimal to Binary Coded Decimal | BCD of Decimal Number 9775 is = | 26215 | decimal_to_bcd |
## geometry
| Id | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 18 | Area of Triangle | Area of triangle with side lengths: 19 3 15 = | (1.3716761698165164e-15+22.401171844347786j) | area_of_triangle |
| 19 | Triangle exists check | Does triangle with sides 13, 6 and 16 exist? | Yes | valid_triangle |
| 22 | Third Angle of Triangle | Third angle of triangle with angles 44 and 43 = | 93 | third_angle_of_triangle |
| 25 | Pythagorean Theorem | The hypotenuse of a right triangle given the other two lengths 3 and 18 = | 18.25 | pythagorean_theorem |
| 29 | Angle of a Regular Polygon | Find the angle of a regular polygon with 10 sides | 144.0 | angle_regular_polygon |
| 32 | Surface Area of Cube | Surface area of cube with side = 6m is | 216 m^2 | surface_area_cube |
| 33 | Surface Area of Cuboid | Surface area of cuboid with sides = 13m, 9m, 14m is | 850 m^2 | surface_area_cuboid |
| 34 | Surface Area of Cylinder | Surface area of cylinder with height = 6m and radius = 18m is | 2714 m^2 | surface_area_cylinder |
| 35 | Volum of Cube | Volume of cube with side = 6m is | 216 m^3 | volume_cube |
| 36 | Volume of Cuboid | Volume of cuboid with sides = 17m, 18m, 14m is | 4284 m^3 | volume_cuboid |
| 37 | Volume of cylinder | Volume of cylinder with height = 27m and radius = 12m is | 12214 m^3 | volume_cylinder |
| 38 | Surface Area of cone | Surface area of cone with height = 14m and radius = 3m is | 163 m^2 | surface_area_cone |
| 39 | Volume of cone | Volume of cone with height = 29m and radius = 14m is | 5952 m^3 | volume_cone |
| 49 | Fourth Angle of Quadrilateral | Fourth angle of quadrilateral with angles 46 , 142, 29 = | 143 | fourth_angle_of_quadrilateral |
| 57 | Trigonometric Values | What is cos(90)? | 0 | basic_trigonometry |
| 58 | Sum of Angles of Polygon | Sum of angles of polygon with 10 sides = | 1440 | sum_of_polygon_angles |
| 60 | Surface Area of Sphere | Surface area of Sphere with radius = 11m is | 1520.5308443374597 m^2 | surface_area_sphere |
| 61 | Volume of Sphere | Volume of sphere with radius 84 m = | 2482712.7095377133 m^3 | volume_sphere |
| 70 | Angle between 2 vectors | angle between the vectors [649.96, 568.55, 241.36, 319.37, 871.85, 576.19, 912.6, 366.59] and [173.42, 829.66, 374.84, 841.87, 307.24, 844.98, 754.21, 645.43] is: | 0.59 radians | angle_btw_vectors |
| 75 | Area of a Sector | Given radius, 40 and angle, 17. Find the area of the sector. | Area of sector = 237.36478 | sector_area |
| 86 | Degrees to Radians | Angle 253 in radians is = | 4.42 | degree_to_rad |
| 87 | Radians to Degrees | Angle 3 in degrees is = | 171.89 | radian_to_deg |
| 95 | Curved surface area of a cylinder | What is the curved surface area of a cylinder of radius, 14 and height, 33? | CSA of cylinder = 2902.83 | curved_surface_area_cylinder |
| 96 | Perimeter of Polygons | The perimeter of a 12 sided polygon with lengths of [37, 5, 34, 97, 120, 104, 97, 23, 22, 72, 66, 59]cm is: | 736 | perimeter_of_polygons |
| 104 | Circumference | Circumference of circle with radius 32 | 201.06192982974676 | circumference |
| 108 | Arc length of Angle | Given radius, 31 and angle, 148. Find the arc length of the angle. | Arc length of the angle = 80.07571 | arc_length |
| 112 | Area of Circle | Area of circle with radius 97 | 29571.142857142855 | area_of_circle |
| 18 | Area of Triangle | Area of triangle with side lengths: 18 18 16 = | 128.9961239727768 | area_of_triangle |
| 19 | Triangle exists check | Does triangle with sides 48, 40 and 48 exist? | Yes | valid_triangle |
| 22 | Third Angle of Triangle | Third angle of triangle with angles 31 and 7 = | 142 | third_angle_of_triangle |
| 25 | Pythagorean Theorem | The hypotenuse of a right triangle given the other two lengths 16 and 6 = | 17.09 | pythagorean_theorem |
| 29 | Angle of a Regular Polygon | Find the angle of a regular polygon with 12 sides | 150.0 | angle_regular_polygon |
| 32 | Surface Area of Cube | Surface area of cube with side = 1m is | 6 m^2 | surface_area_cube |
| 33 | Surface Area of Cuboid | Surface area of cuboid with sides = 9m, 7m, 6m is | 318 m^2 | surface_area_cuboid |
| 34 | Surface Area of Cylinder | Surface area of cylinder with height = 20m and radius = 19m is | 4655 m^2 | surface_area_cylinder |
| 35 | Volum of Cube | Volume of cube with side = 10m is | 1000 m^3 | volume_cube |
| 36 | Volume of Cuboid | Volume of cuboid with sides = 16m, 4m, 11m is | 704 m^3 | volume_cuboid |
| 37 | Volume of cylinder | Volume of cylinder with height = 18m and radius = 13m is | 9556 m^3 | volume_cylinder |
| 38 | Surface Area of cone | Surface area of cone with height = 45m and radius = 19m is | 4049 m^2 | surface_area_cone |
| 39 | Volume of cone | Volume of cone with height = 38m and radius = 12m is | 5730 m^3 | volume_cone |
| 49 | Fourth Angle of Quadrilateral | Fourth angle of quadrilateral with angles 90 , 59, 150 = | 61 | fourth_angle_of_quadrilateral |
| 57 | Trigonometric Values | What is sin(60)? | √3/2 | basic_trigonometry |
| 58 | Sum of Angles of Polygon | Sum of angles of polygon with 6 sides = | 720 | sum_of_polygon_angles |
| 60 | Surface Area of Sphere | Surface area of Sphere with radius = 15m is | 2827.4333882308138 m^2 | surface_area_sphere |
| 61 | Volume of Sphere | Volume of sphere with radius 96 m = | 3705973.4906218923 m^3 | volume_sphere |
| 70 | Angle between 2 vectors | angle between the vectors [848.07, 542.12, 669.74, 765.58, 540.05, 31.8, 476.27, 305.45, 148.71, 605.96, 538.21, 613.01, 342.15, 762.78, 849.08, 888.04, 229.57, 673.21, 522.35, 55.69] and [373.43, 892.36, 108.8, 171.3, 283.51, 791.0, 268.17, 870.8, 351.92, 923.46, 732.98, 290.93, 613.57, 487.0, 623.97, 840.61, 901.9, 176.05, 859.64, 227.87] is: | 0.7 radians | angle_btw_vectors |
| 75 | Area of a Sector | Given radius, 33 and angle, 218. Find the area of the sector. | Area of sector = 2071.72328 | sector_area |
| 86 | Degrees to Radians | Angle 237 in radians is = | 4.14 | degree_to_rad |
| 87 | Radians to Degrees | Angle 2 in degrees is = | 114.59 | radian_to_deg |
| 95 | Curved surface area of a cylinder | What is the curved surface area of a cylinder of radius, 5 and height, 31? | CSA of cylinder = 973.89 | curved_surface_area_cylinder |
| 96 | Perimeter of Polygons | The perimeter of a 7 sided polygon with lengths of [98, 54, 9, 78, 1, 106, 36]cm is: | 382 | perimeter_of_polygons |
| 104 | Circumference | Circumference of circle with radius 93 | 584.3362335677015 | circumference |
| 108 | Arc length of Angle | Given radius, 25 and angle, 190. Find the arc length of the angle. | Arc length of the angle = 82.90314 | arc_length |
| 112 | Area of Circle | Area of circle with radius 34 | 3633.1428571428573 | area_of_circle |
## misc
| Id | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 9 | LCM (Least Common Multiple) | LCM of 4 and 7 = | 28 | lcm |
| 10 | GCD (Greatest Common Denominator) | GCD of 15 and 3 = | 3 | gcd |
| 27 | Prime Factorisation | Find prime factors of 161 | [7, 23] | prime_factors |
| 40 | Common Factors | Common Factors of 33 and 28 = | [1] | common_factors |
| 51 | HCF (Highest Common Factor) | HCF of 3 and 14 = | 1 | hcf |
| 55 | Comparing surds | Fill in the blanks 43^(1/8) _ 97^(1/6) | < | surds_comparison |
| 63 | Profit or Loss Percent | Profit percent when CP = 303 and SP = 585 is: | 93.06930693069307 | profit_loss_percent |
| 66 | Geometric Progression | For the given GP [6, 48, 384, 3072, 24576, 196608] ,Find the value of a,common ratio,7th term value, sum upto 9th term | The value of a is 6, common ratio is 8 , 7th term is 1572864 , sum upto 9th term is 115043766.0 | geometric_progression |
| 67 | Geometric Mean of N Numbers | Geometric mean of 4 numbers 18 , 98 , 77 , 8 = | (18*98*77*8)^(1/4) = 32.28641488711981 | geometric_mean |
| 68 | Harmonic Mean of N Numbers | Harmonic mean of 4 numbers 8 , 70 , 24 , 85 = | 4/((1/8) + (1/70) + (1/24) + (1/85)) = 20.755813953488374 | harmonic_mean |
| 69 | Euclidian norm or L2 norm of a vector | Euclidian norm or L2 norm of the vector[288.6870061903637, 830.0059124436957, 80.85289556157238, 32.95804703487859, 290.00911298156007, 267.3996092514439, 723.9393433047015, 973.3386599711184, 151.93863634100845, 18.71003497862489, 445.18946751284307, 678.1683029551084, 191.406649648846, 909.0851387496899, 599.3623170191328, 702.8900903174056, 568.8716699724164, 570.9365552731333] is: | 2335.475196652018 | euclidian_norm |
| 81 | Celsius To Fahrenheit | Convert 45 degrees Celsius to degrees Fahrenheit = | 113.0 | celsius_to_fahrenheit |
| 82 | AP Term Calculation | Find the term number 44 of the AP series: 15, -12, -39 ... | -1146 | arithmetic_progression_term |
| 83 | AP Sum Calculation | Find the sum of first 27 terms of the AP series: -100, -51, -2 ... | 14499.0 | arithmetic_progression_sum |
| 85 | Converts decimal to Roman Numerals | The number 2662 in Roman Numerals is: | MMDCLXII | decimal_to_roman_numerals |
| 92 | Complex To Polar Form | rexp(itheta) = | 6.0exp(i3.14) | complex_to_polar |
| 93 | Union,Intersection,Difference of Two Sets | Given the two sets a={1, 3, 5, 6, 8, 9} ,b={2, 4, 6}.Find the Union,intersection,a-b,b-a and symmetric difference | Union is {1, 2, 3, 4, 5, 6, 8, 9},Intersection is {6}, a-b is {1, 3, 5, 8, 9},b-a is {2, 4}, Symmetric difference is {1, 2, 3, 4, 5, 8, 9} | set_operation |
| 94 | Base Conversion | Convert CFBE from base 16 to base 6. | 1050114 | base_conversion |
| 98 | Quotient of Powers with Same Base | The Quotient of 2^2 and 2^2 = 2^(2-2) = 2^0 | 1 | quotient_of_power_same_base |
| 99 | Quotient of Powers with Same Power | The Quotient of 31^4 and 13^4 = (31/13)^4 = 2.3846153846153846^4 | 32.335037288610344 | quotient_of_power_same_power |
| 101 | Leap Year or Not | Year 2022 | is not a leap year | is_leap_year |
| 102 | Minute to Hour conversion | Convert 685 minutes to Hours & Minutes | 11 hours and 25 minutes | minutes_to_hours |
| 106 | signum function | signum of 879 is = | 1 | signum_function |
| 109 | Binomial distribution | A manufacturer of metal pistons finds that, on average, 40.94% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 17 pistons will contain no more than 3 rejected pistons? | 3.94 | binomial_distribution |
| 9 | LCM (Least Common Multiple) | LCM of 17 and 1 = | 17 | lcm |
| 10 | GCD (Greatest Common Denominator) | GCD of 16 and 9 = | 1 | gcd |
| 27 | Prime Factorisation | Find prime factors of 86 | [2, 43] | prime_factors |
| 40 | Common Factors | Common Factors of 38 and 100 = | [1, 2] | common_factors |
| 51 | HCF (Highest Common Factor) | HCF of 12 and 9 = | 3 | hcf |
| 55 | Comparing surds | Fill in the blanks 6^(1/4) _ 88^(1/1) | < | surds_comparison |
| 63 | Profit or Loss Percent | Profit percent when CP = 847 and SP = 880 is: | 3.896103896103896 | profit_loss_percent |
| 66 | Geometric Progression | For the given GP [12, 84, 588, 4116, 28812, 201684] ,Find the value of a,common ratio,7th term value, sum upto 6th term | The value of a is 12, common ratio is 7 , 7th term is 1411788 , sum upto 6th term is 235296.0 | geometric_progression |
| 67 | Geometric Mean of N Numbers | Geometric mean of 4 numbers 72 , 93 , 63 , 5 = | (72*93*63*5)^(1/4) = 38.10934633766355 | geometric_mean |
| 68 | Harmonic Mean of N Numbers | Harmonic mean of 3 numbers 68 , 62 and 32 = | 3/((1/68) + (1/62) + (1/32)) = 48.32091690544412 | harmonic_mean |
| 69 | Euclidian norm or L2 norm of a vector | Euclidian norm or L2 norm of the vector[696.4519852852237, 658.9333146828044, 483.3976903342588, 222.67348281350618] is: | 1096.5834614726732 | euclidian_norm |
| 81 | Celsius To Fahrenheit | Convert 73 degrees Celsius to degrees Fahrenheit = | 163.4 | celsius_to_fahrenheit |
| 82 | AP Term Calculation | Find the term number 21 of the AP series: -65, 14, 93 ... | 1515 | arithmetic_progression_term |
| 83 | AP Sum Calculation | Find the sum of first 49 terms of the AP series: -84, -125, -166 ... | -52332.0 | arithmetic_progression_sum |
| 85 | Converts decimal to Roman Numerals | The number 1119 in Roman Numerals is: | MCXIX | decimal_to_roman_numerals |
| 92 | Complex To Polar Form | rexp(itheta) = | 13.0exp(i-1.18) | complex_to_polar |
| 93 | Union,Intersection,Difference of Two Sets | Given the two sets a={1, 2, 4, 5, 6, 7, 8} ,b={1, 5, 6, 8, 9, 10}.Find the Union,intersection,a-b,b-a and symmetric difference | Union is {1, 2, 4, 5, 6, 7, 8, 9, 10},Intersection is {8, 1, 5, 6}, a-b is {2, 4, 7},b-a is {9, 10}, Symmetric difference is {2, 4, 7, 9, 10} | set_operation |
| 94 | Base Conversion | Convert 9E4F from base 16 to base 15. | C01C | base_conversion |
| 98 | Quotient of Powers with Same Base | The Quotient of 37^6 and 37^7 = 37^(6-7) = 37^-1 | 0.02702702702702703 | quotient_of_power_same_base |
| 99 | Quotient of Powers with Same Power | The Quotient of 50^2 and 11^2 = (50/11)^2 = 4.545454545454546^2 | 20.661157024793393 | quotient_of_power_same_power |
| 101 | Leap Year or Not | Year 1933 | is not a leap year | is_leap_year |
| 102 | Minute to Hour conversion | Convert 563 minutes to Hours & Minutes | 9 hours and 23 minutes | minutes_to_hours |
| 106 | signum function | signum of -584 is = | -1 | signum_function |
| 109 | Binomial distribution | A manufacturer of metal pistons finds that, on average, 32.97% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 12 pistons will contain no more than 9 rejected pistons? | 99.95 | binomial_distribution |
## statistics
| Id | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 30 | Combinations of Objects | Number of combinations from 12 objects picked 0 at a time | 1 | combinations |
| 42 | Permutations | Number of Permutations from 17 objects picked 6 at a time = | 8910720 | permutation |
| 52 | Probability of a certain sum appearing on faces of dice | If 3 dice are rolled at the same time, the probability of getting a sum of 18 = | 1/216 | dice_sum_probability |
| 54 | Confidence interval For sample S | The confidence interval for sample [218, 274, 289, 295, 251, 246, 267, 276, 282, 213, 275, 210, 291, 209, 230, 220, 227, 204, 221, 214, 292, 252, 273, 243, 200, 272, 283, 288, 297, 211, 299, 244, 270, 242, 264, 279, 256] with 90% confidence is | (261.7881003640357, 245.07676450082917) | confidence_interval |
| 59 | Mean,Standard Deviation,Variance | Find the mean,standard deviation and variance for the data[37, 32, 45, 26, 36, 28, 17, 36, 47, 36, 34, 49, 47, 31, 5] | The Mean is 33.733333333333334 , Standard Deviation is 129.79555555555555, Variance is 11.392785241351456 | data_summary |
| 76 | Mean and Median | Given the series of numbers [73, 80, 8, 39, 9, 85, 51, 54, 14, 57]. find the arithmatic mean and mdian of the series | Arithmetic mean of the series is 47.0 and Arithmetic median of this series is 52.5 | mean_median |
| 107 | Conditional Probability | Someone tested positive for a nasty disease which only 1.87% of population have. Test sensitivity (true positive) is equal to SN= 94.23% whereas test specificity (true negative) SP= 96.61%. What is the probability that this guy really has that disease? | 34.63% | conditional_probability |
| 30 | Combinations of Objects | Number of combinations from 15 objects picked 5 at a time | 3003 | combinations |
| 42 | Permutations | Number of Permutations from 14 objects picked 7 at a time = | 17297280 | permutation |
| 52 | Probability of a certain sum appearing on faces of dice | If 1 dice are rolled at the same time, the probability of getting a sum of 5 = | 1/6 | dice_sum_probability |
| 54 | Confidence interval For sample S | The confidence interval for sample [274, 205, 285, 208, 269, 231, 246, 238, 212, 278, 266, 270, 243, 297, 295, 283, 249, 296, 279, 294, 255, 277, 239, 245, 203, 288, 287, 253] with 80% confidence is | (266.4148171763757, 252.51375425219572) | confidence_interval |
| 59 | Mean,Standard Deviation,Variance | Find the mean,standard deviation and variance for the data[26, 34, 33, 32, 45, 26, 50, 42, 40, 15, 5, 48, 48, 11, 6] | The Mean is 30.733333333333334 , Standard Deviation is 223.79555555555558, Variance is 14.959797978433919 | data_summary |
| 76 | Mean and Median | Given the series of numbers [43, 48, 78, 71, 82, 32, 49, 26, 76, 3]. find the arithmatic mean and mdian of the series | Arithmetic mean of the series is 50.8 and Arithmetic median of this series is 48.5 | mean_median |
| 107 | Conditional Probability | Someone tested positive for a nasty disease which only 1.48% of population have. Test sensitivity (true positive) is equal to SN= 98.64% whereas test specificity (true negative) SP= 94.56%. What is the probability that this guy really has that disease? | 21.41% | conditional_probability |