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arc length id fix

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lukew3
2020-10-26 13:17:47 -04:00
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@@ -31,111 +31,112 @@ problem, solution = mathgen.genById(0)
| Id | Skill | Example problem | Example Solution | Function Name |
|------|-----------------------------------|--------------------|-----------------------|--------------------------|
[//]: # list start
| 0 | Addition | 46+4= | 50 | addition |
| 1 | Subtraction | 63-13= | 50 | subtraction |
| 2 | Multiplication | 25*0= | 0 | multiplication |
| 3 | Division | 66/99= | 0.6666666666666666 | division |
| 4 | Binary Complement 1s | 011101111= | 100010000 | binary_complement_1s |
| 5 | Modulo Division | 50%72= | 50 | modulo_division |
| 6 | Square Root | sqrt(9)= | 3 | square_root |
| 7 | Power Rule Differentiation | 5x^8 + 8x^1 + 5x^2 + 7x^9 + 9x^6 | 40x^7 + 8x^0 + 10x^1 + 63x^8 + 54x^5 | power_rule_differentiation |
| 8 | Square | 12^2= | 144 | square |
| 9 | LCM (Least Common Multiple) | LCM of 14 and 12 = | 84 | lcm |
| 10 | GCD (Greatest Common Denominator) | GCD of 9 and 20 = | 1 | gcd |
| 11 | Basic Algebra | 9x + 7 = 10 | 1/3 | basic_algebra |
| 12 | Logarithm | log2(16) | 4 | log |
| 13 | Easy Division | 120/24 = | 5 | int_division |
| 14 | Decimal to Binary | Binary of 27= | 11011 | decimal_to_binary |
| 15 | Binary to Decimal | 1101100000 | 864 | binary_to_decimal |
| 16 | Fraction Division | (2/10)/(10/8) | 4/25 | divide_fractions |
| 17 | Integer Multiplication with 2x2 Matrix | 16 * [[1, 1], [5, 0]] = | [[16,16],[80,0]] | multiply_int_to_22_matrix |
| 18 | Area of Triangle | Area of triangle with side lengths: 18 11 18 = | 94.26525075551436 | area_of_triangle |
| 19 | Triangle exists check | Does triangle with sides 10, 26 and 25 exist? | Yes | valid_triangle |
| 20 | Midpoint of the two point | (9,-6),(-9,-18)= | (0.0,-12.0) | midpoint_of_two_points |
| 21 | Factoring Quadratic | x^2+3x+2 | (x+1)(x+2) | factoring |
| 22 | Third Angle of Triangle | Third angle of triangle with angles 18 and 24 = | 138 | third_angle_of_triangle |
| 23 | Solve a System of Equations in R^2 | -8x + 5y = 33, 7x - 3y = -33 | x = -6, y = -3 | system_of_equations |
| 24 | Distance between 2 points | Find the distance between (-3, -18) and (6, -17) | sqrt(82) | distance_two_points |
| 25 | Pythagorean Theorem | The hypotenuse of a right triangle given the other two lengths 19 and 3 = | 19.24 | pythagorean_theorem |
| 26 | Linear Equations | -6x + -19y = 42, -20x + -14y = 140 | x = -7, y = 0 | linear_equations |
| 27 | Prime Factorisation | Find prime factors of 193 | [193] | prime_factors |
| 28 | Fraction Multiplication | (5/4)*(7/10) | 7/8 | fraction_multiplication |
| 29 | Angle of a Regular Polygon | Find the angle of a regular polygon with 11 sides | 147.27 | angle_regular_polygon |
| 30 | Combinations of Objects | Number of combinations from 17 objects picked 3 at a time | 680 | combinations |
| 31 | Factorial | 2! = | 2 | factorial |
| 32 | Surface Area of Cube | Surface area of cube with side = 16m is | 1536 m^2 | surface_area_cube |
| 33 | Surface Area of Cuboid | Surface area of cuboid with sides = 1m, 2m, 7m is | 46 m^2 | surface_area_cuboid |
| 34 | Surface Area of Cylinder | Surface area of cylinder with height = 37m and radius = 11m is | 3317 m^2 | surface_area_cylinder |
| 35 | Volum of Cube | Volume of cube with side = 5m is | 125 m^3 | volume_cube |
| 36 | Volume of Cuboid | Volume of cuboid with sides = 2m, 20m, 8m is | 320 m^3 | volume_cuboid |
| 37 | Volume of cylinder | Volume of cylinder with height = 25m and radius = 5m is | 1963 m^3 | volume_cylinder |
| 38 | Surface Area of cone | Surface area of cone with height = 14m and radius = 4m is | 233 m^2 | surface_area_cone |
| 39 | Volume of cone | Volume of cone with height = 33m and radius = 17m is | 9987 m^3 | volume_cone |
| 40 | Common Factors | Common Factors of 29 and 41 = | [1] | common_factors |
| 41 | Intersection of Two Lines | Find the point of intersection of the two lines: y = -2/2x + 3 and y = -10/2x - 1 | (-1, 4) | intersection_of_two_lines |
| 42 | Permutations | Number of Permutations from 18 objects picked 9 at a time = | 17643225600 | permutation |
| 43 | Cross Product of 2 Vectors | [-3, 6, -11] X [15, -16, 15] = | [-86, -120, -42] | vector_cross |
| 44 | Compare Fractions | Which symbol represents the comparison between 4/8 and 9/7? | < | compare_fractions |
| 45 | Simple Interest | Simple interest for a principle amount of 9046 dollars, 1% rate of interest and for a time period of 9 years is = | 814.14 | simple_interest |
| 46 | Multiplication of two matrices | Multiply<table><tr><td>1</td><td>1</td><td>-1</td></tr><tr><td>-1</td><td>9</td><td>4</td></tr><tr><td>-10</td><td>3</td><td>-8</td></tr></table>and<table><tr><td>6</td><td>-4</td><td>6</td></tr><tr><td>0</td><td>7</td><td>5</td></tr><tr><td>2</td><td>7</td><td>-8</td></tr></table> | <table><tr><td>4</td><td>-4</td><td>19</td></tr><tr><td>2</td><td>95</td><td>7</td></tr><tr><td>-76</td><td>5</td><td>19</td></tr></table> | matrix_multiplication |
| 47 | Cube Root | cuberoot of 335 upto 2 decimal places is: | 6.95 | cube_root |
| 48 | Power Rule Integration | 1x^5 + 3x^1 | (1/5)x^6 + (3/1)x^2 + c | power_rule_integration |
| 49 | Fourth Angle of Quadrilateral | Fourth angle of quadrilateral with angles 64 , 57, 213 = | 26 | fourth_angle_of_quadrilateral |
| 50 | Quadratic Equation | Zeros of the Quadratic Equation 96x^2+191x+81=0 | [-0.61, -1.38] | quadratic_equation |
| 51 | HCF (Highest Common Factor) | HCF of 15 and 12 = | 3 | hcf |
| 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 2 = | 1/6 | dice_sum_probability |
| 53 | Exponentiation | 11^4 = | 14641 | exponentiation |
| 54 | Confidence interval For sample S | The confidence interval for sample [236, 288, 281, 252, 250, 254, 263, 228, 248, 245, 214, 221, 247, 235, 220, 286, 292, 242, 268, 215, 243, 283, 282, 212] with 99% confidence is | (263.2888975746178, 237.12776909204885) | confidence_interval |
| 55 | Comparing surds | Fill in the blanks 13^(1/4) _ 35^(1/1) | < | surds_comparison |
| 56 | Fibonacci Series | The Fibonacci Series of the first 5 numbers is ? | [0, 1, 1, 2, 3] | fibonacci_series |
| 57 | Trigonometric Values | What is cos(30)? | √3/2 | basic_trigonometry |
| 58 | Sum of Angles of Polygon | Sum of angles of polygon with 9 sides = | 1260 | sum_of_polygon_angles |
| 59 | Mean,Standard Deviation,Variance | Find the mean,standard deviation and variance for the data[45, 17, 14, 27, 12, 11, 13, 38, 14, 48, 38, 48, 30, 41, 36] | The Mean is 28.8 , Standard Deviation is 186.69333333333333, Variance is 13.663576886501328 | data_summary |
| 60 | Surface Area of Sphere | Surface area of Sphere with radius = 2m is | 50.26548245743669 m^2 | surface_area_sphere |
| 61 | Volume of Sphere | Volume of sphere with radius 95 m = | 3591364.0018287315 m^3 | volume_sphere |
| 62 | nth Fibonacci number | What is the 37th Fibonacci number? | 24157817 | nth_fibonacci_number |
| 63 | Profit or Loss Percent | Profit percent when CP = 169 and SP = 360 is: | 113.01775147928994 | profit_loss_percent |
| 64 | Binary to Hexidecimal | 100010 | 0x22 | binary_to_hex |
| 65 | Multiplication of 2 complex numbers | (12+17j) * (11-3j) = | (183+151j) | multiply_complex_numbers |
| 66 | Geometric Progression | For the given GP [10, 60, 360, 2160, 12960, 77760] ,Find the value of a,common ratio,11th term value, sum upto 7th term | The value of a is 10, common ratio is 6 , 11th term is 604661760 , sum upto 7th term is 559870.0 | geometric_progression |
| 67 | Geometric Mean of N Numbers | Geometric mean of 4 numbers 16 , 99 , 82 , 40 = | (16*99*82*40)^(1/4) = 47.742730688054316 | geometric_mean |
| 68 | Harmonic Mean of N Numbers | Harmonic mean of 4 numbers 64 , 21 , 60 , 61 = | 4/((1/64) + (1/21) + (1/60) + (1/61)) = 41.53507105403146 | harmonic_mean |
| 69 | Euclidian norm or L2 norm of a vector | Euclidian norm or L2 norm of the vector[508.56178681813515, 829.8393085389811, 141.9778436425696, 157.79854813315953, 936.4111703191011, 60.03432095552797, 309.1650693726604, 532.5680163890804, 249.7649337521495, 693.033334449361, 726.1934281438319, 824.6613026949497, 40.71867012843633] is: | 2000.941549572921 | euclidian_norm |
| 70 | Angle between 2 vectors | angle between the vectors [108.86, 442.35, 675.26, 315.79, 885.28, 45.3, 892.33, 447.4] and [987.81, 887.54, 199.52, 477.21, 587.71, 963.72, 615.65, 226.26] is: | 0.87 radians | angle_btw_vectors |
| 71 | Absolute difference between two numbers | Absolute difference between numbers -55 and 41 = | 96 | absolute_difference |
| 72 | Dot Product of 2 Vectors | [19, -17, -13] . [-16, 11, 5] = | -556 | vector_dot |
| 73 | Binary 2's Complement | 2's complement of 100 = | 100 | binary_2s_complement |
| 74 | Inverse of a Matrix | Inverse of Matrix Matrix([[65, 2, 89], [51, 73, 27], [48, 19, 39]]) is: | Matrix([[-778/25097, -1613/75291, 6443/75291], [231/25097, 579/25097, -928/25097], [845/25097, 1139/75291, -4643/75291]]) | invert_matrix |
| 75 | Area of a Sector | Given radius, 15 and angle, 33. Find the area of the sector. | Area of sector = 64.79535 | sector_area |
| 76 | Mean and Median | Given the series of numbers [68, 8, 77, 86, 93, 66, 6, 65, 41, 26]. find the arithmatic mean and mdian of the series | Arithmetic mean of the series is 53.6 and Arithmetic median of this series is 65.5 | mean_median |
| 77 | Determinant to 2x2 Matrix | Det([[32, 3], [36, 4]]) = | 20 | int_matrix_22_determinant |
| 78 | Compound Interest | Compound interest for a principle amount of 7744 dollars, 10% rate of interest and for a time period of 2 year is = | 9370.24 | compound_interest |
| 79 | Decimal to Hexadecimal | Binary of 803= | 0x323 | decimal_to_hexadeci |
| 80 | Percentage of a number | What is 24% of 7? | Required percentage = 1.68% | percentage |
| 81 | Celsius To Fahrenheit | Convert 50 degrees Celsius to degrees Fahrenheit = | 122.0 | celsius_to_fahrenheit |
| 82 | AP Term Calculation | Find the term number 38 of the AP series: 37, -6, -49 ... | -1554 | arithmetic_progression_term |
| 83 | AP Sum Calculation | Find the sum of first 50 terms of the AP series: -23, 65, 153 ... | 106650.0 | arithmetic_progression_sum |
| 84 | Converts decimal to octal | The decimal number 1900 in Octal is: | 0o3554 | decimal_to_octal |
| 85 | Converts decimal to Roman Numerals | The number 2656 in Roman Numerals is: | MMDCLVI | decimal_to_roman_numerals |
| 86 | Degrees to Radians | Angle 184 in radians is = | 3.21 | degree_to_rad |
| 87 | Radians to Degrees | Angle 0 in degrees is = | 0.0 | radian_to_deg |
| 88 | Differentiation | differentiate w.r.t x : d(tan(x)+9*x^4)/dx | 36*x^3 + tan(x)^2 + 1 | differentiation |
| 89 | Definite Integral of Quadratic Equation | The definite integral within limits 0 to 1 of the equation 93x^2 + 7x + 75 is = | 109.5 | definite_integral |
| 90 | isprime | 96 | False | is_prime |
| 91 | Binary Coded Decimal to Integer | Integer of Binary Coded Decimal 7 is = | 29973 | bcd_to_decimal |
| 92 | Complex To Polar Form | rexp(itheta) = | 15.65exp(i0.46) | complex_to_polar |
| 93 | Union,Intersection,Difference of Two Sets | Given the two sets a={8, 10, 3, 7} ,b={2, 4, 7, 9, 10}.Find the Union,intersection,a-b,b-a and symmetric difference | Union is {2, 3, 4, 7, 8, 9, 10},Intersection is {10, 7}, a-b is {8, 3},b-a is {9, 2, 4}, Symmetric difference is {2, 3, 4, 8, 9} | set_operation |
| 94 | Base Conversion | Convert 3540 from base 10 to base 14. | 140C | base_conversion |
| 95 | Curved surface area of a cylinder | What is the curved surface area of a cylinder of radius, 48 and height, 64? | CSA of cylinder = 19301.95 | curved_surface_area_cylinder |
| 96 | Perimeter of Polygons | The perimeter of a 3 sided polygon with lengths of [23, 3, 55]cm is: | 81 | perimeter_of_polygons |
| 97 | Power of Powers | The 9^5^2 = 9^(5*2) = 9^10 | 3486784401 | power_of_powers |
| 98 | Quotient of Powers with Same Base | The Quotient of 40^3 and 40^5 = 40^(3-5) = 40^-2 | 0.000625 | quotient_of_power_same_base |
| 99 | Quotient of Powers with Same Power | The Quotient of 49^1 and 19^1 = (49/19)^1 = 2.5789473684210527^1 | 2.5789473684210527 | quotient_of_power_same_power |
| 100 | complex Quadratic Equation | Find the roots of given Quadratic Equation 6x^2 + 8x + 1 = 0 | simplified solution : ((-0.14, -1.194)), generalized solution : ((-8 + sqrt(40))/2*6, (-8 - sqrt(40))/2*6) | complex_quadratic |
| 101 | Leap Year or Not | Year 2064 | is a leap year | is_leap_year |
| 102 | Minute to Hour conversion | Convert 442 minutes to Hours & Minutes | 7 hours and 22 minutes | minutes_to_hours |
| 103 | Decimal to Binary Coded Decimal | BCD of Decimal Number 5507 is = | 1583 | decimal_to_bcd |
| 104 | Circumference | Circumference of circle with radius 94 | 590.6194188748811 | circumference |
| 105 | Combine Like terms | 9x^4 + 3x^6 + 9x^1 + 2x^2 + 1x^5 + 2x^3 + 6x^3 + 4x^1 | 13x^1 + 2x^2 + 8x^3 + 9x^4 + 1x^5 + 3x^6 | combine_like_terms |
| 106 | signum function | signum of 697 is = | 1 | signum_function |
| 107 | Conditional Probability | Someone tested positive for a nasty disease which only 1.51% of population have. Test sensitivity (true positive) is equal to SN= 94.60% whereas test specificity (true negative) SP= 93.00%. What is the probability that this guy really has that disease? | 17.16% | conditional_probability |
| 0 | Addition | 14+24= | 38 | addition |
| 1 | Subtraction | 71-17= | 54 | subtraction |
| 2 | Multiplication | 71*1= | 71 | multiplication |
| 3 | Division | 98/53= | 1.849056603773585 | division |
| 4 | Binary Complement 1s | 000001000= | 111110111 | binary_complement_1s |
| 5 | Modulo Division | 19%62= | 19 | modulo_division |
| 6 | Square Root | sqrt(25)= | 5 | square_root |
| 7 | Power Rule Differentiation | 6x^9 + 5x^2 + 1x^7 + 5x^7 | 54x^8 + 10x^1 + 7x^6 + 35x^6 | power_rule_differentiation |
| 8 | Square | 10^2= | 100 | square |
| 9 | LCM (Least Common Multiple) | LCM of 2 and 12 = | 12 | lcm |
| 10 | GCD (Greatest Common Denominator) | GCD of 2 and 14 = | 2 | gcd |
| 11 | Basic Algebra | 2x + 9 = 9 | 0 | basic_algebra |
| 12 | Logarithm | log3(3) | 1 | log |
| 13 | Easy Division | 204/17 = | 12 | int_division |
| 14 | Decimal to Binary | Binary of 61= | 111101 | decimal_to_binary |
| 15 | Binary to Decimal | 10101 | 21 | binary_to_decimal |
| 16 | Fraction Division | (8/2)/(5/3) | 12/5 | divide_fractions |
| 17 | Integer Multiplication with 2x2 Matrix | 3 * [[10, 1], [1, 1]] = | [[30,3],[3,3]] | multiply_int_to_22_matrix |
| 18 | Area of Triangle | Area of triangle with side lengths: 4 10 16 = | (1.7587650643960612e-15+28.722813232690143j) | area_of_triangle |
| 19 | Triangle exists check | Does triangle with sides 8, 29 and 19 exist? | No | valid_triangle |
| 20 | Midpoint of the two point | (-16,7),(11,-1)= | (-2.5,3.0) | midpoint_of_two_points |
| 21 | Factoring Quadratic | x^2+18x+80 | (x+10)(x+8) | factoring |
| 22 | Third Angle of Triangle | Third angle of triangle with angles 75 and 36 = | 69 | third_angle_of_triangle |
| 23 | Solve a System of Equations in R^2 | 6x + y = 25, 6x - 7y = -31 | x = 3, y = 7 | system_of_equations |
| 24 | Distance between 2 points | Find the distance between (-18, 12) and (5, 9) | sqrt(538) | distance_two_points |
| 25 | Pythagorean Theorem | The hypotenuse of a right triangle given the other two lengths 9 and 15 = | 17.49 | pythagorean_theorem |
| 26 | Linear Equations | -8x + 2y = 12, 1x + 11y = -24 | x = -2, y = -2 | linear_equations |
| 27 | Prime Factorisation | Find prime factors of 103 | [103] | prime_factors |
| 28 | Fraction Multiplication | (5/9)*(3/5) | 1/3 | fraction_multiplication |
| 29 | Angle of a Regular Polygon | Find the angle of a regular polygon with 17 sides | 158.82 | angle_regular_polygon |
| 30 | Combinations of Objects | Number of combinations from 13 objects picked 7 at a time | 1716 | combinations |
| 31 | Factorial | 4! = | 24 | factorial |
| 32 | Surface Area of Cube | Surface area of cube with side = 9m is | 486 m^2 | surface_area_cube |
| 33 | Surface Area of Cuboid | Surface area of cuboid with sides = 2m, 16m, 11m is | 460 m^2 | surface_area_cuboid |
| 34 | Surface Area of Cylinder | Surface area of cylinder with height = 5m and radius = 14m is | 1671 m^2 | surface_area_cylinder |
| 35 | Volum of Cube | Volume of cube with side = 17m is | 4913 m^3 | volume_cube |
| 36 | Volume of Cuboid | Volume of cuboid with sides = 18m, 5m, 19m is | 1710 m^3 | volume_cuboid |
| 37 | Volume of cylinder | Volume of cylinder with height = 40m and radius = 4m is | 2010 m^3 | volume_cylinder |
| 38 | Surface Area of cone | Surface area of cone with height = 28m and radius = 17m is | 2657 m^2 | surface_area_cone |
| 39 | Volume of cone | Volume of cone with height = 45m and radius = 8m is | 3015 m^3 | volume_cone |
| 40 | Common Factors | Common Factors of 83 and 21 = | [1] | common_factors |
| 41 | Intersection of Two Lines | Find the point of intersection of the two lines: y = 0/5x + 1 and y = 5/5x - 5 | (6, 1) | intersection_of_two_lines |
| 42 | Permutations | Number of Permutations from 10 objects picked 8 at a time = | 1814400 | permutation |
| 43 | Cross Product of 2 Vectors | [-14, -20, 15] X [12, -11, 11] = | [-55, 334, 394] | vector_cross |
| 44 | Compare Fractions | Which symbol represents the comparison between 7/5 and 5/8? | > | compare_fractions |
| 45 | Simple Interest | Simple interest for a principle amount of 9940 dollars, 6% rate of interest and for a time period of 5 years is = | 2982.0 | simple_interest |
| 46 | Multiplication of two matrices | Multiply<table><tr><td>10</td><td>2</td></tr><tr><td>-8</td><td>0</td></tr></table>and<table><tr><td>3</td><td>-4</td><td>1</td><td>5</td></tr><tr><td>-1</td><td>1</td><td>-10</td><td>-1</td></tr></table> | <table><tr><td>28</td><td>-38</td><td>-10</td><td>48</td></tr><tr><td>-24</td><td>32</td><td>-8</td><td>-40</td></tr></table> | matrix_multiplication |
| 47 | Cube Root | cuberoot of 25 upto 2 decimal places is: | 2.92 | cube_root |
| 48 | Power Rule Integration | 2x^4 + 9x^10 + 7x^1 + 5x^10 + 3x^7 | (2/4)x^5 + (9/10)x^11 + (7/1)x^2 + (5/10)x^11 + (3/7)x^8 + c | power_rule_integration |
| 49 | Fourth Angle of Quadrilateral | Fourth angle of quadrilateral with angles 61 , 128, 38 = | 133 | fourth_angle_of_quadrilateral |
| 50 | Quadratic Equation | Zeros of the Quadratic Equation 22x^2+199x+24=0 | [-0.12, -8.92] | quadratic_equation |
| 51 | HCF (Highest Common Factor) | HCF of 1 and 1 = | 1 | hcf |
| 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 6 = | 1/6 | dice_sum_probability |
| 53 | Exponentiation | 2^10 = | 1024 | exponentiation |
| 54 | Confidence interval For sample S | The confidence interval for sample [200, 254, 212, 257, 239, 235, 250, 203, 227, 281, 275, 291, 224, 216, 249, 293, 266, 264, 278, 265] with 80% confidence is | (256.9254800588742, 240.97451994112578) | confidence_interval |
| 55 | Comparing surds | Fill in the blanks 59^(1/6) _ 50^(1/8) | > | surds_comparison |
| 56 | Fibonacci Series | The Fibonacci Series of the first 3 numbers is ? | [0, 1, 1] | fibonacci_series |
| 57 | Trigonometric Values | What is tan(45)? | 1 | basic_trigonometry |
| 58 | Sum of Angles of Polygon | Sum of angles of polygon with 12 sides = | 1800 | sum_of_polygon_angles |
| 59 | Mean,Standard Deviation,Variance | Find the mean,standard deviation and variance for the data[28, 23, 25, 46, 36, 42, 48, 40, 23, 21, 32, 25, 41, 43, 35] | The Mean is 33.86666666666667 , Standard Deviation is 79.18222222222222, Variance is 8.898439313847245 | data_summary |
| 60 | Surface Area of Sphere | Surface area of Sphere with radius = 19m is | 4536.459791783661 m^2 | surface_area_sphere |
| 61 | Volume of Sphere | Volume of sphere with radius 51 m = | 555647.2094551196 m^3 | volume_sphere |
| 62 | nth Fibonacci number | What is the 55th Fibonacci number? | 139583862445 | nth_fibonacci_number |
| 63 | Profit or Loss Percent | Profit percent when CP = 777 and SP = 861 is: | 10.81081081081081 | profit_loss_percent |
| 64 | Binary to Hexidecimal | 001 | 0x1 | binary_to_hex |
| 65 | Multiplication of 2 complex numbers | (16-6j) * (2+2j) = | (44+20j) | multiply_complex_numbers |
| 66 | Geometric Progression | For the given GP [4, 32, 256, 2048, 16384, 131072] ,Find the value of a,common ratio,6th term value, sum upto 7th term | The value of a is 4, common ratio is 8 , 6th term is 131072 , sum upto 7th term is 1198372.0 | geometric_progression |
| 67 | Geometric Mean of N Numbers | Geometric mean of 4 numbers 45 , 3 , 1 , 97 = | (45*3*1*97)^(1/4) = 10.69735419328368 | geometric_mean |
| 68 | Harmonic Mean of N Numbers | Harmonic mean of 4 numbers 45 , 38 , 75 , 60 = | 4/((1/45) + (1/38) + (1/75) + (1/60)) = 50.9307520476545 | harmonic_mean |
| 69 | Euclidian norm or L2 norm of a vector | Euclidian norm or L2 norm of the vector[591.4087216014599, 881.9117537447569, 886.791583815644, 686.4762274423125, 908.6374557556007, 623.6706969012301, 457.24550363026395] is: | 1951.6255163618057 | euclidian_norm |
| 70 | Angle between 2 vectors | angle between the vectors [441.74, 751.22, 829.23] and [983.73, 131.61, 537.34] is: | 0.77 radians | angle_btw_vectors |
| 71 | Absolute difference between two numbers | Absolute difference between numbers -72 and 18 = | 90 | absolute_difference |
| 72 | Dot Product of 2 Vectors | [-19, 18, 12] . [18, -13, -17] = | -780 | vector_dot |
| 73 | Binary 2's Complement | 2's complement of 1001000001 = | 110111111 | binary_2s_complement |
| 74 | Inverse of a Matrix | Inverse of Matrix Matrix([[61, 3, 14], [4, 5, 7], [13, 8, 95]]) is: | Matrix([[419/24230, -173/24230, -49/24230], [-289/24230, 5613/24230, -371/24230], [-33/24230, -449/24230, 293/24230]]) | invert_matrix |
| 75 | Area of a Sector | Given radius, 39 and angle, 161. Find the area of the sector. | Area of sector = 2136.98986 | sector_area |
| 76 | Mean and Median | Given the series of numbers [52, 72, 62, 2, 15, 95, 33, 55, 66, 32]. find the arithmatic mean and mdian of the series | Arithmetic mean of the series is 48.4 and Arithmetic median of this series is 53.5 | mean_median |
| 77 | Determinant to 2x2 Matrix | Det([[16, 57], [90, 67]]) = | -4058 | int_matrix_22_determinant |
| 78 | Compound Interest | Compound interest for a principle amount of 3519 dollars, 2% rate of interest and for a time period of 4 year is = | 3809.08 | compound_interest |
| 79 | Decimal to Hexadecimal | Binary of 593= | 0x251 | decimal_to_hexadeci |
| 80 | Percentage of a number | What is 11% of 83? | Required percentage = 9.13% | percentage |
| 81 | Celsius To Fahrenheit | Convert -3 degrees Celsius to degrees Fahrenheit = | 26.6 | celsius_to_fahrenheit |
| 82 | AP Term Calculation | Find the term number 87 of the AP series: -37, 4, 45 ... | 3489 | arithmetic_progression_term |
| 83 | AP Sum Calculation | Find the sum of first 91 terms of the AP series: 62, 29, -4 ... | -129493.0 | arithmetic_progression_sum |
| 84 | Converts decimal to octal | The decimal number 432 in Octal is: | 0o660 | decimal_to_octal |
| 85 | Converts decimal to Roman Numerals | The number 2876 in Roman Numerals is: | MMDCCCLXXVI | decimal_to_roman_numerals |
| 86 | Degrees to Radians | Angle 307 in radians is = | 5.36 | degree_to_rad |
| 87 | Radians to Degrees | Angle 2 in degrees is = | 114.59 | radian_to_deg |
| 88 | Differentiation | differentiate w.r.t x : d(sin(x)+2*x^(-4))/dx | cos(x) - 8/x^5 | differentiation |
| 89 | Definite Integral of Quadratic Equation | The definite integral within limits 0 to 1 of the equation 24x^2 + 30x + 41 is = | 64.0 | definite_integral |
| 90 | isprime | 10 | False | is_prime |
| 91 | Binary Coded Decimal to Integer | Integer of Binary Coded Decimal 1 is = | 4436 | bcd_to_decimal |
| 92 | Complex To Polar Form | rexp(itheta) = | 18.0exp(i1.57) | complex_to_polar |
| 93 | Union,Intersection,Difference of Two Sets | Given the two sets a={9, 2, 3} ,b={1, 2, 5, 7, 8, 9}.Find the Union,intersection,a-b,b-a and symmetric difference | Union is {1, 2, 3, 5, 7, 8, 9},Intersection is {9, 2}, a-b is {3},b-a is {8, 1, 5, 7}, Symmetric difference is {1, 3, 5, 7, 8} | set_operation |
| 94 | Base Conversion | Convert 23750 from base 10 to base 16. | 5CC6 | base_conversion |
| 95 | Curved surface area of a cylinder | What is the curved surface area of a cylinder of radius, 36 and height, 11? | CSA of cylinder = 2488.14 | curved_surface_area_cylinder |
| 96 | Perimeter of Polygons | The perimeter of a 12 sided polygon with lengths of [18, 104, 35, 2, 48, 4, 80, 48, 114, 28, 30, 18]cm is: | 529 | perimeter_of_polygons |
| 97 | Power of Powers | The 21^7^10 = 21^(7*10) = 21^70 | 359211830356099179055407266181227770855602632046883281967355597156308256906315688053426887401 | power_of_powers |
| 98 | Quotient of Powers with Same Base | The Quotient of 20^7 and 20^8 = 20^(7-8) = 20^-1 | 0.05 | quotient_of_power_same_base |
| 99 | Quotient of Powers with Same Power | The Quotient of 8^5 and 29^5 = (8/29)^5 = 0.27586206896551724^5 | 0.0015975701800030801 | quotient_of_power_same_power |
| 100 | complex Quadratic Equation | Find the roots of given Quadratic Equation x^2 + 7x + 9 = 0 | simplified solution : ((-1.697, -5.303)), generalized solution : ((-7 + sqrt(13))/2*1, (-7 - sqrt(13))/2*1) | complex_quadratic |
| 101 | Leap Year or Not | Year 1916 | is a leap year | is_leap_year |
| 102 | Minute to Hour conversion | Convert 913 minutes to Hours & Minutes | 15 hours and 13 minutes | minutes_to_hours |
| 103 | Decimal to Binary Coded Decimal | BCD of Decimal Number 3865 is = | 1519 | decimal_to_bcd |
| 104 | Circumference | Circumference of circle with radius 41 | 257.610597594363 | circumference |
| 105 | Combine Like terms | 5x^1 + 5x^1 | 10x^1 | combine_like_terms |
| 106 | signum function | signum of -580 is = | -1 | signum_function |
| 107 | Conditional Probability | Someone tested positive for a nasty disease which only 1.53% of population have. Test sensitivity (true positive) is equal to SN= 90.63% whereas test specificity (true negative) SP= 95.99%. What is the probability that this guy really has that disease? | 25.99% | conditional_probability |
| 108 | Arc length of Angle | Given radius, 4 and angle, 18. Find the arc length of the angle. | Arc length of the angle = 1.25664 | arc_length |