NDA Mathematics Question (2025) — Solution

Step-by-step solution

The given numbers are ^ 10 C_ 3 , ^ 10 C_ 4 , ^ 10 C_ 5 , ^ 10 C_ 6 , and ^ 10 C_ 7 . Calculating their values: ^ 10 C_ 3 = 10 9 8 3 2 1 = 120 ^ 10 C_ 4 = 10 9 8 7 4 3 2 1 = 210 ^ 10 C_ 5 = 10 9 8 7 6 5 4 3 2 1 = 252 ^ 10 C_ 6 = ^ 10 C_ 4 = 210 ^ 10 C_ 7 = ^ 10 C_ 3 = 120 The harmonic mean H of n numbers x_1, x_2, , x_n is given by: H = n 1 x_1 + 1 x_2 + + 1 x_n Here n = 5. The sum of the reciprocals is: S = 1 120 + 1 210 + 1 252 + 1 210 + 1 120 S = 2 120 + 2 210 + 1 252 S = 1 60 + 1 105 + 1 252 Taking the LCM of 60, 105, 252, which is 1260: S = 21 + 12 + 5 1260 = 38 1260 = 19 630 The harmonic mean is: H = 5 S = 5 19 630 = 3150 19 Answer: 3150/19