NDA Mathematics Question (2025) — Solution

Step-by-step solution

Given y = x! and z = (2x)!. We are given z y = 120. Substituting the values of y and z, we get: (2x)! x! = 120 Checking for small integer values of x: For x = 1, 2! 1! = 2 For x = 2, 4! 2! = 24 2 = 12 For x = 3, 6! 3! = 720 6 = 120 Thus, x = 3. We need to find the value of (3x)!. Substituting x = 3, we get (3 3)! = 9!. 9! = 9 8 7 6 5 4 3 2 1 = 362880. Answer: 362880