NDA Mathematics Question (2026) — Solution

Step-by-step solution

Given inequality is ^ 15 C_ r+1 > 2 ^ 15 C_r Using the property ^ n C_ r+1 = n-r r+1 ^ n C_r, we get: 15-r r+1 ^ 15 C_r > 2 ^ 15 C_r Since ^ 15 C_r > 0, we can divide both sides by ^ 15 C_r: 15-r r+1 > 2 15 - r > 2(r + 1) 15 - r > 2r + 2 3r r r Since r must be an integer, the greatest possible value of r is 4. Answer: 4