NDA Mathematics Question (2026) — Solution

Step-by-step solution

Given p, g_1, g_2, q are in GP. Let the common ratio of the GP be r. Then g_1 = pr, g_2 = pr^2, and q = pr^3. The arithmetic mean of p and q is m, so m = p + q 2 p + q = 2m. Consider the expression g_1^2 g_2 + g_2^2 g_1 . Substituting the values of g_1 and g_2: g_1^2 g_2 + g_2^2 g_1 = (pr)^2 pr^2 + (pr^2)^2 pr = p^2r^2 pr^2 + p^2r^4 pr = p + pr^3 Since q = pr^3, we get: = p + q Substituting p + q = 2m: g_1^2 g_2 + g_2^2 g_1 = 2m Answer: 2m