NDA Mathematics Question (2026) — Solution

Step-by-step solution

Since p, q, and r are in AP, let the common difference be d. Then q - p = d and r - q = d. It is given that (q - p), (r - q), and p are in GP. Substituting the values, we get d, d, and p are in GP. Therefore, d^2 = d p. Since p, q, and r are unequal, d 0. Thus, p = d. Now, q = p + d = 2d and r = p + 2d = 3d. We need to find the ratio (p+q) : (q+r) : (r+p). Substituting the values of p, q, and r in terms of d: p + q = d + 2d = 3d q + r = 2d + 3d = 5d r + p = 3d + d = 4d The required ratio is 3d : 5d : 4d = 3 : 5 : 4. Answer: 3:5:4