NDA Mathematics Question (2025) — Solution

Step-by-step solution

Given A^2 + B^2 + C^2 = 0. Since the square of any real number is non-negative, the sum of squares can be zero if and only if each number is zero. Thus, A = 0, B = 0, and C = 0. Substituting these values into the determinant, we get A = 0 = 1, B = 0 = 1, and C = 0 = 1. The given determinant becomes: vmatrix 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 vmatrix Since all rows are identical, the value of the determinant is 0. Answer: 0