NDA Mathematics Question (2025) — Solution

Step-by-step solution

Given equation is [x \ 1 \ 1] pmatrix 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 pmatrix pmatrix 1 \\ 1 \\ x pmatrix = [45] Multiplying the first two matrices: [x(1) + 1(4) + 1(7) x(2) + 1(5) + 1(8) x(3) + 1(6) + 1(9)] pmatrix 1 \\ 1 \\ x pmatrix = [45] [x + 11 2x + 13 3x + 15] pmatrix 1 \\ 1 \\ x pmatrix = [45] Multiplying the resulting row matrix with the column matrix: (x + 11)(1) + (2x + 13)(1) + (3x + 15)(x) = 45 x + 11 + 2x + 13 + 3x^2 + 15x = 45 3x^2 + 18x + 24 = 45 3x^2 + 18x - 21 = 0 x^2 + 6x - 7 = 0 (x + 7)(x - 1) = 0 x = -7 or x = 1 From the given options, x = 1 is a valid value. Answer: 1