NDA Mathematics Question (2026) — Solution

Step-by-step solution

Given the function f(x) as a determinant where only the first row contains the variable x: f(x)= vmatrix 3x^2 & x & - x \\ 6 & -1 & 0 \\ q & q^2 & q^3 vmatrix To differentiate the determinant with respect to x, we differentiate the elements of the first row while keeping the other rows unchanged. Differentiating once with respect to x: f'(x)= vmatrix 6x & - x & - x \\ 6 & -1 & 0 \\ q & q^2 & q^3 vmatrix Differentiating again with respect to x: f''(x)= vmatrix 6 & - x & x \\ 6 & -1 & 0 \\ q & q^2 & q^3 vmatrix Substituting x=0 into the second derivative: f''(0)= vmatrix 6 & -1 & 0 \\ 6 & -1 & 0 \\ q & q^2 & q^3 vmatrix Since the first and second rows of the determinant are identical, the value of the determinant is zero. f''(0) = 0 Answer: 0