NDA Mathematics Question (2026) — Solution

Step-by-step solution

Let = vmatrix a-b & p-q & x-y \\ b-c & q-r & y-z \\ c-a & r-p & z-x vmatrix Applying the row operation R_1 R_1 + R_2 + R_3, we get: = vmatrix (a-b)+(b-c)+(c-a) & (p-q)+(q-r)+(r-p) & (x-y)+(y-z)+(z-x) \\ b-c & q-r & y-z \\ c-a & r-p & z-x vmatrix = vmatrix 0 & 0 & 0 \\ b-c & q-r & y-z \\ c-a & r-p & z-x vmatrix Since all elements of the first row are zero, the value of the determinant is 0. Comparing this with k vmatrix a & b & c \\ p & q & r \\ x & y & z vmatrix , we get k = 0.