The value of \(\begin{vmatrix}1&x&y\\1&x+y&y\\1&x&x+y\end{vmatrix}\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(xy\)
Applying the row operations \(R_2 \to R_2 - R_1\) and \(R_3 \to R_3 - R_1\) (which do not change the value):
\(\displaystyle \Delta = \begin{vmatrix}1&x&y\\0&y&0\\0&0&x\end{vmatrix}\)
Expanding along the first column:
\(\displaystyle \Delta = 1\begin{vmatrix}y&0\\0&x\end{vmatrix} = xy\)
NCERT (2026-27 edition):
Determinants
