Question

If $p , q , r$ are in A.P., then the value of $\begin{vmatrix}x+4 & x+9 & x+p \\ x+5 & x+10 & x+q \\ x+6 & x+11 & x+r\end{vmatrix}$ is

• A. x + 15
• B. x + 20
• C. x + p + q + r
• D. None of these

Answer 1

Answer: (D)

$\begin{vmatrix} x+4 & x+9 & x+p \\ x+5 & x+10 & x+q \\ x+6 & x+11 & x+r \end{vmatrix} $
$=\begin{vmatrix} 0 & 0 & p-2 q+r \\ x+5 & x+10 & x+q \\ x+6 & x+11 & x+r \end{vmatrix} =0$
$[R_{1} \to R_{1} -2R_{2}+R_{3}]$
[since p + r = 2q, hence all entries in first row become 0.]