Thank you for reporting, we will resolve it shortly
Q.
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.
Determinants
Solution:
$\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-2q-r\\ x+5&x+10&x+q\\ x+6&x+11&x+r\end{vmatrix} $
$\left[R_{1} \to R_{1} - 2R_{2} + R_{3}\right]$
= 0 [since p + r = 2q, hence all entries in first row become 0.]