Question

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

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

Answer 1

Answer: (D)

$\left|\begin{array}{ccc}x+4& x+9& x+p\\ x+5& x+10& x+q\\ x+6& x+11& x+r\end{array}\right|$
$=\left|\begin{array}{ccc}0& 0& p-2q+r\\ x+5& x+10& x+q\\ x+6& x+11& x+r\end{array}\right|=0$
$[R_1\to R_1-2R_2+R_3]$
[since p + r = 2q, hence all entries in first row become 0.]