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)

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