Question

If $x,y,z$ are integers in A.P lying between $1$ and $9$, and $x51,y41,$ and $z31$ are three digits numbers, then the value of $\left|\begin{array}{ccc}5& 4& 3\\ x51& y41& z31\\ x& y& z\end{array}\right|$

• A. $x+y+z$
• B. $x-y+z$
• C. $0$
• D. None of these

Answer 1

The correct option is C $0$

As $x,y,z$ are integer in A.P

$\therefore x=ay=a+dz=a+2d$

$\Rightarrow 2y=x+z$

$\left|\begin{array}{ccc}5& 4& 3\\ x51& y41& z31\\ x& y& z\end{array}\right|$

If $x=5y=4z=3$

determinant of given matrix becomes zero and option A and B don't satisfy