NIMCET 2016 Question Paper with solutions

We have, ${\left[\mathit{A}\right]}_{\mathit{x}\times \mathit{x}+5}$
[where x = number at rows and $\mathit{x}+5$ = number of column]
and ${\left[\mathit{B}\right]}_{\mathit{y}\times \left(11-\mathit{y}\right)}$
where y = number of rows and $11-\mathit{y}$ = number of columns]
According to the matrix rule AB exist if
⇒Number of column of A = number of raw of B
$\Rightarrow \mathit{x}+5=\mathit{y}$...(i)
and BA exist if
⇒ Number of column of B = Number of raw of A
$\Rightarrow 11-\mathit{y}=\mathit{x}$...(ii)
By solving Eq. (i) and Eq. (ii), we get
$\mathit{x}=3$ and $\mathit{y}=8$