NIMCET 2015 Question Paper with solutions

We have, equation of line is $\mathit{x}+\mathit{y}=1$...(i)
A line perpendicular to the given line is $-\mathit{x}+\mathit{y}=\mathit{\lambda }$
This line is passing through (2, 4).
$\therefore -2+4=\mathit{\lambda }$
$\Rightarrow \mathit{\lambda }=2$
Hence, equation of line is $-\mathit{x}+\mathit{y}=2$...(ii)
Solving Eqs. (i) and (ii), we get
$\mathit{x}=\frac{-1}{3}$ and $\mathit{y}=\frac{3}{2}$
∴ foot of perpendicular is$\left(\frac{-1}{2},\frac{3}{2}\right)$