Explanation

(b)
$\because\$Point $P(a,b)$ lies on $3x + 2y = 13$
$\therefore 3a + 2b = 13$ ...(i)
and point $\mathcal{Q}(b,a)$ is lies on $4x - y = 5$
$\therefore 4b - a = 5$ …(ii)
On solving Eqs. (i) and (ii), we get $a = 3,\ b = 2$
Therefore, the coordinates of $P$ and $\mathcal{Q}$ are (3, 2) and (2, 3)
respectively.
Now, equation of $P\mathcal{Q}$ is
$y - 2 = \frac{3 - 2}{2 - 3}(x - 3)\ \Rightarrow \ x + y = 5$