a) and b)
No of relations in both (a) and (b) = $\begin{align*} 2^{\left ( n^2 - 1 \right )} \end{align*}$
(c)
No of relations such that no pair in $R$ has $a$ as its first element = $\begin{align*} 2^{\left ( n^2 - n \right )} \end{align*}$
(d)
No of relations such that at least one ordered pair in $R$ has $a$ as its first element = $\begin{align*} 2^{\left ( n^2 \right )} - 2^{\left ( n^2 - n \right )} \end{align*}$
(e)
Here we are not allowing a as first element or b as second element of any pair ($x$,$y$) $\in$ $R$
No of such relation = $\begin{align*} 2^{n^2 - \left ( 2n-1 \right )} \end{align*}$
(f)
Here we must have atleast one pair ($x$,$y$) such that $a$ is the first element or $b$ is second element.
No of such relation = $\begin{align*} 2^{n^2} - 2^{n^2 - \left ( 2n-1 \right )} \end{align*}$