What are $X$ and $Y$ in the following reactions?

If $x^y=y^x$, then $x(x-y \log x) \frac{d y}{d x}$ is equal to :

The major product in the following reaction is:

The electron affinity of sulfur is........

$A$ current $I$ flows in an infinitely long wire with a cross-section in the form of a semicircular ring of radius $R$. The magnitude of the magnetic induction along its axis is

Let $S$ be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces (numbered $1$ to $6$) and let $E_k = \{(a, b) \in S : ab = k\}$ for $k \geq 1$. If $p_k = P(E_k)$ for $k \geq 1$, then which of the following is correct?