In an argon atom,how many electrons have $m_{\ell} = 1$?

"Pairing of electrons in the orbitals belonging to the same subshell does not occur unless each orbital belonging to that subshell has got one electron each." This statement is known as

$\Psi_{310}$ has

Explain,giving reasons,which of the following sets of quantum numbers are not possible.
$(a)$ $n=0, l=0, m_{l}=0, m_{s}=+\frac{1}{2}$
$(b)$ $n=1, l=0, m_{l}=0, m_{s}=-\frac{1}{2}$
$(c)$ $n=1, l=1, m_{l}=0, m_{s}=+\frac{1}{2}$
$(d)$ $n=2, l=1, m_{l}=0, m_{s}=-\frac{1}{2}$
$(e)$ $n=3, l=3, m_{l}=-3, m_{s}=+\frac{1}{2}$
$(f)$ $n=3, l=1, m_{l}=0, m_{s}=+\frac{1}{2}$

Which of the following are correct?
$(1)$ Electron density in $XY$ plane for $d_{x^2-y^2}$ orbital is zero.
$(2)$ The energy of $3p$-orbital is higher than the energy of $2p$-orbital.
$(3)$ $3p_z$-orbital has one angular node.
$(4)$ $4f$-orbital has no radial node.

Which one of the following is the correct set of four quantum numbers $(n, l, m, s)$?