Answer
a) $1$, $0$, $0$, $+\frac{1}{2}$, $-\frac{1}{2}$
b) $2$, $1$, $1$, $\frac{1}{2}$
c) Magnetic quantum number has to be either $-2$, $-1$, $0$, $1$ or $2$. It can not be equal to $3$.
d) $3$, $2$, $2$, $+\frac{1}{2}$
e) $2$, $1$, $-1$, $+\frac{1}{2}$ or $2$, $1$, $-1$, $-\frac{1}{2}$
f) $3$, $1$, $-1$, $-\frac{1}{2}$ or $3$, $2$, $-1$, $-\frac{1}{2}$
Work Step by Step
a) According to Pauli Exclusion Principle, there can not be 2 electrons in the same orbital and with the same spin quantum number. Therefore, one of the electrons has to have a spin quantum number equal to $-\frac{1}{2}$.
b) Since principal quantum number is equal to $2$, angular quantum number can be either $0$ or $1$. If $l=0$, then $m_{l}$ could be only $0$. Since $m_{l}=1$, angular quantum number has to be equal to $1$.
c) Magnetic quantum number can be either $-2$, $-1$, $0$, $1$ or $2$, since angular quantum number equals $2$. It can not be equal to $3$.
d) Since principal quantum number is equal to $3$ and magnetic is equal to $2$, angular quantum number can be only $2$.
e) Spin quantum number can not be equal to $0$. It has to be $+\frac{1}{2}$ or $-\frac{1}{2}$.
f) Since principal quantum number is equal to $3$ and magnetic is equal to $-1$, angular quantum number can be only $1$ or $2$.