Which set has the same number of unpaired electrons in their ground state?

Identify which of the following sets of quantum numbers are not possible and explain why.
$(a) n = 0, l = 0, m_l = 0, m_s = +1/2$
$(b) n = 1, l = 0, m_l = 0, m_s = -1/2$
$(c) n = 1, l = 1, m_l = 0, m_s = +1/2$
$(d) n = 2, l = 1, m_l = 0, m_s = -1/2$
$(e) n = 3, l = 3, m_l = 3, m_s = +1/2$
$(f) n = 3, l = 1, m_l = 0, m_s = +1/2$

Nickel atom can lose two electrons to form $Ni^{2+}$ ion. The atomic number of nickel is $28$. From which orbital will nickel lose two electrons?

Which of the following sets of quantum numbers is correct for an electron in $4f$ orbital?

Which of the following orbitals has two angular nodes?

The electronic configuration $1s^2 2s^2 2p^6 3s^2 3p^6 3d^6$ corresponds to: