Pairs of elements with the same number of electrons in their...

The electronic configurations of the given elements are:

Eu (63): [Xe] $4f^7 6s^2$
Gd (64): [Xe] $4f^7 5d^1 6s^2$
Dy (66): [Xe] $4f^{10} 6s^2$
Ho (67): [Xe] $4f^{11} 6s^2$
Tm (69): [Xe] $4f^{13} 6s^2$
Yb (70): [Xe] $4f^{14} 6s^2$
Lu (71): [Xe] $4f^{14} 5d^1 6s^2$
Hf (72): [Xe] $4f^{14} 5d^2 6s^2$

From the above configurations:
Eu and Gd both have 7 electrons in their $4f$ orbitals.
Yb and Hf both have 14 electrons in their $4f$ orbitals.
Dy and Ho have 10 and 11 electrons respectively in their $4f$ orbitals.
Lu and Tm have 14 and 13 electrons respectively in their $4f$ orbitals.

Thus, pairs A (Eu and Gd) and C (Yb and Hf) have the same number of electrons in their respective $4f$ orbitals.

Answer: A and C Only