What is the number of unpaired electrons present in $f$-orbital at $+3$ oxidation state of $Lu (Z=71)$?

Which one of the following statements concerning lanthanide elements is false?

Determine whether the following statements are True $(T)$ or False $(F)$:
$(a)$ Actinoid contraction increases from one element to the next.
$(b)$ Actinoid contraction decreases from one element to the next.
$(c)$ Lanthanoid contraction occurs,but actinoid contraction does not occur.

Assertion : Ionisation enthalpies of the early actinoids are lower than for early lanthanoids.
Reason : $5f$ electrons are more effectively shielded from nuclear charge than $4f$ electrons.

The ionic radius of $La^{3+}$ is $1.06 \ \mathop{A}\limits^o$. Which of the following is the closest value for the ionic radius of $Lu^{3+}$ in $\mathop{A}\limits^o$? $(Lu = 71, La = 57)$

Which of the following elements have half-filled $f$-orbitals in their ground state?
(Given: atomic number $Sm = 62$; $Eu = 63$; $Tb = 65$; $Gd = 64$; $Pm = 61$)
$A.$ $Sm$ $B.$ $Eu$ $C.$ $Tb$ $D.$ $Gd$ $E.$ $Pm$
Choose the correct answer from the options given below: