Electronic configuration and general nature

The elements are:

• $\mathrm{Zn}: [Ar]3d^{10}4s^2$
• $\mathrm{Cd}: [Kr]4d^{10}5s^2$
• $\mathrm{Hg}: [Xe]4f^{14}5d^{10}6s^2$

Since the $d$-subshell is completely filled in their common states, these elements behave somewhat differently from typical transition metals.

Check statement A

A. They exhibit high enthalpy of atomization as the $d$-subshell is full.

This is incorrect. A completely filled $d^{10}$ configuration means weaker metallic bonding compared with many transition metals having partially filled $d$-orbitals. Hence $\mathrm{Zn}, \mathrm{Cd}, \mathrm{Hg}$ do not have high enthalpy of atomization for this reason.

So, A is false.

Check statement B

B. $\mathrm{Zn}$ and $\mathrm{Cd}$ do not show variable oxidation state while $\mathrm{Hg}$ shows $+\mathrm{I}$ and $+\mathrm{II}$.

This is correct:

• $\mathrm{Zn}$ commonly shows only $+2$
• $\mathrm{Cd}$ commonly shows only $+2$
• $\mathrm{Hg}$ shows both $+1$ and $+2$

Note: In the $+1$ state, mercury exists as the dimeric ion $\mathrm{Hg_2^{2+}}$.

So, B is true.

Check statement C

C. Compounds of $\mathrm{Zn}, \mathrm{Cd}$ and $\mathrm{Hg}$ are paramagnetic in nature.

This is incorrect. Their common ions are:

• $\mathrm{Zn^{2+}}: 3d^{10}$
• $\mathrm{Cd^{2+}}: 4d^{10}$
• $\mathrm{Hg^{2+}}: 5d^{10}$

All are completely filled $d^{10}$ systems, so they are generally diamagnetic, not paramagnetic.

So, C is false.

Check statement D

D. $\mathrm{Zn}, \mathrm{Cd}$ and $\mathrm{Hg}$ are called soft metals.

This is correct. These are relatively soft metals with low melting/boiling characteristics compared with many transition metals; mercury is liquid at room temperature.

So, D is true.

Final selection

Correct statements are: $B \text{ and } D$

Therefore, the correct option is: $\boxed{\text{D}}$