Compare the structures of $(CH_3)_3N$ and $(SiH_3)_3N$

In trimethylamine, $(CH_3)_3N$, nitrogen has three $N-C$ sigma bonds and one lone pair. Normally, this gives a pyramidal geometry around nitrogen, like ammonia.

In trisilylamine, $(SiH_3)_3N$, an important additional effect operates: the lone pair on nitrogen can interact with vacant orbitals on silicon through $p\pi-d\pi$ / back-bonding-type delocalization (in JEE language often described as donation of nitrogen lone pair toward silicon), making the nitrogen approximately $sp^2$-hybridized and the molecule more nearly planar.

So, compared to $(CH_3)_3N$:

• $(CH_3)_3N$ is pyramidal
• $(SiH_3)_3N$ is planar

Compare basic strengths

Basicity depends on the availability of the lone pair on nitrogen for protonation.

• In $(CH_3)_3N$, the lone pair is localized on nitrogen and alkyl groups show a $+I$ effect, increasing electron density on nitrogen. Hence it is fairly basic.
• In $(SiH_3)_3N$, the lone pair is less available because it is involved in interaction with silicon atoms. Therefore, protonation becomes less favorable.

Hence,

Check each option

• A: planar and more basic than $(CH_3)_3N$ $\rightarrow$ planar is correct, more basic is wrong.
• B: pyramidal and more basic $\rightarrow$ both wrong.
• C: pyramidal and less basic $\rightarrow$ geometry wrong.
• D: planar and less basic $\rightarrow$ both correct.

Final answer

The correct statement is: