Applications of Dimensional Analysis question from JEE Main 2016 (10 Apr, Shift 1 (one Or More Correct))

Answer: (b)

1. $\ln(BD)$ needs $BD$ dimensionless, so $[B] = 1/[D]$; then $[AD] = [C]$.
2. (a) $[B^2C^2] = C^2/D^2 = [A^2]$: meaningful. (c) $[A/B] = [AD] = [C]$: meaningful.
3. (b) $A$ and $C$ differ by the factor $[D]$, so $A - C$ cannot be formed: not meaningful.
4. So the answer is (b).