$$L$$, $$C$$ and $$R$$ represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula $$M L^2 T^{-4} A^{-2}$$ corresponds to _______.

Dimension given

L → M L² T⁻² A⁻²
C → M⁻¹ L⁻² T⁴ A²
R → M L² T⁻³ A⁻²

now check option A:

$$R/\sqrt{\ LC}$$

first find $$\sqrt{\ LC}$$:

LC = (M L² T⁻² A⁻²)(M⁻¹ L⁻² T⁴ A²)
= T²

so:

$$\sqrt{\ LC}=T$$

now:

$$R/\sqrt{\ LC}=(ML^2T⁻^3A⁻^2)/T$$
= M L² T⁻⁴ A⁻²

this matches exactly

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