If $$R$$, $$X_L$$ and $$X_C$$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:

Resistance $$R$$, inductive reactance $$X_L$$, and capacitive reactance $$X_C$$ all have the same dimensions of electrical resistance (Ohm, $$\Omega$$).

For a quantity to be dimensionless, the dimensions in the numerator and denominator must cancel.

Checking option 2: $$\dfrac{R}{\sqrt{X_L X_C}}$$

Dimensions of numerator: $$[\Omega]$$

Dimensions of denominator: $$\sqrt{[\Omega][\Omega]} = [\Omega]$$

$$ \dfrac{R}{\sqrt{X_L X_C}} = \dfrac{[\Omega]}{[\Omega]} = \text{dimensionless} $$

This is the quality factor related quantity, and it is indeed dimensionless.