Let $x = \pi R \left( \frac{P^2 - Q^2}{2} \right)$,where $P, Q$ and $R$ are lengths. The physical quantity $x$ is

Given below are two statements :
Statement $(I)$ : Dimensions of specific heat are $\left[L^2 \,T^{-2} \,K^{-1}\right]$.
Statement $(II)$ : Dimensions of gas constant are $\left[ML^2 \,T^{-1} \,K^{-1}\right]$.

Is it possible for a physical quantity to have dimensions but no units?

What is the spring constant of a spring? Write its unit and dimensional formula.

Let $[{\varepsilon _0}]$ denote the dimensional formula of the permittivity of vacuum. If $M =$ mass,$L =$ length,$T =$ time and $A =$ electric current,then:

The dimensions of $(\mu_0 \varepsilon_0)^{-1/2}$ are