Select the pair whose dimensions are the same.

Define dimensional formula and dimensional equation by using suitable examples.

In the equation $\frac{dy}{dt} = 2\omega \sin(\omega t + \theta_0)$,what are the dimensions of $(\omega t + \theta_0)$?

Dimensions of time in power are

Match List-$I$ with List-$II$:

List-$I$	List-$II$
$(a)$ $h$ (Planck's constant)	$(i)$ $[M L T^{-1}]$
$(b)$ $E$ (kinetic energy)	$(ii)$ $[M L^2 T^{-1}]$
$(c)$ $V$ (electric potential)	$(iii)$ $[M L^2 T^{-2}]$
$(d)$ $P$ (linear momentum)	$(iv)$ $[M L^2 I^{-1} T^{-3}]$

Choose the correct answer from the options given below:

Let $[\varepsilon_0]$ be the dimensional formula of the permittivity of free space. If $M = \text{mass}$,$L = \text{length}$,$T = \text{time}$,and $A = \text{electric current}$,then which of the following is correct?