Which of the following statements is incorrect?

Assertion $(A) :$ To check the dimensional correctness of an equation,we use the principle of homogeneity of dimensions.
Reason $(R) :$ If the dimensions of all terms in the equation are not the same,then the equation is wrong.

Due to an explosion underneath water,a bubble started oscillating. If this oscillation has a time period $T$,which is proportional to $p^\alpha S^\beta E^\gamma$,where $p$ is static pressure,$S$ is the density of water,and $E$ is the total energy of the explosion,determine $\alpha, \beta$,and $\gamma$.

If velocity $[V]$,time $[T]$,and force $[F]$ are chosen as the base quantities,the dimensions of mass will be:

Let force $F = A \sin(Ct) + B \cos(Dx)$,where $x$ and $t$ are displacement and time respectively. The dimensions of $\frac{C}{D}$ are the same as the dimensions of

The time dependence of a physical quantity $P$ is given by $P = P_0 \exp(-\alpha t^2)$,where $\alpha$ is a constant and $t$ is time. The constant $\alpha$: