Which of the given dimensional formula represents heat capacity

Find the value of '$$n$$' in the given equation $$P=\rho^n v^2$$ where '$$P$$' is the pressure, '$$\rho$$' density and '$$v$$' velocity.

The time dependence of a physical quantity P is give by $$\mathrm{P=P}_0 \exp \left(-\alpha t^2\right)$$ where $$\alpha$$ is a constant and $$t$$ is time. The constant $$\alpha$$ will

A tentative explanation of observations without assuming that it is true is called