In the equation $y = pq \tan(qt)$,$y$ represents position,$p$ and $q$ are unknown physical quantities,and $t$ is time. The dimensional formula of $p$ is

$A$ force $F$ is given by $F = at + bt^2$,where $t$ is time. What are the dimensions of $a$ and $b$?

Force $F$ is given by the equation $F = \frac{X}{\text{Linear density}}$. Then the dimensions of $X$ are:

The dimensions of Stefan-Boltzmann's constant $\sigma$ can be written in terms of Planck's constant $h$,Boltzmann's constant $k_B$ and the speed of light $c$ as $\sigma=h^\alpha k_B^\beta c^\gamma$. Here,

In the Van der Waals equation $\left[ P + \frac{a}{V^2} \right] [V - b] = RT$,where $P$ is pressure,$V$ is volume,$R$ is the universal gas constant,and $T$ is temperature,the ratio of constants $\frac{a}{b}$ is dimensionally equal to:

The speed of a wave produced in water is given by $v = \lambda^a g^b \rho^c$. Where $\lambda$,$g$,and $\rho$ are the wavelength of the wave,acceleration due to gravity,and density of water,respectively. The values of $a$,$b$,and $c$ are,respectively: