The density of a material in $SI$ units is $128 \ kg \ m^{-3}$. In a system of units where the unit of length is $25 \ cm$ and the unit of mass is $50 \ g$,the numerical value of the density of the material is:

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

In an experiment,four quantities $a, b, c$ and $d$ are measured with percentage errors of $1\%, 2\%, 3\%$ and $4\%$ respectively. Quantity $w$ is calculated as follows: $w = \frac{a^4 b^3}{c^2 \sqrt{d}}$. The percentage error in the measurement of $w$ is .......... $\%$.

If $C$ is the velocity of light,$h$ is Planck's constant,and $G$ is the gravitational constant,and these are taken as fundamental quantities,then the dimensional formula of mass is:

Which of the following equations is dimensionally incorrect?
Where $t=$ time,$h=$ height,$s=$ surface tension,$\theta=$ angle,$\rho=$ density,$a, r=$ radius,$g=$ acceleration due to gravity,$v=$ volume,$p=$ pressure,$W=$ work done,$\Gamma=$ torque,$\varepsilon=$ permittivity,$E=$ electric field,$J=$ current density,$L=$ length.

If energy $E = G^p h^q c^r$,where $G$ is the universal gravitational constant,$h$ is Planck's constant,and $c$ is the speed of light,find the values of $p, q$,and $r$ respectively.