What could be a correct expression for the speed of ocean waves in terms of its wavelength $\lambda$,the depth $h$ of the ocean,the density $\rho$ of sea water,and the acceleration of free fall $g$?

$A$ quantity $x$ is given by $(IF v^{2} / WL^{4})$ in terms of moment of inertia $I$,force $F$,velocity $v$,work $W$,and length $L$. The dimensional formula for $x$ is the same as that of:

Which of the following relations cannot be deduced using dimensional analysis? [the symbols have their usual meanings]

The volume of a liquid flowing out per second of a pipe of length $l$ and radius $r$ is written by a student as $V = \frac{\pi p r^4}{8 \eta l}$,where $p$ is the pressure difference between the two ends of the pipe and $\eta$ is the coefficient of viscosity of the liquid having the dimensional formula $[M^1 L^{-1} T^{-1}]$. Check whether the equation is dimensionally correct.

In terms of potential difference $V$,electric current $I$,permittivity $\varepsilon_0$,permeability $\mu_0$,and speed of light $c$,the dimensionally correct equation$(s)$ is(are):
$(A)$ $\mu_0 I^2 = \varepsilon_0 V^2$
$(B)$ $\varepsilon_0 I = \mu_0 V$
$(C)$ $I = \varepsilon_0 cV$
$(D)$ $\mu_0 cI = V$

The force $F$ is given in terms of time $t$ and displacement $x$ by the equation $F = A \cos(Bx) + C \sin(Dt)$. The dimensional formula of $\frac{AD}{B}$ is -