If the dimensional formula of $(\text{Energy} \times \text{speed})$ is $[M^{a} L^{b} T^{c}]$,then $a, b,$ and $c$ are:

The quantum Hall resistance $R_H$ is a fundamental constant with dimensions of resistance. If $h$ is Planck's constant and $e$ is the electron charge,then the dimension of $R_H$ is the same as

The equation of a stationary wave is $y = 2A \sin \left(\frac{2 \pi ct}{\lambda}\right) \cos \left(\frac{2 \pi x}{\lambda}\right)$. Which of the following statements is wrong?

If the formula is $X = 3 Y Z^{2}$,where $X$ and $Z$ have dimensions of capacitance and magnetic induction respectively,then the dimensions of $Y$ in the $MKSQ$ system are:

Planck's constant $h$,speed of light $c$,and gravitational constant $G$ are used to form a unit of length $L$ and a unit of mass $M$. Then the correct option$(s)$ is(are):
$(A)$ $M \propto \sqrt{c}$
$(B)$ $M \propto \sqrt{G}$
$(C)$ $L \propto \sqrt{h}$
$(D)$ $L \propto \sqrt{G}$

The refractive index of the medium is $\mu = A + \frac{B}{\lambda^{2}}$,where $A$ and $B$ are constants and $\lambda$ is the wavelength of light. The dimensions of $B$ are the same as that of