If the speed of light (c), Planck's constant (h), and gravitational constant (G) are chosen as fundamental units, then the dimension of time is:

The refractive index of a material is given by the equation $n = \frac{{A\; + B}}{{{\lambda ^2}}},$, where A and B are constant. The dimensional formula for B is

The equation $P = \frac{{mx}}{A}$ gives a relation between mass m, kept on a surface of area A and pressure P exerted on this area. The dimensions of x are

Which of the following is dimensionally correct

If the unit of force is 'N', the unit of acceleration is 'm/s$^2$', and the unit of time is 's', what is the unit of energy?

If the velocity of light c, gravitational constant G and Planck’s constant h are chosen as fundamental units, the dimensions of length L in the new system is

If $v = \frac{A}{t} + B{t^2} + C{t^3}$ , where $v$ is velocity, t is time and A,B and C are constants, then the dimensional formula of B is

Given the expression for the escape velocity $v_e = \sqrt{\frac{2GM}{R}}$, where $G$ is the gravitational constant, $M$ is mass, and $R$ is radius. If a new quantity $Y$ is defined as $Y = \frac{v_e^3}{\sqrt{GM}}$, what are the dimensions of $Y$?

The equation of a wave is given by $Y; = ;A\sin \omega \left( {\begin{array}{*{20}{c}}

{\frac{x}{\upsilon } - k}\

;

\end{array}} \right)$where$\omega $ is the angular velocity and υ is the linear velocity. The dimension of k is

The equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right) = \frac{{Rheta }}{V}$ . Where P is the pressure, V the volume, $heta$ the absolute temperature and a and b are constants. The dimensional formula of a is

A gas bubble from an explosion under water oscillates with a time period T, depends upon static pressure p, density of water $\rho$ and the total energy of explosion E. Find the expression for the time period T.(where, k is a dimensionless constant)