If force $F$ , velocity $V$ and time $T$ are taken as fundamental units then dimension of force in the pressure is
$3$
$5$
$6$
$1$
The dimension of $\frac{\mathrm{B}^{2}}{2 \mu_{0}}$, where $\mathrm{B}$ is magnetic field and $\mu_{0}$ is the magnetic permeability of vacuum, is
If time $(t)$, velocity $(u)$, and angular momentum $(I)$ are taken as the fundamental units. Then the dimension of mass $({m})$ in terms of ${t}, {u}$ and ${I}$ is
The speed of light $(c)$, gravitational constant $(G)$ and planck's constant $(h)$ are taken as fundamental units in a system. The dimensions of time in this new system should be
Force $F$ is given in terms of time $t$ and distance $x$ by $F = a\, sin\, ct + b\, cos\, dx$, then the dimension of $a/b$ is
Match List $I$ with List $II$ and select the correct answer using the codes given below the lists :
List $I$ | List $II$ |
$P.$ Boltzmann constant | $1.$ $\left[ ML ^2 T ^{-1}\right]$ |
$Q.$ Coefficient of viscosity | $2.$ $\left[ ML ^{-1} T ^{-1}\right]$ |
$R.$ Planck constant | $3.$ $\left[ MLT ^{-3} K ^{-1}\right]$ |
$S.$ Thermal conductivity | $4.$ $\left[ ML ^2 T ^{-2} K ^{-1}\right]$ |
Codes: $ \quad \quad P \quad Q \quad R \quad S $