Three rods each of length $L$ and mass $M$ are placed along $X$,$Y$,and $Z$-axes such that one end of each rod is at the origin. The moment of inertia of this system about the $Z$-axis is:

$A$ conducting bar is pulled with a constant speed $v$ on a smooth conducting rail. The region has a steady magnetic field of induction $B$ as shown in the figure. If the speed of the bar is doubled then the rate of heat dissipation will

In the diagram,$I_1$ and $I_2$ are the strengths of the currents in the loop and the infinitely long straight conductor,respectively. Given $OA = AB = R$. The net magnetic field at the centre $O$ is zero. Then the ratio of the currents in the loop and the straight conductor $(I_1/I_2)$ is:

The equations of motion of a projectile are given by $x = 36 t$ metre and $2 y = 96 t - 9.8 t^2$ metre. The angle of projection is:

The major product of the following reaction is

$n$ moles of an ideal gas at temperature $T$ (in kelvin) occupy $V \ L$ of volume,exerting a pressure of $P$ atmospheres. What is the concentration (in $mol / L$)?