The number of rational terms in the expansion of $(3^{1/4} + 7^{1/6})^{144}$ is

$A$ coil of wire of radius $r$ has $600$ turns and a self-inductance of $108 \ mH$. The self-inductance of a coil with the same radius and $500$ turns is (in $mH$)

If $ad \neq 0$ and two of the lines represented by $ax^3+3bx^2y+3cxy^2+dy^3=0$ are perpendicular,then

Lichens indicate $SO_2$ pollution because they

$A$ parallel plate capacitor with a dielectric slab of dielectric constant $K$ between its plates has a capacitance $C$ and is charged to a potential $V$. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system is:

The average force applied on the walls of a closed container depends on $T^{x}$ where $T$ is the temperature of an ideal gas. The value of '$x$' is