$5.6 \ L$ of helium gas at $STP$ is adiabatically compressed to $0.7 \ L$. Taking the initial temperature to be $T_1$,the work done in the process is

If $(1+2x+3x^2)^{10} = a_0+a_1x+a_2x^2+\ldots+a_{20}x^{20}$,then $\frac{a_2}{a_1}$ is equal to

$A$ mass $m$ moves with a velocity $v$ and collides inelastically with another identical mass initially at rest. After collision,the first mass moves with velocity $\frac{v}{\sqrt{3}}$ in a direction perpendicular to its initial direction of motion. The speed of the second mass after collision is:

In a compound microscope,the focal lengths of two lenses are $1.5 \, cm$ and $6.25 \, cm$. An object is placed at $2 \, cm$ from the objective lens and the final image is formed at $25 \, cm$ from the eye lens. The distance between the two lenses is.......$cm$.

Shown in the figure is a circular loop of radius $r$ and resistance $R$. $A$ variable magnetic field of induction $B = B_0e^{-t}$ is established inside the coil. If the key $(K)$ is closed,the electrical power developed right after closing the switch is equal to

Which of the following statements is not correct when a junction diode is in forward bias?