$f(x) = e^x \sin x$, then $f^{(6)}(x)$ is equal to :

If the angles of a triangle are in the ratio $4:1:1$,then the ratio of the longest side to the perimeter is

The velocities of three particles of masses $20 \ g$,$30 \ g$ and $50 \ g$ are $10 \hat{i}$,$10 \hat{j}$ and $10 \hat{k}$,respectively. The velocity of the centre of mass of the three particles is

$A$ bullet of mass $10 ~g$ is fired horizontally with a velocity $1000 ~ms^{-1}$ from a rifle situated at a height $50 ~m$ above the ground. If the bullet reaches the ground with a velocity $500 ~ms^{-1}$,the work done against air resistance in the trajectory of the bullet is : $(g=10 ~ms^{-2})$ (in $~J$)

Sodium and copper have work functions of $2.3 \ eV$ and $4.5 \ eV$ respectively. The ratio of their threshold wavelengths is nearest to:

Which of the following reactions occurs at the cathode during the charging of a lead storage battery?