The resistance in the following circuit is increased at a particular instant. At this instant,the value of resistance is $10 \, \Omega$. The current in the circuit will be now:

Which process is used for the removal of hardness of water?

$\frac{(1+i)^{2011}}{(1-i)^{2009}}$ is equal to

$A$ body of mass $2 ~kg$ starts from rest and moves with uniform acceleration. It acquires a velocity $20 ~ms^{-1}$ in $4 ~s$. The power exerted on the body in $2 ~s$ in watts is

Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300\,K$. The piston of $A$ is free to move,while that of $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $30\,K$,then the rise in temperature of the gas in $B$ is .... $K$.

If $\frac{d^2y}{dx^2} + \sin x = 0$,then the solution of the differential equation is: