One turn of insulated wire in the form of a planar square frame with side $l = 0.2\,m$ and resistance $R = 1\,\Omega$ is placed in a uniform magnetic field perpendicular to the plane of the frame. The current passing through the turn when the magnetic field starts to decrease at a constant rate of $0.1\,T/s$ is......$mA$.

An inductor $(L = 0.03 \ H)$ and a resistor $(R = 0.15 \ k\Omega)$ are connected in series to a battery of $15 \ V$ $EMF$ in a circuit as shown below. The key $K_1$ has been kept closed for a long time. Then at $t = 0$,$K_1$ is opened and key $K_2$ is closed simultaneously. At $t = 1 \ ms$,the current in the circuit will be ....... $mA$ $(e^5 \cong 150)$.

$A$ projectile is projected with speed $u$ at an angle of $60^o$ with the horizontal from the foot of an inclined plane. If the projectile hits the inclined plane horizontally,the range on the inclined plane will be :-

If $a \sin^2 \theta + b \cos^2 \theta = c$,then $\tan^2 \theta$ is equal to

$A$ gas at $27 ^oC$ has a volume $V$ and pressure $P$. On heating, its pressure is doubled and volume becomes three times. The resulting temperature of the gas will be ....... $^oC$.

A small block of mass $m$ slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration $a_{0}$. The angle between the inclined plane and ground is $ heta$ and its base length is $L$. Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane is . . . . . . . .