The circuit shown here has two batteries of \(8.0\,V\) and \(16.0\,V\) and three resistors \(3\,\Omega ,\,9\,\Omega \) and \(9\,\Omega \) and a capacitor of \(5.0\,\mu F.\) How much is the current \(I\) in the circuit in steady state? ................... \(A\)

Assume there are two identical simple pendulum Clocks\(-1\) is placed on the earth and Clock\(-2\) is placed on a space station located at a height \(h\) above the earth surface. Clock\(-1\) and Clock\(-2\) operate at time periods \(4\,s\) and \(6\,s\) respectively. Then the value of \(h\) is \(....km\) (consider radius of earth \(R _{ E }=6400\,km\) and \(g\) on earth \(10\,m / s ^{2}\) )

The frequency of a car horn encountered a change from \(400\, {Hz}\) to \(500\, {Hz}\), when the car approaches a vertical wall. If the speed of sound is \(330\, {m} / {s}\). Then the speed of car is \(.....\,{km} / {h} .\)

A bi-convex lens has radius of curvature of both the surfaces same as \(1 / 6 \mathrm{~cm}\). If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides \(\left(R_1 \neq R_2\right)\), without any change in lens power then possible combination of \(R_1\) and \(R_2\) is :

Two guns \(A\) and \(B\) can fire bullets at speed \(1\, km/s\) and \(2\, km/s\) respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is

Two planets, \(A\) and \(B\) are orbiting a common star in circular orbits of radius \(R_A\) and \(R_B\), respectively, with \(R_B=2 R_A\). The planet \(B\) is \(4 \sqrt{2}\) times more massive than planet \(A\). The ratio \(\left(\frac{L_B}{L_A}\right)\) of angular momentum \(\left(L_B\right)\) of planet \(B\) to that of planet \(A\left(L_A\right)\) is closest to integer ________.

An electric dipole of dipole moment \(6 \times 10^{-6} \mathrm{Cm}\) is placed in uniform electric field of magnitude \(10^6 \mathrm{~V} / \mathrm{m}\). Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be ____ J.

The vernier scale used for measurement has a positive zero error of \(0.2\, mm\). If while taking a measurement it was noted that \('0'\) on the vernier scale lies between \(8.5\, cm\) and \(8.6\, cm\) vernier coincidence is \(6,\) then the correct value of measurement is ............. \(cm\). (least count \(=0.01\, cm )\)

A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time the magnet will

An object is located at \(2\, km\) beneath the surface of the water. If the fractional compression \(\frac{\Delta V }{ V }\) is \(1.36\, \%,\) the ratio of hydraulic stress to the corresponding hydraulic strain will be ......... . [Given : density of water is \(1000\, kg m ^{-3}\) and \(\left. g =9.8 \,ms ^{-2} .\right]\)

Consider two identical metallic spheres of radius \(R\) each having charge \(Q\) and mass \(m\). Their centers have an initial separation of \(4 R\). Both the spheres are given an initial speed of \(u\) towards each other. The minimum value of \(u\), so that they can just touch each other is:
(Take \(k=\frac{1}{4 \pi \epsilon_0}\) and assume \(k Q^2>G m^2\) where G is the Gravitational constant)

For a given transistor amplifier circuit in \(CE\) configuration \(V_{C C}=1 V , R_c=1 k \Omega, R_b=100 k \Omega\) and \(\beta=100\). Value of base current \(I_b\) is

Mass per unit area of a circular disc of radius \(\mathrm{a}\) depends on the distance \(\mathrm{r}\) from its centre as \(\sigma(\mathrm{r})=\mathrm{A}+\mathrm{Br} .\) The moment of inertia of the disc about the the axis, perpendicular to the plane and passing through its centre is