A Zener diode is connected to a battery and a load as show below: The currents, \(I, I_Z\) and \(I_L\) are respectively .

In a meter bridge experiment to determine the value of unknown resistance, first the resistances \(2 \Omega\) and \(3 \Omega\) are connected in the left and right gaps of the bridge and the null point is obtained at a distance \(l cm\) from the left. Now when an unknown resistance \(x \Omega\) is connected in parallel to \(3 \Omega\) resistance, the null point is shifted by 10 cm to the right of wire. The value of unknown resistance \(x\) is _________ \(\Omega\).

A thin smooth rod of length \(L\) and mass \(M\) is rotating freely with angular speed \({\omega _0}\) about an axis perpendicular to the rod and passing through its centre. Two beads of mass \(m\) and negligible size are at the centre of the rod initially. The beads are free to slide along the rod. The angular speed of the system, when the beads reach the opposite ends of the rod will be

The figure given below shows an \(LCR\) series circuit with two switches \(S_1\) and \(S_2\). When switch \(S_1\) is closed keeping \(S_2\) open, the phase difference \((\phi)\) between the current and source voltage is \(30°\) and phase difference is \(60°\) when \(S_2\) is closed keeping \(S_1\) open. The value of \((3L_1 - L_2)\) is _______ H.

A bob of mass \(m\) is suspended at a point \(O\) by a light string of length \(l\) and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity \(v_0\) at the point ' A ', the string becomes slack when, the bob reaches at the point ' D '. The ratio of the kinetic energy of the bob at the points \(B\) and \(C\) is ______ -.

Given below are two statements : Statement \(I\) : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well. Statement \(II\) : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube. In the light of the above statements, choose the correct answer from the options given below :

When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is 3.2 V . If a second light having wavelength twice of first light is used, the stopping potential drops to 0.7 V . The wavelength of first light is _________ m .
\(\left( h =6.63 \times 10^{-34} J . s , e =1.6 \times 10^{-19} C , c =3 \times 10^8 m / s \right)\)

An alpha-particle of mass \(m\) suffers \(1-\) dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, \(64\%\) of its initial kinetic energy. The mass of the nucleus is .......... \(\mathrm{m}\)

An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density \(1000 \mathrm{~kg} / \mathrm{m}^3\). If the pressure inside the bubble is \(2100 \mathrm{~N} / \mathrm{m}^2\) greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )

A plane electromagnetic wave propagates along the \(+x\) direction in free space. The components of the electric field, \(\vec{E}\) and magnetic field, \(\vec{B}\) vectors associated with the wave in Cartesian frame are

Two circular discs of radius each 10 cm are joined at their centres by a rod of length 30 cm and mass 600 gm as shown in figure.
If the mass of each disc is 600 gm and applied torque between two discs is \(43 \times 10^{5}\) dyne cm, the angular acceleration of the discs about the given axis \(AB\) is ___________\(rad/s^{2}\).