For the circuit shown below, the current through the Zener diode is......\(mA\)

A particle is moving \(5\) times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is \(1.878 \times 10^{-4}\). The mass of the particle is close to

Train A is moving along two parallel rail tracks towards north with speed \(72 \mathrm{~km} / \mathrm{h}\) and train B is moving towards south with speed \(108 \mathrm{~km} / \mathrm{h}\). Velocity of train \(B\) with respect to \(A\) and velocity of ground with respect to \(B\) are _______ (in \(\mathrm{ms}^{-1}\) ).

Two batteries with e.m.f \(12\ V\) and \(13\ V\) are connected in parallel across a load resistor of \(10\,\Omega\) . The internal resistances of the two batteries are \(1\,\Omega\) and \(2\,\Omega\) respectively. The voltage across the load lies between

A signal of \(0.1\, kW\) is transmitted in a cable. The attenuation of cable is \(-5 \,dB\) per \(km\) and cable length is \(20\, km\). The power received at receiver is \(10^{-x} \, W\). The value of \(x\) is ....... . \(\left[\right.\) Gain in \(\left. dB =10 \log _{10}\left(\frac{ P _{0}}{ P _{i}}\right)\right]\)

A projectile of mass \(M\) is fired so that the horizontal range is \(4\, km\). At the highest point the projectile explodes in two parts of masses \(M/4\) and \(3M/4\) respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is .................. \(\mathrm{km}\)

Match the List-I with List-II

	List-I		List-II
A	Radio-wave	I	is produced by Magnetron value
B	Micro-wave	II	Due to change in the vibrational modes of atoms
C	Infrared-wave	II	Due to inner shell electrons moving from higher energy level to lower energy level
D	X-ray	IV	Due to rapid acceleration of electrons

Choose the correct answer from the options given below:

A coaxial cable consists of an inner wire of radius \('a'\) surrounded by an outer shell of inner and outer radii ' \({b}\) ' and '\(c\)' respectively. The inner wire carries an electric current is, which is distributed uniformly across cross-sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance \({x}\) from the axis when \((i)\) \({x}<{a}\) and \((ii)\) \({a}<{x}<{b}\) ?

Within a spherical charge distribution of charge density \(\rho \left( r \right)\), \(N\) equipotential surfaces of potential \({V_0},{V_0} + \Delta V,{V_0} + 2\Delta V,\)\(.....{V_0} + N\Delta V\left( {\Delta V > 0} \right),\) are drawn and have increasing radii \(r_0, r_1, r_2,......r_N\), respectively. If the difference in the radii of the surfaces is constant for all values of \(V_0\) and \(\Delta V\) then