Two cars A and B each of mass \(10^3 kg\) are moving on parallel tracks separated by a distance of 10 m , in same direction with speeds \(72 km / h\) and \(36 km / h\). The magnitude of angular momentum of car \(A\) with respect to car \(B\) is _________ J.s.

Match List I with List II

List - I	List - II
A. AM Broadcast	I. \(88-108 MHz\)
B. FM Broadcast	II. \(540-1600 kHz\)
C. Television	III. \(3.7-4.2GHz\)
D. Satellite Communication	IV. \(54 MHz-590MHz\)

Choose the correct answer from the options given below:

A magnet of total magnetic moment \({10\,^{ - 2}}\hat i\,A - {m^2}\) is placed in a time varying magnetic field, \(B\,\hat i\,\left( {\cos \,\omega t} \right)\) where \(B = 1\, Tesla\) and \(\omega  = 0.125\, rad/s\). The work done for reversing the direction of the magnetic moment at \(t = 1\, second\), is

A uniform electric field \(E =(8\,m / e ) V / m\) is created between two parallel plates of length \(1 m\) as shown in figure, (where \(m =\) mass of electron and \(e=\) charge of electron). An electron enters the field symmetrically between the plates with a speed of \(2\,m / s\). The angle of the deviation \((\theta)\) of the path of the electron as it comes out of the field will be........

A soap bubble of radius \(3\, {cm}\) is formed inside the another soap bubble of radius \(6\, {cm}\). The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is .......... \({cm}\) 

Under isothermal condition, the pressure of a gas is given by \(P = aV ^{-3}\), where \(a\) is a constant and \(V\) is the volume of the gas. The bulk modulus at constant temperature is equal to \(..........\,P\)

In an ideal gas at temperature \(T,\)  the average force that a molecule applies on the walls of a closed container depends on \(T\) as \(T^q\) . A good estimate for \(q\) is

A huge circular arc of length \(4.4\) \(ly\) subtends an angle \('4 {s}'\) at the centre of the circle. How long it would take for a body to complete \(4\) revolution if its speed is \(8 \;AU\;per\, second \;?\) Given : \(1\, {ly}=9.46 \times 10^{15} \,{m},\) \(\, {AU}=1.5 \times 10^{11}\, {m}\)

Two persons pull a wire towards themselves. Each person exerts a force of \(200 \mathrm{~N}\) on the wire. Young's modulus of the material of wire is \(1 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\). Original length of the wire is \(2 \mathrm{~m}\) and the area of cross section is \(2 \mathrm{~cm}^2\). The wire will extend in length by _______ \(\mu \mathrm{m}\).

In a radioactive decay chain, the initial nucleus is \({}_{90}^{232}Th\).  At the end there are \(6\,\,\alpha -\) particles and \(4\,\,\beta -\) particles with are emitted. If the end nucleus is \({}_Z^AX\,,\,A\) and \(Z\) are given by

The ratio of de Broglie wavelength of a deutron with kinetic energy \(E\) to that of an alpha particle with kinetic energy \(2 E\), is \(n: 1\). The value of \(n\) is ___________.
(Assume mass of proton = mass of neutron) :

A nucleus of mass \(M\) at rest splits into two parts having masses \(\frac{M^{\prime}}{3}\) and \(\frac{2 M^{\prime}}{3}\left(M^{\prime} < M\right)\). The ratio of de Broglie wavelength of two parts will be.