Two satellites \(A\) and \(B\) of masses \(200\, kg\) and \(400\, kg\) are revolving round the earth at height of \(600\, km\) and \(1600\, km\) respectively. If \(T _{ A }\) and \(T _{ B }\) are the time periods of \(A\) and \(B\) respectively then the value of \(T _{ B }- T _{ A }\) [Given : radius of earth \(=6400\, km\), mass of earth \(=6 \times 10^{24}\, kg\) ]

In an experiment to determine the Young's modulus, steel wires of five different lengths \((1,2,3,4\) and \(5\,m )\) but of same cross section \(\left(2\,mm ^{2}\right)\) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is \(x \times 10^{11}\,Nm ^{-2}\), then the value of \(x\) is

Match List \(I\) with List \(II\) :

List \(I\)	List \(II\)
\(A\) Isothermal Process	\(I\) Work done by the gas decreases internal energy
\(B\) Adiabatic Process	\(II\) No change in internal energy
\(C\) Isochoric Process	\(III\) The heat absorbed goes partly to increase internal energy and partly to do work
\(D\) Isobaric Process	\(IV\) No work is done on or by the gas

Choose the correct answer from the options given below :

A bead \(P\) sliding on a frictionless semi-circular string \((A C B)\) and it is at point \(S\) at \(t =0\) and at this instant the horizontal component of its velocity is \(v\). Another bead \(Q\) of the same mass as \(P\) is ejected from point \(A\) at \(t =0\) along the horizontal string \(A B\), with the speed \(v\), friction between the beads and the respective strings may be neglected in both cases. Let \(t_p\) and \(t_Q\) be the respective times taken by beads \(P\) and \(Q\) to reach the point \(B\), then the relation between \(t_p\) and \(t_Q\) is

The increase in the pressure required to decrease the volume \((\Delta V)\) of water is \(6.3 \times 10^7\) N/m\(^2\). The percentage decrease in the volume is _____. (Bulk modulus of water \(= 2.1 \times 10^9\) N/m\(^2\).)

In photo electric effect \(A.\) The photocurrent is proportional to the intensity of the incident radiation. \(B.\) Maximum Kinetic energy with which photoelectrons are emitted depends on the intensity of incident light. \(C.\) Max. \(K.E\) with which photoelectrons are emitted depends on the frequency of incident light. \(D.\) The emission of photoelectrons require a minimum threshold intensity of incident radiation. \(E.\) Max. K.E of the photoelectrons is independent of the frequency of the incident light. Choose the correct answer from the options given below:

A bar magnet with a magnetic moment \(5.0\,Am ^2\) is placed in parallel position relative to a magnetic field of \(0.4\,T\). The amount of required work done in turning the magnet form parallel to antiparallel position relative to the field direction is \(.........\,J\)

Match List \(- I\) with List \(- II\)

List\(-I\) (Layer of atmosphere)	List\(-II\) (Approximate height over earth's surface)
\((A)\) \(F_1\) - Layer	\((I)\) \(10\,km\)
\((B)\) \(D-\) Layer	\((II)\) \(170-190\,km\)
\((C)\) Troposphere	\((III)\) \(100\,km\)
\((D)\) \(E-\)layer	\((IV)\) \(65-75\,km\)

Choose the correct answer from the options given below:

A solenoid of \(1200\) turns is wound uniformly in a single layer on a glass tube \(2\,m\) long and \(0.2\,m\) in diameter. The magnetic intensity at the center of the solenoid when a current of \(2\,A\) flows through it is: