Two solids \(A\) and \(B\) of mass \(1\, kg\) and \(2\, kg\) respectively are moving with equal linear momentum. The ratio of their kinetic energies \((K.E.)_{ A }:( K.E. )_{ B }\) will be \(\frac{ A }{1},\) so the value of \(A\) will be ..... .

In series \(LCR\) circuit, the capacitance is changed from \(\mathrm{C}\) to \(4 \mathrm{C}\). To keep the resonance frequency unchanged, the new inductance should be _______.

An observer is riding on a bicycle and moving towards a hill at \(18\,km\,h ^{-1}\). He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is \(640\,\,Hz\) and velocity of the sound in air is \(320\,m / s\), the beat frequency between the two sounds heard by observer will be \(...Hz\).

\(c_P\) and \(c_V\) are specific heats at constant pressure and constant volume respectively. It is observed that \(c_P - c_V = a\) for hydrogen gas \(c_P - c_V = b\) for nitrogen gas The correct relation between \(a\) and \(b\) is

Moment of inertia \((M.I.)\) of four bodies, having same mass and radius, are reported as; \(I _{1}= M\). of thin circular ring about its diameter. \(I _{2}=\) \(M.I.\) of circular disc about an axis perpendicular to the disc and going through the centre, \(I _{3}=\) \(M.I.\) of solid cylinder about its axis and \(I _{4}= M . I.\) of solid sphere about its diameter. Then

A tennis ball (treated as hollow spherical shell) starting from \(O\) rolls down a hill. At point \(A\) the ball becomes air borne leaving at an angle of \(30^o\) with the horizontal. The ball strikes the ground at \(B\). What is the value of the distance \(AB\) ? (Moment of inertia of a spherical shell of mass \(m\) and radius \(R\) about its diameter .......... \(m\). \(= \frac {2}{3}\,mR^2\))

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

List \(I\)	List \(II\)
\(A\) Troposphere	\(I\) Approximate \(\quad 65-75\, km\) over Earth's surface
\(B\) E-Part of Stratosphere	\(II\) Approximate \(300\,km\) over Earth's surface
\(C\) \(F _2\)-Part of Thermosphere	\(III\)  Approximate \(10\,km\) over Earth's surface
\(D\) \(F _2\)-Part of Thermosphere	\(IV\) Approximate \(100\,km\) over Earth's surface

Choose the correct answer from the options given below:

A flask contains argon and oxygen in the ratio of \(3: 2\) in mass and the mixture is kept at \(27^{\circ} C\). The ratio of their average kinetic energy per molecule respectively will be ...........

The equation of wave is given by \(Y=10^{-2} \sin 2 \pi\left(160 t-0.5 x+\frac{\pi}{4}\right)\) Where \(x\) and \(Y\) are in \(m\) and \(t\) in \(s\). The speed of the wave is \(.....\,km h ^{-1}\)

Two forces \(P\) and \(Q\), of magnitude \(2F\) and \(3F\), respectively, are at an angle \(\theta \) with each other. If the force \(Q\) is doubled, then their resultant also gets doubled. Then, the angle \(\theta \) is ....... \(^o\)

A biconvex lens of refractive index \(1.5\) has a focal length of \(20 \mathrm{~cm}\) in air. Its focal length when immersed in a liquid of refractive index \(1.6\) will be: