A source of sound \(S\) is moving with the velocity of \(50\,m/s\) towards a stationary observer. The observer measures the frequency of the sound as \(1000\,Hz.\) What will be the apparent frequency of the source when it is moving away from the observer after crossing him ... \(Hz\) ? (Take velocity of sound in air is \(350\,m/s\) )

Five identical cells each of internal resistance \(1\, \Omega\) and \(emf \;5\, {V}\) are connected in series and in parallel with an external resistance \('R'.\) For what value of \('R',\) current in series and parallel combination will remain the same ? (in \(\Omega\))

A roller is mad e by joining  together two cones at their vertices \(O\). It is kept on two rails \(AB\) and \(CD\), which are placed asymmetrically (see figure) , with its axis perpendicular to \(CD  \) and its centre \(O\) at the centre ofline joining \(AB\) and \(CD\) (see figure) . It is given a light push so that it \(A\) starts rolling with its centre \(O\) moving parallel to \(CD\) in the direction shown. As it moves, the roller will tend to

Arrange the following electromagnetic radiations per quantum in the order of increasing energy :- \(A\) : Blue light \(B\) : Yellow light \(C\) : X-ray \(D\) : Radiowave

Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth \(d=\frac{R}{2}\) from the surface of earth, if its werght on the surface of earth is \(200\,N\), will be \(...........\,N\) ( \(Given R =\) Radrus of earth)

The ratio of momentum of the photons of the \(1^{st}\) and \(2^{nd}\) line of Balmer series of Hydrogen atoms is \(\alpha/\beta\). The possible values of \(\alpha\) and \(\beta\) are:-

The equivalent capacitance between points \(A\) and \(B\) in below shown figure will be..........\(\mu F\).

A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be \(t_1\) and \(t_2\), respectively, then...

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

List\(-I\)	List\(-II\)
\((a)\) \(\omega L\,>\,\frac{1}{\omega C}\)	\((i)\) Current is in phase with \(emf\)
\((b)\) \(\omega {L}=\frac{1}{\omega {C}}\)	\((ii)\) Current lags behind the applied \(emf\)
\((c)\) \(\omega {L}\, < \,\frac{1}{\omega {C}}\)	\((iii)\) Maximum current occurs
\((d)\) resonant frequency	\((iv)\) Current leads the \(emf\)

Choose the correct answer from the options given below :

Match the LIST-I with LIST-II

LIST-I	LIST-II
(A) Boltzmann constant	I. \(\mathrm{ML}^2 \mathrm{~T}^{-1}\)
(B) Coefficient of viscosity	II. \(\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\)
(C) Planck's constant	III. \(\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\)
(D) Thermal conductivity	IV. \(\mathrm{ML}^{-1} \mathrm{~T}^{-1}\)

Choose the correct answer from the options given below :

The current in a conductor is expressed as \(I=3 t^2+4 t^3\), where \(I\) is in Ampere and \(t\) is in second. The amount of electric charge that flows through a section of the conductor during \(t=1\) s to \(t=2 \mathrm{~s}\) is _______ \(\mathrm{C}\).