The number density of free electrons in copper is nearly \(8 \times 10^{28}\,m ^{-3} . A\) copper wire has its area of cross section \(=2 \times 10^{-6}\,m ^2\) and is carrying a current of \(3.2\,A\). The drift speed of the electrons is \(.....\times 10^{-6}\,ms ^{-1}\).

The angle of projection for a projectile to have same horizontal range and maximum height is _______.

The equation of the electric field of an electromagnetic wave propagating through free space is given by :
E \(=\sqrt{377} \sin \left(6.27 \times 10^3 t -2.09 \times 10^{-5} x \right)\) N/C
he average power of the electromagnetic wave is\(\left(\frac{1}{\alpha}\right) W / m ^2\). The value of \(\alpha\) is ___________
\(\left(\right.\) Take \(\sqrt{\frac{\mu_0}{\varepsilon_0}}=377\) in SI units \()\)

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 :

A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a power of \(24\,W\) The radius of curvature of hemisphere is \(10\,cm\) and the inner surface is completely reflecting. The force on the hemisphere due to the light falling on it is \(..........\times 10^{-8}\,N\).

The equivalent resistance between \(A\) and \(B\) is \(......\)

The give graph shown variation (with distance \(r\) from centre) of

A uniform sphere of mass \(500\; g\) rolls without slipping on a plane horizontal surface with its centre moving at a speed of \(5.00\; \mathrm{cm} / \mathrm{s}\). Its kinetic energy is

In the circuit shown in the figure, the total charge in \(750\, \mu C\) and the voltage across capacitor \(C _{2}\) is \(20\, V\). Then the charge on capacitor \(C _{2}\) is\(....\mu C\)

Given below are two statements: one is labelled as Assertion \((A)\) and the other is labelled as Reason \((R)\). \(Assertion\) \((A)\) : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun. \(Reason\) \((R)\): The moon takes less time to move around the earth than the time taken by the earth to move around the sun. In the light of the above statements, choose the most appropriate answer from the options given below:

A capacitor of capacitance \(150.0\,\mu F\) is connected to an alternating source of \(emf\) given by \(E =36\) \(\sin (120 \pi t ) V\). The maximum value of current in the circuit is approximately equal to \(......\,A\)