A particle of mass \(m\) projected with a velocity ' \(u\) ' making an angle of \(30^{\circ}\) with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height \(\mathrm{h}\) is _______.

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

If an optical medium possesses a relative permeability of \(\frac{10}{\pi}\) and relative permittivity of \(\frac{1}{0.0885}\), then the velocity of light is greater in vacuum than that in this medium by ________ times.
\(\left(\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}, \epsilon_0=8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right.\)
\(\left.\mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)\)

Two particles \({A}\) and \({B}\) having charges \(20\, \mu {C}\) and \(-5\, \mu {C}\) respectively are held fixed with a separation of \(5\, {cm}\). At what position a third charged particle should be placed so that it does not experience a net electric force?

A cylinder of fixed capacity of \(44.8 \,litres\) contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by \(20.0^{\circ} C\) will be ..............  \(J\)(Given gas constant \(R =8.3 \,JK ^{-1}- moI ^{-1}\) )

A gas can be taken from \(A\) to \(B\) via two different processes \(ACB\) and \(ADB\). When path \(ACB\) is used \(60\, J\) of heat flows into the system and \(30\, J\) of work is done by the system. If path \(ADB\) is used work down by the system is \(10\, J\). the heat flow into the system in path \(ADB\) is ..... \(J\)

Identify the correct statements :
A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.
B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric.
C. Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance.
D. For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces.
Choose the correct answer from the options given below.

Shown in the figure is a shell made of a conductor. It has inner radius \(a\) and outer radius \(b\), and carries charge \(Q\). At its centre is a dipole  \(\vec P\) as shown. In this case

A \(9\, V\) battery with internal resistance of \(0.5\,\Omega \) is connected across an infinite network as shown in the figure. All ammeters \(A_1 , A_2, A_3\) and voltmeter \(V\) are ideal. Choose correct statement

A heat engine operates with the cold reservoir at temperature \(324 K\). The minimum temperature of the hot reservoir, if the heat engine takes \(300 \; J\) heat from the hot reservoir and delivers \(180 \; J\) heat to the cold reservoir per cycle, is \(\dots \; K .\)

In the following nuclear rection, \(D \stackrel{\alpha}{\longrightarrow} D _{1} \stackrel{\beta-}{\longrightarrow} D _{2} \stackrel{\alpha}{\longrightarrow} D _{3} \stackrel{\gamma}{\longrightarrow} D _{4}\) Mass number of \(D\) is \(182\) and atomic number is \(74\) . Mass number and atomic number of \(D _{4}\) respectively will be