Point out the right statements about the validity of Kirchhoff's junction rule,

Potential energy of 2 charge \(10 \mathrm{nC}\) each separated by a distance of \(0.09 \mathrm{~m}\) in air is

In the diagram shown below, \(m_1\) and \(m_2\) are the masses of two particles and \(x_1\) and \(x_2\) are their respective distances from the origin \(O\).


The centre of mass of the system is

A proton is moving along negative X axis. If a uniform magnetic field is applied parallel to the positive Z axis, then choose the correct answer from the following options;
1. The proton will experience magnetic force along positive Y direction and will move along a circular path in the XY plane
2. The proton will experience magnetic force along negative Y direction and will move along a circular path in the XY plane
3. The proton will experience magnetic force along positive Y direction and will move along a circular path in the XZ plane
4. The proton will experience magnetic force along negative Y direction and will move along a circular path in the XZ plane

What is the minimum band-gap of the LED diode?

A ray of light incident on one face of an equilateral prism at \(60^{\circ}\) enters and leaves the prism symmetrically. Refractive index of the prism material is

A boy is running along a straight horizontal road with a constant speed \(5 \mathrm{~ms}^{-1}\). While running he throws a stone with a velocity \(30 \mathrm{~ms}^{-1}\) at an angle \(60^{\circ}\) with the horizontal. Then the time of flight of the stone is: (Given \(g=10 \mathrm{~ms}^{-2}\) )

Which of the following will show geometrical isomerism?

A plano-convex lens made of refractive index 1.5 and having radius of curvature \(\mathrm{R}=4 \mathrm{~cm}\) fits exactly into a planoconcave lens made of refractive index 1.3 and having the same radius of curvature \(R=4 \mathrm{~cm}\) such that their plane surfaces are parallel to each other. The focal length of the combination is:

Formation of coloured solution is possible, when metal ion in the compound contains

\(\int_\limits{-1}^1 \dfrac{d}{d x}\left(\tan ^{-1} \dfrac{1}{x}\right) d x \text { is }\)

The difference between heat capacity at constant pressure and heat capacity at constant volume is

A vertical spring of spring constant \(24 \mathrm{Nm}^{-1}\) is fixed on a table. A ball of mass 0.5 kg at a height 2 m above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance of 50 cm . The net work done in the process is: