Five charges \(+q,+5 q,-2 q,+3 q\) and \(-4 q\) are situated as shown in the figure. The electric flux due to this configuration through the surface \(S\) is _______.

Two particles \(A\) and \(B\) of equal masses are suspended from two massless springs of spring constants \(K _{1}\) and \(K _{2}\) respectively.If the maximum velocities during oscillations are equal, the ratio of the amplitude of \(A\) and \(B\) is

If \(V\) is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be:-

A rod of length 5 L is bent right angle keeping one side length as 2 L.

The position of the centre of mass of the system: (Consider \(\mathrm{L}=10 \mathrm{~cm}\))

Particle \(A\) of mass \(m _{1}\) moving with velocity \((\sqrt{3} \hat{i}+\hat{j})\, ms ^{-1}\) collides with another particle \(B\) of mass \(m _{2}\) which is at rest initially. Let \(\overrightarrow{ V }_{1}\) and \(\overrightarrow{ V }_{2}\) be the velocities of particles \(A\) and \(B\) after collision respectively. If \(m _{1}=2\, m _{2}\) and after collision \(\overrightarrow{ V }_{1}=(\hat{ i }+\sqrt{3} \hat{ j })\, ms ^{-1},\) the angle between \(\overrightarrow{ V }_{1}\) and \(\overrightarrow{ V }_{2}\) is\(......^o\)

The ratio of escape velocity of a planet to the escape velocity of earth will be:Given : Mass of the planet is \(16\) times mass of earth and radius of the planet is \(4\) times the radius of earth.

The magnetic field of a plane electromagnetic wave is given by \(\overrightarrow{ B }=2 \times 10^{-8} \sin \left(0.5 \times 10^{3} x +1.5 \times 10^{11} t \right) \hat{ j } T\) The amplitude of the electric field would be.

A \(100 \,\Omega\) resistance, a \(0.1\, \mu {F}\) capacitor and an inductor are connected in series across a \(250 \,{V}\) supply at variable frequeny. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is \(60\, {Hz}\). (In \({H}\))

In a hypothetical fission reaction \({ }_{92} \mathrm{X}^{236} \rightarrow{ }_{56} \mathrm{Y}^{141}+{ }_{36} \mathrm{Z}^{92}+3 \mathrm{R}\) The identity of emitted particles \((R)\) is _______.

A cylindrical conductor of length 2m and area of cross-section \( 0.2\,mm^{2} \) carries an electric current of 1.6 A when its ends are connected to a 2V battery. Mobility of electrons in the conductor is \( \alpha\times10^{-3} m^{2}/V.s \). The value of \( \alpha \) is:
(electron concentration \( =5\times10^{28}/m^{3} \) and electron charge \( =1.6\times10^{-19} C \))

Given below are two statements: Statement \(I:\) Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface. Statement \(II:\) Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light. In the light of above statements, choose the correct answer from the options given below: