Two projectiles are projected at \(30^{\circ}\) and \(60^{\circ}\) with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:

A parallel plate capacitor of area \(60\, cm^2\) and separation \(3\, mm\) is charged initially to \(90\, \mu C\). If the medium between the plate gets slightly conducting and the plate loses the charge initially at the rate of \(2.5\times10^{-8}\, C/s\), then what is the magnetic field between the plates ?

A cylinder with fixed capacity of \(67.2\, lit\) contains helium gas at \(STP\). The amount of heat needed to raise the temperature of the gas by \(20\,^oC\) is ..... \(J\) [Given that \(R = 8.31\, J\, mol^{-1}\, K^{-1}\)]

For \(a\) gas \(C_{p}-C_{V}=R\) in a state \(P\) and \(C_{p}-C_{V}=1.10 R\) in a state \(Q, T_{p}\) and \(T_{Q}\) are the temperatures in two different states \(P\) and \(Q\) respectively. Then

A particle is moving in a straight line such that its velocity is increasing at \(5\,ms ^{-1}\) per meter. The acceleration of the particle is \(ms ^{-2}\) at a point where its velocity is \(20\,ms ^{-1}\).

In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are \(70 \mathrm{~ms}^{-1}\) and \(65 \mathrm{~ms}^{-1}\) respectively. If the wing area is \(2 \mathrm{~m}^2\) the lift of the wing is _______ \(\mathrm{N}\). (Given density of air \(=1.2 \mathrm{~kg} \mathrm{~m}^{-3}\) )

A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height \(h\) is \(....\,S.\)

Identify the operation performed by the circuit given below

A fighter jet is flying horizontally at a certain altitude with a speed of \(200 \; ms ^{-1}\). When it passes directly overhead an anti-aircraft gun, bullet is fired from the gun, at an angle \(\theta\) with the horizontal, to hit the jet. If the bullet speed is \(400 \; m / s\), the value of \(\theta\) will be \(\dots \; {}^o\)

The first member of the Balmer series of hydrogen atom has a wavelength of \(6561\; \mathring A\). The wavelength of the second member of the Balmer series (in \(nm\)) is