The output \(\mathrm{Y}\) of following circuit for given inputs is _______.

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil is _______.(specific gravity of Kerosene oil \(=0.8\), specific gravity of ice \(=0.9\) )

If \(X\) and \(Y\) are the inputs, the given circuit works as _______.

A ray of light \(AO\) in vacuum is incident on a glass slab at angle \(60^o\) and refracted at angle \(30^o\) along \(OB\) as shown in the figure. The optical path length of light ray from \(A\) to \(B\) is

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are \(Y_{1}\) and \(Y_{2}\). The combination behaves as a single wire then its Young's modulus is:

The time period of a satellite, revolving above earth's surface at a height equal to \(R\) will be (Given \(g =\pi^2 m / s ^2, R =\) radius of earth)

A car travels a distance of \(x\) with speed \(v_1\) and then same distance \(x\) with speed \(v_2\) in the same direction. The average speed of the car is

A boy’s catapult is made of rubber cord which is \(42\, cm\) long, with \(6\, mm\) diameter of cross -section and of negligible mass. The boy keeps a stone weighing \(0.02\, kg\) on it and stretches the cord by \(20\, cm\) by applying a constant force. When released, the stone flies off with a velocity of \(20\, ms^{-1}\). Neglect the change in the area of cross section of the cord while stretched. The Young’s modulus of rubber is closest to

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 \(.....\times 10^{-6}\,ms ^{-1}\).

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 \(20\,ms ^{-1}\).

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\(......^o\)