A light wave travelling linearly in a medium of dielectric constant \(4,\) incident on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be (Given : relative permeability of medium \(\mu_{ s }=1)\) 

Following statements are given : \((1)\) The average kinetic energy of a gas molecule decreases when the temperature is reduced. \((2)\) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature. \((3)\) The average kinetic energy of a gas molecule decreases with increases in volume. \((4)\) Pressure of a gas increases with increase in temperature at constant pressure. \((5)\) The volume of gas decreases with increase in temperature. Choose the correct answer from the options given below:

A large block of wood of mass \(M =5.99\, kg\) is hanging from two long massless cords. A bullet of mass \(m =10\, g\) is fired into the block and gets embedded in it. The (block \(+\) bullet) then swing upwards, their centre of mass rising a vertical distance \(h =9.8\,cm\) before the (block \(+\) bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is: (Take \(g =9.8\, ms ^{-2}\) ) (in \(m/s\))

A \(70\, kg\) man leaps vertically into the air from a crouching position. To take the leap the man pushes the ground with a constant force \(F\) to raise himself The center of gravity rises by \(0.5\, m\) before he leaps. After the leap the \(c.g.\) rises by another \(1\, m\). The maximum power delivered by the muscles is : (Take \(g\, = 10\, ms^{-2}\))

An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true\(?\) \((A)\) the mean free path of the molecules decreases. \((B)\) the mean collision time between the molecules decreases. \((C)\) the mean free path remains unchanged. \((D)\) the mean collision time remains unchanged.

The disintegration energy \(Q\) for the nuclear fission of \({ }^{235} \mathrm{U} \rightarrow{ }^{140} \mathrm{Ce}+{ }^{94} \mathrm{Zr}+\mathrm{n}\) is _______ \(\mathrm{MeV}\). Given atomic masses of \({ }^{235} \mathrm{U}: 235.0439 \mathrm{u},{ }^{140} \mathrm{Ce} ; 139.9054 \mathrm{u},\) \({ }^{94} \mathrm{Zr}: 93.9063 \mathrm{u} ; \mathrm{n}: 1.0086 \mathrm{u},\) Given Value of \(\mathrm{c}^2=931 \mathrm{MeV} / \mathrm{u}\)

A beam of light travelling along \(X\)-axis is described by the electric field \(E _{ y }=900 \sin \omega( t - x / c )\). The ratio of electric force to magnetic force on a charge \(q\) moving along \(Y\)-axis with a speed of \(3 \times 10^{7}\,ms ^{-1}\) will be. [Given speed of light \(=3 \times 10^{8}\,ms ^{-1}\) ]

Consider a Young’s double slit experiment as shown in figure. What should be the slit separation \(d\) in terms of wavelength \(\lambda \) such that the first minima occurs directly in front of the slit \((S_1)\)?

A solenoid of \(1200\) turns is wound uniformly in a single layer on a glass tube \(2\,m\) long and \(0.2\,m\) in diameter. The magnetic intensity at the center of the solenoid when a current of \(2\,A\) flows through it is:

An electric power line having total resistance of 2 Ω, delivers 1 kW of power of 250 V. The percentage efficiency of transmission line is: __________ .

A wire of length \(2\,L\) is made by joining two wires \(A\) and \(B\) of same lengths but different radii \(r\) and \(2r\) and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire \(A\) is \(p\) and that in \(B\) is \(q\) then the ratio \(p : q\) is

A bottle has an opening of radius \(a\) and length \(b\). A cork of length band radius \(\left( {a + \Delta a} \right)\) where \(\left( {\Delta a <  < a} \right)\) is compressed to fit into the opening completely (see figure). If the bulk modulus of cork is \(B\) and frictional coefficient between the bottle and cork is \(\mu \) then the force needed to push the cork into the bottle is