A parallel plate capacitor of capacitance \(2\; F\) is charged to a potential \(V\). The energy stored in the capacitor is \(E_1\). The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is \(E _2\). The ratio \(E _2 / E _1\) is

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A :\) Earth has atmosphere whereas moon doesn't have any atmosphere. Reason \(R\) : The escape velocity on moon is very small as compared to that on earth. In the light of the above statement, choose the correct answer from the options given below :

A hollow spherical shell at outer radius \(R\) floats just submerged under the water surface. The inner radius of the shell is \(r\). If the specific gravity of the shell material is \(\frac{27}{8}\) \(w.r.t.\) water, the value of \(r\) is\(......R\)

A man (mass \(= 50\, kg\)) and his son (mass \(= 20\, kg\)) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of \(0.70\, ms^{-1}\) with respect to the man. The speed of the man with respect to the surface is ........ \(ms^{-1}\)

An engine approaches a hill with a constant speed. When it is at a distance of \(0.9\, km\), it blows a whistle whose echo is heard by the driver after \(5\, seconds\). If the speed of sound in air is \(330\, m/s\), then the speed of the engine is .... \(m/s\)

A bead of mass \(m\) stays at point \(P ( a , b )\) on a wire bent in the shape of a parabola \(y=4 Cx ^{2}\) and rotating with angular speed \(\omega\) (see figure). The value of \(\omega\) is (neglect friction)

The correct truth table for the given input data of the following logic gate is:

The energy levels of an atom is shown is figure. Which one of these transitions will result in the emission of a photon of wavelength \(124.1\,nm\) ?Given \(\left( h =6.62 \times 10^{-34}\,Js \right)\)

An object of mass ' \(m\) ' initially at rest on a smooth horizontal plane starts moving under the action of force \(F=2 N\). In the process of its linear motion, the angle \(\theta\) (as shown in figure) between the direction of force and horizontal varies as \(\theta= kx\), where \(k\) is a constant and \(x\) is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be \(E =\frac{ n }{ k } \sin \theta\). The value of \(n\) is \(.....\)

A piston of mass \(M\) is hung from a massless spring whose restoring force law goes as \(\mathrm{F}=-\mathrm{kx}^3\), where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with ' \(n\) ' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height \(\mathrm{L}_0\) to \(\mathrm{L}_1\), the total energy delivered by the filament is (Assume spring to be in its natural length before heating)

In a Young's double slit experiment, an angular width of the fringe is \(0.35^{\circ}\) on a screen placed at \(2\,m\) away for particular wavelength of \(450\,nm\). The angular width of the fringe, when whole system is immersed in a medium of refractive index \(7 / 5\), is \(\frac{1}{\alpha}\). The value of \(\alpha\) is ..............

Match List - I with List - II.

List-I	List-II
(A) Angular Impulse	(I) \(\left[M^0 L^2 T^{-2}\right]\)
(B) Latent Heat	(II) \(\left[M L^2 T^{-3} A^{-1}\right]\)
(C) Electrical resistivity	(III) \(\left[M L^2 T^{-1}\right]\)
(D) Electromotive force	(IV) \(\left[M L^3 T^{-3} A^{-2}\right]\)