The electric field between the two parallel plates of a capacitor of \(1.5 \mu \mathrm{F}\) capacitance drops to one third of its initial value in \(6.6 \mu \mathrm{s}\) when the plates are connected by a thin wire. The resistance of this wire is _______ \(\Omega\). (Given, \(\log 3=1.1)\)

Given is a thin convex lens of glass (refractive index \(\mu\) ) and each side having radius of curvature \(R\). One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself ?

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

A radioactive sample has an average life of \(30\, {ms}\) and is decaying. A capacitor of capacitance \(200\, \mu\, {F}\) is first charged and later connected with resistor \(^{\prime}{R}^{\prime}\). If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of \(^{\prime}R^{\prime}\) should be \(....\,\Omega\)

A cylindrical container of volume \(4.0 \times 10^{-3} \,{m}^{3}\) contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is \(400 \,{K}\) The pressure of the mixture of gases is: [Take gas constant as \(8.3\, {J} {mol}^{-1} {K}^{-1}\)]

Two projectiles are fired from ground with same initial speeds from same point at angles \(\left(45^{\circ}+\alpha\right)\) and \(\left(45^{\circ}-\alpha\right)\) with horizontal direction. The ratio of their times of flights is

What will be the nature of flow of water from a circular tap, when its flow rate increased from \(0.18\, L / min\) to \(0.48\, L / min\) ? The radius of the tap and viscosity of water are \(0.5\, cm\) and \(10^{-3}\, Pa s\), respectively. (Density of water : \(10^{3}\, kg / m ^{3}\) )

Three masses \(m,\,2\,m\) and \(3\,m\) are moving in \(x-y\) plane with speed \(3\,u,\,2\,u\,\) and \(u\) respectively as shown in figure. The three masses collide at the same point at \(P\) and stick together. The velocity of resulting mass will be

In \(1^{\text {st }}\) case, Carnot engine operates between temperatures \(300\,K\) and \(100\,K\). In \(2^{\text {nd }}\) case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in \(2^{\text {ad }}\) case) will be.

A positive charge \('q'\) of mass \('m'\) is moving along the \(+ x\) axis. We wish to apply a uniform magnetic field \(B\) for time \(\Delta t\) so that the charge reverses its direction crossing the \(y\) axis at a distance \(d.\) Then

In the circuit diagrams \((A, B, C\) and \(D\)) shown below, \(R\) is a high resistance and \(S\) is a resistance of the order of galvanometer resistance \(G\). The correct circuit, corresponding to the half deflection method for finding the resistance and figure of merit of the galvanometer, is the circuit labelled as