An alternating current is given by \(\mathrm{I}=\mathrm{I}_{\mathrm{A}} \sin \omega \mathrm{t}+\mathrm{I}_{\mathrm{B}} \cos \omega \mathrm{t}\). The r.m.s current will be ______.

In the given arrangement of a doubly inclined plane two blocks of masses \(\mathrm{M}\) and \(\mathrm{m}\) are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is \(0.25\) . The value of \(\mathrm{m}\), for which \(\mathrm{M}=10\) \(\mathrm{kg}\) will move down with an acceleration of \(2 \mathrm{~m} / \mathrm{s}^2\), is _______. (take \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) and \(\left.\tan 37^{\circ}=3 / 4\right)\)

For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is _______.

Select the correct statement from the following

One mole of an ideal gas at \(27^{\circ} {C}\) is taken from \({A}\) to \({B}\) as shown in the given \({PV}\) indicator diagram. The work done by the system will be \(......\times 10^{-1} \,{J}\) [Given : \(R=8.3\, {J} /\,mole\,{K}, \ln 2=0.6931\) ] (Round off to the nearest integer)

Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is : (in pF)

In a photoelectric experiment, the wavelength of the light incident on a metal is changed from \(300\, nm\) to \(400\, nm\). The decrease in the stopping potential is close to ................ \(V\) \(\left( {\frac {{hc}}{e} = 1240\,nm - V} \right)\)

A solid sphere, of radius \(R\) acquires a terminal velocity \(\nu_1 \) when falling (due to gravity) through a viscous fluid having a coefficient of viscosity \(\eta \). The sphere is broken into \(27\) identical solid spheres. If each of these spheres acquires a terminal velocity, \(\nu_2\), when falling through the same fluid, the ratio \((\nu_1/\nu_2)\) equals

A square shaped wire with resistance of each side \(3\, \Omega\) is bent to form a complete circle. The resistance between two diametrically opposite points of the circle in unit of \(\Omega\) will be ......

A parallel plate capacitor has charge \(5 \times 10^{-6} \mathrm{C}\). A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is \(4 \times 10^{-6} \mathrm{C}\) then the dielectric constant of the slab is ________.