In a meter bridge experiment \(\mathrm{S}\) is a standard resistance. \(\mathrm{R}\) is a resistance wire. It is found that balancing length is \(l=25 \;\mathrm{cm} .\) If \(\mathrm{R}\) is replaced by a wire of half length and half diameter that of \(\mathrm{R}\) of same material, then the balancing distance \(\left.l^{\prime} \text { (in } \mathrm{cm}\right)\) will now be

In a common emitter configuration with suitable bias, it is given than \(R_L\) is the load resistance and \(R_{BE}\)  is small signal dynamic resistance (input side). Then, voltage gain, current gain and power gain are given, respectively, by: [ \(\beta \) is current gain, \(I_B\) , \(I_C\) , \(I_E\) are respectively base, collector and emitter currents]

A beam of light has two wavelengths of \(4972\,\mathop A\limits^o \) and \(6216\,\mathop A\limits^o \) with a total intensity of \(3 .6 \times  10^{- 3}\,\,Wm^{-2}\) equally distributed among the two wavelengths. The beam falls normally on an area of \(1\,cm^2\) of a clean metallic surface of work function \( 2.3\,eV.\) Assume that there is no loss of light by reflection and that each capable photon ejects one electron. The number of photoelectrons liberated in \(2\,s\) is approximately

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason \(R\) Assertion \(A:\) The beam of electrons shows wave nature and exhibit interference and diffraction. Reason \(R\) : Davisson Germer Experimentally verified the wave nature of electrons. In the light of the above statements. Choose the most appropriate answer from the options given below :

Given below are two statements; one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) Electromagnets are made of soft iron. Reason \(R:\) Soft iron has high permeability and low retentivity. In the light of above, statements, choose the most appropriate answer from the options given below.

A charge \(Q\) is placed at a distance \(a/2\) above the centre of the square surface of edge \(a\) as shown in the figure. The electric flux through the square surface is

To project a body of mass \(m\) from earth's surface to infinity, the required kinetic energy is _______. (assume, the radius of earth is \(R_E, g=\) acceleration due to gravity on the surface of earth)

The ratio of momentum of the photons of the \(1^{st}\) and \(2^{nd}\) line of Balmer series of Hydrogen atoms is \(\alpha/\beta\). The possible values of \(\alpha\) and \(\beta\) are:-

A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of \(\theta ,\) where \(\theta \) is the angle by which it has rotated, is given as \(k\theta ^2.\) If its moment of inertia is \(I\) then the angular acceleration of the disc is

A slit of width \(a\) is illuminated by light of wavelength \(\lambda\). The linear separation between \(1^{st}\) and \(3^{rd}\) minima in the diffraction pattern produced on a screen placed at a distance \(D\) from the slit system is _____.