Two objects \(A\) and \(B\) are placed at \(15\,cm\) and \(25\,cm\) from the pole in front of a concave mirror having radius of curvature \(40 cm\). The distance between images formed by the mirror is \(..........\,cm\)

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]

Given below are two statements : Statement \(I:\) If the Brewster's angle for the light propagating from air to glass is \(\theta_{ B }\), then Brewster's angle for the light propagating from glass to air is \(\frac{\pi}{2}-\theta_B\). Statement \(II:\) The Brewster's angle for the light propagating from glass to air is \(\tan ^{-1}\left(\mu_{ g }\right)\) where \(\mu_{ g }\) is the refractive index of glass. In the light of the above statements, choose the correct answer from the options given below :

A nucleus of masss \(M\) emits \(\gamma\)-ray photon of frequency \('v'.\) The loss of internal energy by the nucleus is:

A metre scale is balanced on a knife edge at its centre. When two coins, each of mass \(10\, g\) are put one on the top of the other at the \(10.0\, cm\) mark the scale is found to be balanced at \(40.0\, cm\) mark. The mass of the metre scale is found to be \(x \times 10^{-2}\) \(kg\). The value of \(x\) is

Two particles move at right angle to each other. Their de Broglie wavelengths are \({\lambda _1}\) and \({\lambda _2}\) respectively. The particles suffere perfectly inelastic collision. The de Broglie wavelength \(\lambda \) , of the final particle, is given by

In the figure, a very large plane sheet of positive charge is shown. \(P _{1}\) and \(P _{2}\) are two points at distance \(l\) and \(2 \,l\) from the charge distribution. If \(\sigma\) is the surface charge density, then the magnitude of electric fields \(E_{1}\) and \(E_{2}\) at \(P _{1}\) and \(P _{2}\) respectively are

A boy of mass \(20\, kg\) is standing on a \(80\, kg\) free to move long cart. There is negligible friction between cart and ground. Initially, the boy is standing \(25\, m\) from a wall. If he walks \(10\, m\) on the cart towards the wall, then the final distance of the boy from the wall will be ........ \(m\)

If \(‘M’\) is the mass of water that rises in a capillary tube of radius \(‘r’,\) then mass of water which will rise in a capillary tube of radius \(‘2r’\) is