The atomic mass of \({ }_6 \mathrm{C}^{12}\) is \(12.000000\ \mathrm{u}\) and that of \({ }_6 \mathrm{C}^{13}\) is \(13.003354 \ \mathrm{u}\). The required energy to remove a neutron from \({ }_6 \mathrm{C}^{13}\), if mass of neutron is \(1.008665 \ \mathrm{u}\), will be :

A light wave travelling linearly in a medium of dielectric constant \(4,\) incident on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be (Given : relative permeability of medium \(\mu_{ s }=1)\) 

In the figure shown, a circuit contains two identical resistors with resistance \(R = 5\,\Omega \) and an inductance with \(L = 2\, mH\). An ideal battery of \(15\, V\) is connected in the circuit. What will be the current through the battery long after the switch is closed?......\(A\)

Consider a cylinder of mass \(M\) resting on a rough horizontal rug that is pulled out from under it with acceleration \('a'\) perpendicular to the axis of the cylinder. What is \(F_{friction}\) at point \(P\) ? It is assumed that the cylinder does not slip

A transformer consisting of \(300\) turns in the primary and \(150\) turns in the secondary gives output power of \(2.2\, kW\). If the current in the secondary coils is \(10\, A\), then the input voltage and current in the primary coil are

In a transverse wave the distance between a crest and neighbouring trough at the same instant is \(4.0\, cm\) and the distance between a crest and trough at the same place is \(1 .0\, cm\) . The next crest appears at the same place after a time interval of \(0.4\,s\). The maximum speed of the vibrating particles in the medium is

An iron rod of volume \(10^{-3}\, m ^{3}\) and relative permeability \(1000\) is placed as core in a solenoid with \(10\) \(turns/cm.\) If a current of \(0.5\, A\) is passed through the solenoid, then the magnetic moment of the rod will be\(...........Am^2\)

In the given circuit diagram, the currents, \({I_1} =  - \,0.3\,A,\,{I_4} = 0.8\,A\) and \({I_5} = 0.4\,A,\) are flowing as shown. The currents \(I_2,\,I_3\) and \(I_6,\) respectively are

A \(\sqrt{34}\,m\) long ladder weighing \(10\,kg\) leans on a frictionless wall. Its feet rest on the floor \(3\,m\) away from the wall as shown in the figure. If \(F_{f}\) and \(F_{w}\) are the reaction forces of the floor and the wall, then ratio of \(F _{ a } / F _{f}\) will be: (Use \(\left.g=10\,m / s ^{2}\right)\)

As shown in the figure. a configuration of two equal point charges \(\left( q _0=+2 \mu C \right)\) is placed on an inclined plane. Mass of each point charge is \(20\,g\). Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height \(h = x \times 10^{-3}\,m\) The value of \(x\) is \(..........\).(Take \(\left.\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\,Nm ^2 C ^{-2}, g=10\,ms ^{-1}\right)\)