A motor operating on 100 V draws a current of 1 A. If the efficiency of the motor is \(91.6 \%\), then the loss of power in units of \(\mathrm{cal} / \mathrm{s}\) is _________.

Consider the following statements : \(A.\) Atoms of each element emit characterstics spectrum. \(B.\) According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit. \(C.\) The density of nuclear matter depends on the size of the nucleus. \(D.\) A free neutron is stable but a free proton decay is possible. \(E.\) Radioactivity is an indication of the instability of nuclei. Choose the correct answer from the options given below 

The Boolean expression \(\mathrm{Y}=\mathrm{A} \overline{\mathrm{B}} \mathrm{C}+\overline{\mathrm{A}} \overline{\mathrm{C}}\) can be realised with which of the following gate configurations.
A. One 3-input AND gate, 3 NOT gates and one 2input OR gate, One 2-input AND gate,
B. One 3-input AND gate, 1 NOT gate, One 2input NOR gate and one 2-input OR gate
C. 3-input OR gate, 3 NOT gates and one 2-input AND gate
Choose the correct answer from the options given below.

A cylindrical wire of radius \(0.5 \,mm\) and conductivity \(5 \times 10^{7}\, S / m\) is subjected to an electric field of \(10 \,mV / m .\) The expected value of current in the wire will be \(x ^{3} \,\pi mA\). The value of \(x\) is ......

A thin smooth rod of length \(L\) and mass \(M\) is rotating freely with angular speed \({\omega _0}\) about an axis perpendicular to the rod and passing through its centre. Two beads of mass \(m\) and negligible size are at the centre of the rod initially. The beads are free to slide along the rod. The angular speed of the system, when the beads reach the opposite ends of the rod will be

For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where \(\gamma\) is the ratio of specific heats):

Velocity-time graph for a body of mass \(10\, kg\) is shown in figure. Work-done on the body in first two seconds of the motion is  ................ \(\mathrm{J}\)

The equivalent resistance between \(A\) and \(B\) is \(......\)

The \(rms\) speeds of the molecules of Hydrogen, Oxygen and Carbondioxide at the same temperature are \({V}_{{H}}, {V}_{0}\) and \({V}_{{C}}\) respectively then

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 ________.

A series \(LCR\) circuit is connected to an ac source of \(220\,V , 50 Hz\). The circuit contain a resistance \(R=100 \Omega\) and an inductor of inductive reactance \(X_L=79.6 \Omega\). The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be \(..........\mu F\).

What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature \(T \,?\left( k _{ B }\right.\) is Boltzmann constant)