What is the conductivity of a semiconductor sample having electron concentration of \(5 \times 10^{18}\, m^{-3}\), hole concentration of \(5 \times  10^{19}\, m^{-3}\), electron mobility of \(2 .0\, m^2\, v^{-1}\, s^{-1}\) and hole mobility of \(0.01\, m^2\, v^{ -1}\, s^{-1}\) ?........\({\left( {\Omega  - m} \right)^{ - 1}}\) (Take charge of electron as \(1.6 \times 10^{-19}\, C\))

Two identical cells each of emf \(1.5 \,V\) are connected in parallel across a parallel combination voltmeter connected in the circuit measures \(1.2 \,V\). The internal resistance of each cell is.................\(\Omega\)

A block moving horizontally on a smooth surface with a speed of \(40\, {m} / {s}\) splits into two parts with masses in the ratio of \(1: 2\). If the smaller part moves at \(60\, {m} / {s}\) in the same direction, then the fractional change in kinetic energy is :-

First, a set of \({n}\) equal resistors of \(10\; \Omega\) each are connected in series to a battery of emf \(20\; {V}\) and internal resistance \(10\; \Omega .\) A current \(I\) is observed to flow. Then, the \(n\) resistors are connected in parallel to the same battery. It is observed that the current is increased \(20\) times, then the value of \(n\) is .... .

A rectangular loop of sides \(12 \mathrm{~cm}\) and \(5 \mathrm{~cm}\), with its sides parallel to the \(x\)-axis and \(y\)-axis respectively moves with a velocity of \(5 \mathrm{~cm} / \mathrm{s}\) in the positive \(\mathrm{x}\) axis direction, in a space containing a variable magnetic field in the positive \(z\) direction. The field has a gradient of \(10^{-3} \mathrm{~T} / \mathrm{cm}\) along the negative \(\mathrm{x}\) direction and it is decreasing with time at the rate of \(10^{-5} \mathrm{~T} / \mathrm{s}\). If the resistance of the loop is \(6 \mathrm{~m} \Omega\), the power dissipated by the loop as heat is _______ \(\times 10^{-9} \mathrm{~W}\).

A quantity Q is formulated as \(\mathrm{X}^{-2} \mathrm{Y}^{+\frac{3}{2}} \mathrm{Z}^{-\frac{2}{5}} \cdot \mathrm{X}, \mathrm{Y}\) and Z are independent parameters which have fractional errors of \(0.1,0.2\) and 0.5 , respectively in measurement. The maximum fractional error of Q is _______.

In photoelectric effect an em-wave is incident on a metal surface and electrons are ejected from the surface. If the work function of the metal is 2.14 eV and stopping potential is 2 V , what is the wavelength of the em-wave ?
(Given hc \(=1242 \mathrm{eVnm}\) where h is the Planck's constant and c is the speed of light in vaccum.)

A circular hole of radius \(\frac{R}{4}\) is made in a thin uniform disc having mass \(M\) and radius \(R\), as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point \(O\) and perpendicular to the plane of the disc is

In the circuit, given in the figure currents in different branches and value of one resistor are shown. Then potential at point \(B\) with respect to the point \(A\) is\(.......V\)

In an experiment, brass and steel wires of length \(1\,m\) each with areas of cross section \(1\,mm^2\) are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress requires to produced a new elongation of \(0.2\,mm\) is [Given, the Young’s Modulus for steel and brass are respectively \(120\times 10^9\,N/m^2\) and \(60\times 10^9\,N/m^2\) ]