Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of \(\mathrm{Li}^{++}\)ion in its ground state is given by \(\frac{1}{X} a_0\), where \(X=\) _______. (Where \(\mathrm{a}_0\) is the first Bohr's radius.)

A particle executes simple harmonic motion and is located at \(x = a, b\)  and  \(c\) at times \(t_0, 2t_0\) and \(3t_0\) respectively. The frequency of the oscillation is

Which of the following Maxwell's equations is valid for time varying conditions but not valid for static conditions

A sample of radioactive material \(A\), that has an activity of \(10\, mCi\, (1\, Ci = 3.7 \times 10^{10}\, decays/s)\), has twice the number of nuclei as another sample of different radioactive material \(B\) which has an activity of \(20\, mCi\). The correct choices for half-lives of \(A\) and \(B\) would then be respectively

Water of volume \(2\, L\) in a closed container is heated with a coil of \(1\,kW\). While water is heated, the container loses energy at a rate of \(160\, J/s\) . In how much time will the temperature of water rise from \(27\,^oC\) to \(77\,^oC\) ? (Specific heat of water is \(4.2\, kJ/kg\) and that of the container is negligible)

In the circuit diagram shown in figure given below, the current flowing through resistance \(3\, \Omega\) is \(\frac{ x }{3}\,A\). The value of \(x\) is \(...........\)

An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as \(100\) Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by \(30^{\circ}\) in clockwise direction, the intensity of emerging light will be .......... Lumens.

A plane electromagnetic wave with frequency of \(30 {MHz}\) travels in free space. At particular point in space and time, electric field is \(6 {V} / {m}\). The magnetic field at this point will be \({x} \times 10^{-8} {T}\). The value of \({x}\) is ..... .

In a scries \(LCR\) resonance circuit, if we change the resistance only, from a lower to higher value

A rod of length \(L\) at room temperature and uniform area of cross section \(A\), is made of a metal having coefficient of linear expansion \(\alpha {/^o}C\). It is observed that an external compressive force \(F\), is applied on each of its ends, prevents any change in the length of the rod, when it temperature rises by \(\Delta \,TK\). Young’s modulus, \(Y\), for this metal is

A thin disc of radius \(b = 2a\)  has a concentric hole of radius \('a'\) in it (see figure). It carries uniform surface charge \('\sigma '\) on it. If the electric field on its axis at height \('h'\) \((h << a)\) from its centre is given as \('Ch'\) then value of \('C'\) is