An electron in the ground state of the hydrogen atom has the orbital radius of \(5.3 \times 10^{-11} \mathrm{~m}\) while that for the electron in third excited state is \(8.48 \times 10^{-10} \mathrm{~m}\). The ratio of the de Broglie wavelengths of electron in the excited state to that in the ground state is _______.

Match List \(I\) with List \(II\) :

List \(I\) (Physical Quantity)	List \(II\) (Dimensional Formula)
\((A)\) Pressure gradient	\((I)\) \(\left[ M ^0 L ^2 T ^{-2}\right]\)
\((B)\) Energy density	\((II)\) \(\left[ M ^1 L ^{-1} T ^{-2}\right]\)
\((C)\) Electric Field	\((III)\) \(\left[ M ^1 L ^{-2} T ^{-2}\right]\)
\((D)\) Latent heat	\((IV)\) \(\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]\)

Choose the correct answer from the options given below:

The colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor is:

The equivalent capacitance between points \(A\) and \(B\) in below shown figure will be..........\(\mu F\).

The energy released in the fusion of \(2 \mathrm{~kg}\) of hydrogen deep in the sun is \(\mathrm{E}_{\mathrm{H}}\) and the energy released in the fission of \(2 \mathrm{~kg}\) of \({ }^{235} \mathrm{U}\) is \(E_U\). The ratio \(\frac{E_H}{E_U}\) is approximately _______. (Consider the fusion reaction as \(4{ }_1^1 \mathrm{H}+2 \mathrm{e}^{-} \rightarrow{ }_2^4 \mathrm{He}+2 \mathrm{v}+6 \gamma+26.7 \mathrm{MeV}\), energy released in the fission reaction of \({ }^{235} \mathrm{U}\) is \(200 \mathrm{MeV}\) per fission nucleus and \(\mathrm{N}_{\mathrm{A}}=6.023 \times 10^{23}\) )

A charge particle moving in magnetic field \(B\), has the components of velocity along \(B\) as well as perpendicular to \(B\). The path of the charge particle will be

A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws \(n\) balls per second, the maximum height the balls can reach is

A capacitor of capacitance \(500\,\mu F\) is charged completely using a dc supply of \(100\,V\). It is now connected to an inductor of inductance \(50\,mH\) to form an \(LC\) circuit. The maximum current in \(LC\) circuit will be \(.........A\).

A wire having a linear mass density \(9.0 \times 10^{-4} \;{kg} / {m}\) is stretched between two rigid supports with a tension of \(900\; {N}\). The wire resonates at a frequency of \(500\;{Hz}\). The next higher frequency at which the same wire resonates is \(550\; {Hz}\). The length of the wire is \(...... {m}\)

Radiation \(p\) with wavelength \(6561\;\mathring A\) falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of \(3 \times 10^{-4}\; T\). If the radius of the largest circular path followed by the electrons is \(10 \;\mathrm{mm},\) the work function of the metal is close to ............... \(eV\)

Consider two charged metallic spheres \(S_{1}\) and \(\mathrm{S}_{2}\) of radii \(\mathrm{R}_{1}\) and \(\mathrm{R}_{2},\) respectively. The electric \(\left.\text { fields }\left.\mathrm{E}_{1} \text { (on } \mathrm{S}_{1}\right) \text { and } \mathrm{E}_{2} \text { (on } \mathrm{S}_{2}\right)\) on their surfaces are such that \(\mathrm{E}_{1} / \mathrm{E}_{2}=\mathrm{R}_{1} / \mathrm{R}_{2} .\) Then the ratio \(\left.\mathrm{V}_{1}\left(\mathrm{on}\; \mathrm{S}_{1}\right) / \mathrm{V}_{2} \text { (on } \mathrm{S}_{2}\right)\) of the electrostatic potentials on each sphere is 

A force acts on a \(2\,kg\) object so that its position is given as a function of time as \(x= 3t^2 + 5.\) What is the work done by this force in first \(5\,seconds\) ? ................ \(\mathrm{J}\)

An inductor coil stores \(64\, {J}\) of magnetic field energy and dissipates energy at the rate of \(640\, {W}\) when a current of \(8\, {A}\) is passed through it. If this coil is joined across an ideal battery, find the time constant of the circuit in seconds