A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is \(x \times 10^{15}\,Hz\). The value of \(x\) is (Given \(h =4.25 \times 10^{-15}\,eVs\) )

A person whose mass is \(100\, {kg}\) travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as \(10\) \({m} / {s}^{2}\) and \(4 \,{m} / {s}^{2}\) respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time.

The height of victoria falls is \(63\, {m}\). What is the difference in temperature of water at the top and at the bottom of fall ? (In \(^{\circ} {C}\)) [Given \(1\, {cal}=4.2\, {J}\) and specific heat of water \(\left.=1 \,{cal} \,{g}^{-1}\;{ }^{\circ}\, {C}^{-1}\right]\)

The average kinetic energy of a molecule of the gas is

A Carnot freezer takes heat from water at \(0\,^oC\) inside it and rejects it to the room at a temperature of \(27\,^oC\). The latent heat of ice is \(336 \times 10^3\, J\,kg^{-1}\).  lf \(5\, kg\) of water at \(0\,^oC\) is converted into ice at  \(0\,^oC\) by the freezer, then the energy consumed by the freezer is close to

A uniformly tapering conical wire is made from a material of Young's modulus \(Y\)  and has a normal, unextended length \(L.\) The radii, at the upper and lower ends of this conical wire, have values \(R\) and \(3R,\)  respectively. The upper end of the wire is fixed to a rigid support and a mass \(M\) is suspended from its lower end. The equilibrium extended length, of this wire, would equal 

The electric field in a region is given \(\overrightarrow{ E }=\left(\frac{3}{5} E _{0} \hat{ i }+\frac{4}{5} E _{0} \hat{ j }\right) \frac{ N }{ C } .\) The ratio of flux of reported field through the rectangular surface of area \(0.2\, m ^{2}\) (parallel to \(y - z\) plane) to that of the surface of area \(0.3\, m ^{2}\) (parallel to \(x - z\) plane \()\) is \(a : b ,\) where \(a =\) ............. [Here \(\hat{ i }, \hat{ j }\) and \(\hat{ k }\) are unit vectors along \(x , y\) and \(z-\)axes respectively]

In the experimental setup of meter bridge shown in the figure, the null point is obtained at a distance of \(40\,cm\) from \(A\). If a \(10\,\Omega \) resistor is connected in series with \(R_1\), the null point shifts by \(10\,cm\). The resistance that should be connected in parallel with \(\left( {{R_1} + 10} \right)\,\Omega \) such that the null point shifts back to its initial position is .............. \(\Omega\)

Calculate the limit of resolution of a telescope objective having a diameter of \(200\, cm\), if it has to detect light of wavelength \(500\, nm\) coming from a star