The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is

Two isolated conducting spheres \(S_{1}\) and \(S_{2}\) of radius \(\frac{2}{3} R\) and \(\frac{1}{3} R\) have \(12\, \mu C\) and \(-3\, \mu C\) charges, respectively, and are at a large distance from each other. They are now  onnected by a conducting wire. A long time after this is done the charges on \(S_{1}\) and \(S_{2}\) are respectively

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity \(C\) remains constant. If during this process the relation of pressure \(P\) and volume \(V\) is given by \(PV^n =\) constant, then n is given by (Here \(C_p\) and \(C_v\) are molar specific heat at constant pressure and constant volume, respectively) :

In the cube of side \(a\) shown in the figure, the vector from the central point of the face \(ABOD\) to the central point of the face \(BEFO\) will be

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights \(h_{sph}\) and \(h_{cyl}\) on the incline. The radio \(\frac{{{h_{sph}}}}{{{h_{cyl}}}}\) is given by

The Young's double slit interference experiment is performed using light consisting of 480 nm and 600 nm wavelengths to form interference patterns. The least number of the bright fringes of 480 nm light that are required for the first coincidence with the bright fringes formed by 600 nm light is _______.

Two satellites \(S _{1}\) and \(S _{2}\) are revolving in circular orbits around a planet with radius \(R _{1}=3200 \,km\) and \(R _{2}=800\, km\) respectively. The ratio of speed of satellite \(S_{1}\) to the speed of satellite \(S_{2}\) in their respective orbits would be \(\frac{1}{ x }\) where \(x =\)

A rod \(C D\) of thermal resistance \(10.0\; {KW}^{-1}\) is joined at the middle of an identical rod \({AB}\) as shown in figure, The end \(A, B\) and \(D\) are maintained at \(200^{\circ} {C}, 100^{\circ} {C}\) and \(125^{\circ} {C}\) respectively. The heat current in \({CD}\) is \({P}\) watt. The value of \({P}\) is ... .

Magnetic flux (in weber) in a closed circuit of resistance \(20\,\Omega\) varies with time \(t(s)\) as \(\phi=8 t ^{2}-9 t +5\). The magnitude of the induced current at \(t =0.25\,s\) will be \(...mA\)

One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, \(27\,^oC\).The work done on the gas will be

Interference pattern is observed at \('P'\) due to superimposition of two rays coming out from a source \('S'\) as shown in the figure. The value of \('I'\) for which maxima is obtained at \('P'\) is: ( \(R\) is perfect reflecting surface)

Consider following statements for refraction of light through prism, when angle of deviation is minimum.
(A) The refracted ray inside prism becomes parallel to the base.
(B) Larger angle prisms provide smaller angle of minimum deviation.
(C) Angle of incidence and angle of emergence becomes equal.
(D) There are always two sets of angle of incidence for which deviation will be same except at minimum deviation setting.
(E) Angle of refraction becomes double of prism angle.
Choose the correct answer from the options given below.