A monochromatic light of frequency \(5 \times 10^{14} \mathrm{~Hz}\) travelling through air, is incident on a medium of refractive index ' 2 '. Wavelength of the refracted light will be :

An ideal battery of \(4\, V\) and resistance \(R\) are connected in series in the primary circuit of a potentiometer of length \(1\, m\) and resistance \(5\,\Omega \) . The value of \(R\), to give a difference of \(5\, mV\) across \(10\, cm\) of potentiometer wire, is: ................ \(\Omega\)

Two equal resistances when connected in series to a battery, consume electric power of \(60\,W.\) If these resistances are now connected in parallel combination to the same battery, the electric power consumed will be .............. \(W\)

A porter lifts a heavy suitcase of mass \(80\, {kg}\) and at the destination lowers it down by a distance of \(80\, {cm}\) with a constant velocity. Calculate the workdone by the porter in lowering the suitcase. (take \(g=9.8\, {ms}^{-2}\) ) (In \({J}\))

A uniform rod of length \('l'\) is pivoted at one of its ends on a vertical shaft of negligible radius When the shaft rotates at angular speed \(\omega\) the rod makes an angle \(\theta\) with it (see figure). To find \(\theta\) equate the rate of change of angular momentum (direction going into the paper ) \(\frac{ m \ell^{2}}{12} \omega^{2} \sin \theta \cos \theta\) about the centre of mass \((CM)\) to the torque provided by the horizontal and vertical forces \(F_{H}\) and \(F_{V}\) about the CM. The value of \(\theta\) is then such that:

If two charges \(q _1\) and \(q _2\) are separated with distance ' \(d\) ' and placed in a medium of dielectric constant \(K\). What will be the equivalent distance between charges in air for the same electrostatic force?

A source of potential difference \(V\) is connected to the combination of two identical capacitors as shown in the figure. When key ' \(K\) ' is closed, the total energy stored across the combination is \(E _{1}\). Now key ' \(K\) ' is opened and dielectric of dielectric constant 5 is introduced between the plates of the capacitors. The total energy stored across the combination is now \(E _{2}\). The ratio \(E _{1} / E _{2}\) will be :

Math List \(I\) with List \(II\) Choose the correct answer from the option given below:

A vessel of depth \(d\) is half filled with oil of refractive index \(n_1\) and the other half is filled with water of refractive index \(n_2\). The apparent depth of this vessel when viewed from above will be

Two electrons each are fixed at a distance \('2d'\). A third charge proton placed at the midpoint is displaced slightly by a distance \(x ( x << d )\) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency : \(( m =\) mass of charged particle)

Following figure shows two processes \(A\) and \(B\) for a gas. If \(\Delta Q_A\) and \(\Delta Q_B\) are the amount of heat absorbed by the system in two cases, and \(\Delta U_A\) and \(\Delta U_B\) are changes in internal energies, respectively, then

Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths \(\lambda _N,\,\lambda _A\)  respectively. The ratio \(\frac{{{\lambda _N}}}{{{\lambda _A}}}\)  is closest to

A spherical surface separates two media of refractive indices 1 and 1.5 as shown in figure. Distance of the image of an object ' O ' is :
( C is the center of curvature of the spherical surface and \(R\) is the radius of curvature)