A zener diode of power rating \(2\, {W}\) is to be used as a voltage regulator. If the zener diode has a breakdown of \(10 \,{V}\) and it has to regulate voltage fluctuated between \(6\, {V}\) and \(14\, {V}\), the value of \({R}_{{s}}\) for safe operation should be \(....\Omega\)

Match List - I with List - II.

List - I	List - II
(A) Electric field inside (distance \(r>0\) from center) of a uniformly charged spherical shell with surface charge density \(\sigma\), and radius R.	(I) \(\sigma / \epsilon_0\)
(B) Electric field at distance \(r >0\) from a uniformly charged infinite plane sheet with surface charge density \(\sigma\).	(II) \(\sigma / 2 \epsilon_0\)
(C) Electric field outside (distance \(r>0\) from center) of a uniformly charged spherical shell with surface charge density \(\sigma\), and radius R.	(III) \(0\)
(D) Electric field between 2 oppositely charged infinite plane parallel sheets with uniform surface charge density \(\sigma\).	(IV) \(\frac{\sigma R^2}{\epsilon_0 r^2}\)

Choose the correct answer from the options given\(\text{ }\)below\(\text{ }\):

A deviation of \(2^{\circ}\) is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass are \(0.02\) and \(0.03\) respectively and refractive index for yellow light for these glasses are \(1.5\) and \(1.6\) respectively. The refracting angles for crown glass prism will be \(........\,^{\circ}\) (in degree) (Round off to the Nearest Integer)

A granite rod of \(60\ cm\) length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is \(2.7 \times 10^3 \) \(kg/m^3\) and its Young's modulus is \(9.27 \times 10^{10}\) \(Pa\) What will be the fundamental frequency of the longitudinal vibrations .... \(kHz\) ?

A thin transparent film with refractive index 1.4 , is held on circular ring of radius 1.8 cm . The fluid in the film evaporates such that transmission through the film at wavelength 560 nm goes to a minimum every 12 seconds. Assuming that the film is flat on its two sides, the rate of evaporation is ____ \(\pi \times 10^{-13} \mathrm{~m}^3 / \mathrm{s}\).

Consider an electrical circuit containing a two way switch \(^{\prime}{S}^{\prime}\). Initially \({S}\) is open and then \({T}_{1}\) is connected to \({T}_{2} .\) As the current in \({R}=6 \,\Omega\) attains a maximum value of steady state level, \({T}_{1}\) is disconnected from \({T}_{2}\) and immediately connected to \({T}_{3} .\) Potential drop across \({r}=3\, \Omega\) resistor immediately after \(T_{1}\) is connected to \(T_{3}\) is \(....\,V.\) (Round off to the Nearest Integer)

A rod of length \(50\,cm\) is pivoted at one end. It is raised such that if makes an angle of \(30^o\) fro the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in \(rad\,s^{-1}\) ) will be \((g = 10\,ms^{-2})\)

A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is \(\sqrt 3\) , then the angle of incidence....\(^o\)