A thin glass plate of thickness is \(\frac{{2500}}{3}\,\lambda \) (\(\lambda \) is wavelength of light used) and refractive index \(\mu  = 1.5\) is inserted between one of the slits and the screen in Young's double slit experiment. At a point on the screen equidistant from the slits, the ratio of the intensities before and after the introduction of the glass plate is

The stopping potential in the context of photoelectric effect depends on the following property of incident electromagnetic radiation

A conducting circular loop made of a thin wire, has area \(3.5 \times 10^{-3}\, m^2\) and resistance \(10\,\Omega \). It is placed perpendicular to a time dependent magnetic field \(B(t) = (0.4\,T)\, sin\, (50\, \pi t)\). The field is uniform in space. Then the net charge flowing through the loop during \(t = 0\, s\) and \(t = 10\, ms\) is close to.......\(mC\)

Match List I with List \(II\) Choose the correct answer from the options given below:

In a Vernier Calipers. \(10\) divisions of Vernier scale is equal to the \(9\) divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of \(zero\) of the main scale and \(4^{\text {th }}\) Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to \(1\,mm\). While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between \(30\) and \(31\) divisions of main scale reading and \(6^{\text {th }}\) Vernier scale division exactly. coincides with the main scale reading. The diameter of the spherical body will be \(.......cm\)

The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation: \(K(x) = K_0 + \lambda x\) ( \(\lambda  =\) constant) The capacitance \(C,\) of the capacitor, would be related to its vacuum capacitance \(C_0\) for the relation

The bulk moduli of ethanol, mercury and water are given as \(0.9, 25\) and \(2 .2\) respectively in units of \(10^9\, Nm^{-2}\) . For a given value of pressure, the fractional compression in volume is \(\frac{{\Delta V}}{V}\). Which of the following statements about \(\frac{{\Delta V}}{V}\) for these three liquids is correct ?

From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-captain respectively of the team should be included. Then the total number of ways such a selection can be made, is

A zener diode of power rating \(1.6\,W\) is to be used as voltage regulator. If the zener diode has a breakdown of \(8\,V\) and it has to regulate voltage fluctuating between \(3\,V\) and \(10 \,V\). The value of resistance \(R_5\) for safe operation of diode will be \(.........\Omega\)

An electric field is given by \((6 \hat{i}+5 \hat{j}+3 \hat{k}) \ N / C\). The electric flux through a surface area \(30 \hat{\mathrm{i}}\; m^2\) lying in \(YZ-\)plane (in SI unit) is _______.

Two poles, \(\mathrm{AB}\) of length \(a\) metres and \(\mathrm{CD}\) of length \(\mathrm{a}+\mathrm{b}(\mathrm{b} \neq \mathrm{a})\) metres are erected at the same horizontal level with bases at \(\mathrm{B}\) and \(\mathrm{D} .\) If \(\mathrm{BD}=\mathrm{x}\) and \(\tan \angle\,ACB=\frac{1}{2}\), then:

A thin uniform bar of length \(L\) and mass \(8\,m\) lies on a smooth horizontal table. Two point masses \(m\) and \(2\,m\) moving in the same horizontal plane from opposite sides of the bar with speeds \(2v\) and \(v\) respectively. The masses stick to the bar after collision at a distance \(\frac{L}{3}\) and \(\frac{L}{6}\) respectively from the centre of the bar. If the bar starts rotating about its center of mass as a result of collision, the angular speed of the bar will be

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is