In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius \(0.5 \times 10^{-10}\,m\). If the speed of electron is \(2.2 \times 10^{6} \;{m} / {s}\), then the current associated with the electron will be \(....\,\times 10^{-2} \;{mA}\). [Take \(\pi\) as \(\left.\frac{22}{7}\right]\)

A concave-convex lens of refractive index 1.5 and the radii of curvature of its surfaces are 30 cm and 20 cm , respectively. The concave surface is upwards and is filled with a liquid of refractive index 1.3. The focal length of the liquid-glass combination will be _______.

The equation of a wave travelling on a string is \(\mathrm{y}=\sin [20 \pi \mathrm{x}+10 \pi \mathrm{t}]\), where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

Two trains ' \(A\) ' and ' \(B\) ' of length ' \(l\) ' and ' \(4 l\) ' are travelling into a tunnel of length ' \(L\) ' in parallel tracks from opposite directions with velocities \(108\,km / h\) and \(72\,km / h\), respectively. If train '\(A\)' takes \(35\,s\) less time than train ' \(B\) ' to cross the tunnel then, length ' \(L\) ' of tunnel is \(...........\,m\) \(\text { (Given } L=60 l \text { ) }\)

The equation of a circle is given by \(x^2+y^2=a^2\), where \(a\) is the radius. If the equation is modified to change the origin other than \((0,0)\), then find out the correct dimensions of \(A\) and \(B\) in a new equation: \((x-A t)^2+\left(y-\frac{t}{B}\right)^2=a^2\).The dimensions of \(t\) is given as \(\left[ T ^{-1}\right]\).

Given below are two statements: one is labelled as Assertion\((A)\) and the other is labelled as Reason \((R).\) \(Assertion\) \((A)\) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading. \(Reason\) \((R)\) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling. In the light of the above statements, choose the correct answer from the options given below :

The following logic gate is equivalent to

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is \(1: 4\), then \(A.\) The \(r.m.s\). velocity of gas molecules in two vessels will be the same. \(B.\) The ratio of pressure in these vessels will be \(1: 4\) \(C.\) The ratio of pressure will be \(1: 1\) \(D.\) The \(r.m.s.\) velocity of gas molecules in two vessels will be in the ratio of \(1: 4\)

If the potential energy between two molecules is given by \(U =\frac{-A }{ r ^{6}}+\frac{ B }{ r ^{12}},\) then at equilibrium, separation between molecules, and the potential energy are

If the refractive index of the material of a prism is \(\cot \left(\frac{A}{2}\right)\), where \(A\) is the angle of prism then the angle of minimum deviation will be

An unknown transistor needs to be identified as a \(npn\)  or  \(pnp\) type. A multimeter, with \(+ve\) and \(-ve\)  terminals, is used to measure resistance between different terminals of transistor. If terminal \(2\) is the base of the transistor then which of the following is correct for a \(pnp\) transistor?