A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time the magnet will

The circuit shown below is working as a \(8\; \mathrm{V}\;dc\) regulated voltage source. When \(12 \;\mathrm{V}\) is used as input, the power dissipated (in \(\mathrm{mW}\) ) in each diode is (considering both zener diodes are identical)

In the given figure, the value of \(V_{0}\) will be \(.....V\).

The height of any point \(P\) above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point \(P\) will be : (Given \(g=\) acceleration due to gravity at the surface of earth)

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

\(10\) divisions on the main scale of a Vernier calliper coincide with \(11\) divisions on the Vernier scale. If each division on the main scale is of \(5\) units, the least count of the instrument is _______.

The acceleration due to gravity on the surface of earth is \(g\). If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :

A \(27\, mW\) lager beam has a cross -sectional area of \(10\, mm^2\). The magnitude of the maximum electric field in this electromagnetic wave is given by:........\(kV/m\) [Given permittivity of space \({ \in _0} = 9 \times {10^{ - 12}}\, SI\, units\), speed of light \(c = 3 \times 10^8\, m/s\)]

Let \(f(x)=4 \cos ^3 x+3 \sqrt{3} \cos ^2 x-10\). The number of points of local maxima of \(f\) in interval \((0,2 \pi)\) is:

 Let \(y=y(x)\) be the solution curve of the differential equation \(\frac{d y}{d x}=\frac{y}{x}\left(1+x y^2\left(1+\log _e x\right)\right)\) \(x > 0, y(1)=3\). Then \(\frac{y^2(x)}{9}\) is equal to :

If for the matrix, \(A =\left[\begin{array}{cc}1 & -\alpha \\ \alpha & \beta\end{array}\right], AA ^{ T }= I _{2},\) then the value of \(\alpha^{4}+\beta^{4}\) is ....... .

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 \(.......cm\)

A committee of \(4\) persons is to be formed from \(2\) ladies, \(2\) old men and \(4\) young men such that it includes at least \(1\) lady, at least \(1\) old man and at most \(2\) young men. Then the total number of ways in which this committee can be formed is