At what distance above and below the surface of the earth a body will have same weight? (take radius of earth as \(R\).)

The horizontal component of earth's magnetic field at a place is \(3.5 \times 10^{-5} \mathrm{~T}\). A very long straight conductor carrying current of \(\sqrt{2} A\) in the direction from South east to North West is placed. The force per unit length experienced by the conductor is _______ \(\times 10^{-6} \mathrm{~N} / \mathrm{m}\).

A freshly prepared radioactive source of half life \(2\) hours \(30\) minutes emits radiation which is \(64\) times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be hours.

A travelling microscope has \(20\) divisions per \(cm\) on the main scale while its Vernier scale has total \(50\) divisions and \(25\) Vernier scale divisions are equal to \(24\) main scale divisions, what is the least count of the travelling microscope \(..........\,cm\)

Two simple harmonic motion, are represented by the equations \({y}_{1}=10 \sin \left(3 \pi {t}+\frac{\pi}{3}\right)\) \(y_{2}=5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t)\) Ratio of amplitude of \({y}_{1}\) to \({y}_{2}={x}: 1\). The value of \({x}\) is ...... .

The velocity of upper layer of water in a river is \(36 kmh ^{-1}\). Shearing stress between horizontal layers of water is \(10^{-3} Nm ^{-2}\). Depth of the river is \(m\). (Co-efficiency of viscosity of water is \(10^{-2} \,Pa . s\) )

Asseretion \(A:\) If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is \(5\, {mm}\) and there are \(50\) total divisions on circular scale, then least count is \(0.001\, {cm}\). Reason \(R:\) Least Count \(=\frac{\text { Pitch }}{\text { Total divisions on circular scale }}\) In the light of the above statements, choose the most appropriate answer from the options given below:

From the \(v\) - \(t\) graph shown. the ratio of distance to displacement in \(25\,s\) of motion

A linearly polarized electromagnetic wave in vacuum is \(E=3.1 \cos \left[(1.8) z-\left(5.4 \times 10^{6}\right) {t}\right] \hat{\text { i }}\, {N} / {C}\) is incident normally on a perfectly reflecting wall at \(z=a\). Choose the correct option

The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in the visible region?

Two light beams of intensities \(4\,I\) and \(9\,I\) interfere on a screen. The phase difference between these beams on the screen at point \(A\) is \(zero\) and at point \(B\) is \(\pi\). The difference of resultant intensities, at the point \(A\) and \(B\), will be \(....I\).

Given below are two statements: Statement \(I:\) If heat is added to a system, its temperature must increase. Statement \(II:\) If positive work is done by a system in a thermodynamic process, its volume must increase. In the light of the above statements, choose the correct answer from the options given below