A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is \(6.4\) m. The speed of the bullets from the gun is ______ m/s.
(take \(g=10\) m/s\(^2\))

A Carnot engine absorbs \(1000\,J\) of heat energy from a reservoir at \(127\,^oC\) and rejects \(600\,J\) of heat energy during each cycle. The efficiency of engine and temperature of sink will be

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases.
Reason (R): Free expansion of an ideal gas is an irreversible and an adiabatic process.
In the light of the above statements, choose the correct answer from the options given below :

10 mole of oxygen is heated at constant volume from \(30^{\circ} C\) to \(40^{\circ} C\). The change in the internal energy of the gas is _________ cal. (The molecular specific heat of oxygen at constant pressure, \(C _{ p }=7 cal . / mol ^{\circ} C\) and \(\left.R =2 cal . / mol ^{\circ} C .\right)\)

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 :

The density of a material in \(SI\, units\) is \(128\, kg\, m^{-3}\). In certain units in which the unit of length is \(25\, cm\) and the unit of mass \(50\, g\), the numerical value of density of the material is

In a Young's double slit experiment, the source is white light. One of the slits is covered by red filter and another by a green filter. In this case...

A swimmer wants to cross a river from point \(A\) to point \(B\). Line \(A B\) makes an angle of \(30^{\circ}\) with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle \(\theta\) with the line \({AB}\) should be \(^{\circ}\), so that the swimmer reaches point \({B}\).

A straight wire carrying a current of \(14\,A\) is bent into a semicircular are of radius \(2.2\,cm\) as shown in the figure. The magnetic field produced by the current at the centre \((O)\) of the arc. is \(.........\,\times 10^{-4}\, T\)

An electromagnetic wave travelling in the \(x-\) direction has frequency of \(2 \times 10^{14}\,Hz\) and electric field amplitude of \(27\,Vm^{-1}\) . From the options given below, which one describes the magnetic field for this wave ?

The magnetic flux through a coil perpendicular to its plane is varying according to the relation \(\phi=\) \(\left(5 t^{3}+4 t^2+2 t-5\right) \; Weber\). If the resistant of the coil is \(5 \; ohm\), then the induced current through the coil at \(t =2 \; sec\) will be \(....\,A\)

An electron is released from rest near an infinite non-conducting sheet of uniform charge density ' \(-\sigma\) '. The rate of change of de-Broglie wave length associated with the electron varies inversely as \(\mathrm{n}^{\text {th }}\) power of time. The numerical value of \(n\) is ________.