The frequency of echo will be \(.......Hz\) if the train blowing a whistle of frequency \(320\,Hz\) is moving with a velocity of \(36\,km / h\) towards a hill from which an echo is heard by the train driver. Velocity of sound in air is \(330\,m / s\).

The refractive index of a prism with apex angle \(A\) is \(\cot A / 2\). The angle of minimum deviation is _______.

The figure shows a region of length \('l'\) with a uniform magnetic field of \(0.3\, T\) in it and a proton entering the region with velocity \(4 \times 10^{5}\, ms ^{-1}\) making an angle \(60^{\circ}\) with the field. If the proton completes \(10\) revolution by the time it cross the region shown, \(l\) is close to....... \(m\) (mass of proton \(=1.67 \times 10^{-27} \,kg ,\) charge of the proton \(\left.=1.6 \times 10^{-19}\, C \right)\)

A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from \(440\, Hz\) to \(480 \,Hz ,\) when it gets reflected from the wall. If the speed of sound in air is \(345 \,m / s ,\) then the speed of the car is \(.......km/hr\)

When Uranium is bombarded with neutrons, it undergoes fission. The fission reaction can be written as  \({}_{92}{U^{235}} + {}_0{n^1} \to {}_{56}B{a^{141}} + {}_{36}K{r^{92}} + 3x + Q{\rm{( energy)}}\) where three particles named \(x\) are produced and energy \(Q\) is released. What is the name of the particle \(x\) ?

If Rydberg's constant is \(R\), the longest wavelength of radiation in Paschen series will be \(\frac{\alpha}{7 R}\), where \(\alpha=\)____________

One \(kg\) of water, at \(20\,^oC\), is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of \(20\, \Omega \). The rms voltage in the mains is \(200\, V\). Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to.......... \(\min\) [Specific heat of water \(= 4200\, J/kg\, ^oC\)), Latent heat of water \(= 2260\, k\,J/kg\)]

Figure represents the extension (\(\Delta l\)) of a wire of length \(1\) meter, suspended from the ceiling of the room at one end with a load \(W\) connected to the other end. If the cross-sectional area of the wire is \(10^{-5}\) m\(^2\) then the Young's modulus of the wire is __________ N/m\(^2\).

The time period of a satellite in a circular orbit of radius \(R\) is \(T\). The period of another satellite in a circular orbit of radius \(9 R\) is............ \(T\)

In a single slit experiment, a parallel beam of green light of wavelength \(550 \mathrm{~nm}\) passes through a slit of width \(0.20 \mathrm{~mm}\). The transmitted light is collected on a screen \(100 \mathrm{~cm}\) away. The distance of first order minima from the central maximum will be \(\mathrm{x} \times 10^{-5} \mathrm{~m}\). The value of \(\mathrm{x}\) is _______.

Two persons \(A\) and \(B\) perform same amount of work in moving a body through a certain distance \({d}\) with application of forces acting at angle \(45^{\circ}\) and \(60^{\circ}\) with the direction of displacement respectively. The ratio of force applied by person \(A\) to the force applied by person \(B\) is \(\frac{1}{\sqrt{x}}\). The value of \(x\) is ...... .

Given below are two statements : Statement-I: When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be \(0^{\circ}\). Statement-II: The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well : In the light of above statement, choose the correct answer from the options given below.