The equation of a plane progressive wave is given by \(y = 5\cos\pi\left(200t - \dfrac{x}{150}\right)\) where \(x\) and \(y\) are in cm and \(t\) is in second. The velocity of the wave is _______ m/s.

The initial mass of a rocket is \(1000\, {kg} .\) Calculate at what rate the fuel (In \({kg} {s}^{-1}\)) should be burnt so that the rocket is given an acceleration of \(20 \,{ms}^{-2}\). The gases come out at a relative speed of \(500\, {ms}^{-1}\) with respect to the rocket : [Use \( g = 10\, {m} / {s}^{2}\) ]

In a common emitter amplifier circuit using an \(n-p-n\) transistor, the phase difference between the input and the output voltages will be.....\(^o\)

Let a total charge \(2Q\) be distributed in a sphere of radius \(R\), with the charge density given by \(\rho(r) = kr\), where \(r\) is the distance from the centre. Two charges \(A\) and \(B\), of \(-Q\) each, are placed on diametrically opposite points, at equal distance, \(a\), from the centre. If \(A\) and \(B\) do not experience any force, then

Three masses \(M =100\,kg , m _{1}=10\,kg\) and \(m_{2}=20\,kg\) are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. \(A\) force \(F\) is applied on the system so that the mass \(m_{2}\) moves upward with an acceleration of \(2\,ms ^{-2}\). The value of \(F\) is \(......N\) \(\left(\right.\) Take \(\left.g =10\,ms ^{-2}\right)\)

Two inclined planes are placed as shown in figure. A block is projected from the Point \(A\) of inclined plane \(A B\) along its surface with a velocity just sufficient to carry it to the top Point \(B\) at a height \(10 m\). After reaching the Point \(B\) the block slides down on inclined plane \(BC\). Time it takes to reach to the point \(C\) from point \(A\) is \(t (\sqrt{2}+1) s\). The value of \(t\) is........(use \(g =10 m / s ^{2}\) )

A rectangular loop of length \(2.5 \mathrm{~m}\) and width \(2 \mathrm{~m}\) is placed at \(60^{\circ}\) to a magnetic field of \(4 \mathrm{~T}\). The loop is removed from the field in \(10 \ \mathrm{sec}\). The average emf induced in the loop during this time is

An artillery piece of mass \(M_1\) fires a shell of mass \(\mathrm{M}_2\) horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is _______.

A particle of mass \(4\, {M}\) at rest disintegrates into two particles of mass \({M}\) and \(3 \,{M}\) respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass \(M\) to that of mass \(3\, {M}\) will be :

The potential energy \((U)\) of a diatomic molecule is a function dependent on \(r\) (interatomic distance) as \(U =\frac{\alpha}{ r ^{10}}-\frac{\beta}{ r ^{5}}-3\) where, \(\alpha\) and \(\beta\) are positive constants. The equilibrium distance between two atoms will be \(\left(\frac{2 \alpha}{\beta}\right)^{\frac{a}{b}},\) where a \(=\) ..........

With reference to the observations in photo-electric effect, identify the correct statements from below: \(A.\) The square of maximum velocity of photoelectrons varies linearly with frequency of incident light. \(B.\) The value of saturation current increases on moving the source of light away from the metal surface. \(C.\) The maximum kinetic energy of photo-electrons decreases on decreasing the power of LED (light emitting diode) source of light. \(D.\) The immediate emission of photo-electrons out of metal surface can not be explained by particle nature of light/electromagnetic waves. \(E.\) Existence of threshold wavelength can not be explained by wave nature of light/electromagnetic waves. Choose the correct answer from the options given below:

In an adiabatic process, the density of a diatomic gas becomes \(32\) times its initial value. The final pressure of the gas is found to be \(n\) times the initial pressure. The value of \(n\) is

An electron accelerated through a potential difference \(V_1\) has a de-Broglie wavelength of \(\lambda\). When the potential is changed to \(V _2\), its de-Broglie wavelength increases by \(50 \%\). The value of \(\left(\frac{ V _1}{ V _2}\right)\) is equal to :