A train blowing a whistle of frequency \(320\,Hz\) approaches an observer standing on the platform at a speed of \(66\,m / s\). The frequency observed by the observer will be (given speed of sound \(=330\,ms ^{-1}\) ) \(.............Hz\).

Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are \(1\, hour\) and \(8\, hours\) respectively. The radius of the orbit of nearer satellite is \(2 \times 10^{3}\, {km}\). The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is \(\frac{\pi}{{x}}\, {rad} \,{h}^{-1}\) where \({x}\) is ..... .

A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains:

A \(9\, V\) battery with internal resistance of \(0.5\,\Omega \) is connected across an infinite network as shown in the figure. All ammeters \(A_1 , A_2, A_3\) and voltmeter \(V\) are ideal. Choose correct statement

An engine operating between the boiling and freezing points of water will have \(1.\) efficiency more than \(27 \%\) \(2.\) efficiency less than the efficiency a Carnot engine operating between the same two temperatures. \(3.\) efficiency equal to \(27 \%\) \(4.\) efficiency less than \(27 \%\)

The total kinetic energy of \(1\) mole of oxygen at \(27^{\circ} \mathrm{C}\) is : [Use universal gas constant \((R)=8.31 \mathrm{~J} / \mathrm{mole} \mathrm{K}\) ]

Find the distance of the image from object \(O\), formed by the combination of lenses in the figure : (in \(cm\))

Which of the following combinations has the dimension of electrical resistance ( \({ \varepsilon _0}\) is the permittivity of vacuum and \({\mu _0}\) is the permeability of vacuum) ?

Within a spherical charge distribution of charge density \(\rho \left( r \right)\), \(N\) equipotential surfaces of potential \({V_0},{V_0} + \Delta V,{V_0} + 2\Delta V,\)\(.....{V_0} + N\Delta V\left( {\Delta V > 0} \right),\) are drawn and have increasing radii \(r_0, r_1, r_2,......r_N\), respectively. If the difference in the radii of the surfaces is constant for all values of \(V_0\) and \(\Delta V\) then

A solid metal cube of edge length \(2\, cm\) is moving in a positive \(y-\) direction at a constant speed of \(6\, m/s\). There is a uniform magnetic field of \(0.1\, T\) in the positive \(z-\) direction. The potential difference between the two faces of the cube perpendicular to the \(x-\) axis, is.....\(mV\)