A musician using an open flute of length \(50\,cm\) produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of \(10 \,km/h.\) If the wave speed is \(330\,m/s,\) the frequency heard by the running person shall be close to...... \(Hz\)

Two planets have masses \(M\) and \(16\, M\) and their radii are \(a\) and \(2\, a\) respectively. The separation between the centres of the planets is \(10\, a.\) A body of mass \(m\) is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firing speed needed is

If one were to apply Bohr model to a particle of mass \('m'\) and charge \('q'\) moving in a plane under the influence of a magnetic field \('B',\) the energy of the charged particle in the \(n^{th}\) level will be

The box of a pin hole camera, of length \(L\), has a hole of radius \(a\). It is assumed that when the hole is illuminated by a parallel beam of light of wavelength \(\lambda\), the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size ( say \(b_{min}\)) when

A wheel is rotaing freely with an angular speed \(\omega\) on a shaft. The moment of inertia of the wheel is \(I\) and the moment of inertia of the shaft is negligible. Another wheel of momet of inertia \(3I\) initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is :

A particle moving in a straight line covers half the distance with speed \(6 \mathrm{~m} / \mathrm{s}\). The other half is covered in two equal time intervals with speeds 9 \(\mathrm{m} / \mathrm{s}\) and \(15 \mathrm{~m} / \mathrm{s}\) respectively. The average speed of the particle during the motion is _______.

A radiation is emitted by \(1000\, W\) bulb and it generates an electric field and magnetic field at \(P\), placed at a distance of \(2\, m\). The efficiency of the bulb is \(1.25 \%\). The value of peak electric field at \(P\) is \(x \times 10^{-1} \,V / m\). Value of \(x\) is. (Rounded-off to the nearest integer) [Take \(\varepsilon_{0}=8.85 \times 10^{-12} C ^{2} N ^{-1} m ^{-2}, c =3 \times 10^{8}\) \(ms ^{-1}\) ]

The magnetic field of an electromagnetic wave is given by \(\vec B = 1.6 \times {10^{ - 6}}\,\cos \,\left( {2 \times {{10}^7}z + 6 \times {{10}^{15}}t} \right)\left( {2\hat i + \hat j} \right)\frac{{Wb}}{{{m^2}}}\) The associated electric field will be

A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in figure. The established torque produces an angular acceleration of \(2 \mathrm{~rad} / \mathrm{s}^2\). Moment of inertia of the wheel is _____ \(\mathrm{kg} \mathrm{m}^2\).
(Acceleration due to gravity \(=10 \mathrm{~m} / \mathrm{s}^2\))

A hydraulic automobile lift is designed to lift vehicles of mass \(5000\,kg\). The area of cross section of the cylinder carrying the load is \(250\,cm ^2\). The maximum pressure the smaller piston would have to bear is [Assume \(g=10\,m / s ^2\)]

In the given figure \(R_1=10 \Omega, R_2=8 \Omega, R_3=4 \Omega\) and \(R_4=8 \Omega\). Battery is ideal with emf \(12 \mathrm{~V}\). Equivalent resistant of the circuit and current supplied by battery are _______ respectively.

A particle executes simple harmonic motion and is located at \(x = a, b\)  and  \(c\) at times \(t_0, 2t_0\) and \(3t_0\) respectively. The frequency of the oscillation is