A set of \(20\) tuning forks is arranged in a series of increasing frequencies. If each fork gives \(4\) beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is \(\dots \; Hz\).

Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to \(A\) and \(T,\)  respectively. At time \(t=0\) one particle has displacement \(A\) while the other one has displacement \(\frac {-A}{2}\) and they are moving towards each other. If they cross each other at time \(t,\) then \(t\) is

Two point charges \(8 \, \mu C\) and \(-2 \, \mu C\) are located at \(x = 2\) cm and \(x = 4\) cm, respectively on the \(x\)-axis. The ratio of electric flux due to these charges through two spheres of radii \(3\) cm and \(5\) cm with their centers at the origin is _______.

Maatch Liat \(I\) List \(II\) Chose the correct answer from the options given below

A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height \(h\) as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height \(h = \alpha R\). The value of \(\alpha\) is _______.

An object viewed from a near point distance of \(25\, {cm}\), using a microscopic lens with magnification \('6',\) gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length \(0.6\, {m}\), if the focal length of the eyepiece is euqal to \(.... \,{cm} .\)

A proton (mass \(m\) ) accelerated by a potential difference \(V\)  flies through a uniform transverse magnetic field \(B.\) The field occupies a region of space by width \('d'\). If \(\alpha \) be the angle of deviation of proton from initial direction of motion (see figure), the value of \(sin\,\alpha \) will be

An object of mass \(m _{1}\) collides with another object of mass \(m _{2}\), which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses \(m _{2}: m _{1}\) is

Monochromatic light of frequency \(6 \times 10^{14} \mathrm{~Hz}\) is produced by a laser. The power emitted is \(2 \times 10^{-3} \mathrm{~W}\). How many photons per second on an average, are emitted by the source? (Given \(\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}\) )

The moment of inertia of semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is \(\frac{1}{ x } MR ^2\), where \(R\) is the radius and \(M\) is the mass of semicircular ring. The value of \(x\) will be \(...........\)

Two electrons are moving in orbits of two hydrogen like atoms with speeds \(3 \times 10^5 m / s\) and \(2.5 \times 10^5 m / s\) respectively. If the radii of these orbits are nearly same then the possible order of energy states are _________ respectively.