The power of a biconvex lens is \(10\) dioptre and the radius of curvature of each surface is \(10\) cm. The refractive index of the material of the lens is:

A point mass \(m\) is moved in a vertical circle of radius \(r\) with the help of a string. The velocity of the mass is \(\sqrt{7gr} \) at the lowest point. The tension in the string at the lowest point is:

Two coherent sources of light interfere and produce fringe patterns on a screen. For the central maximum, the phase difference between the two waves will be: 
1. zero
2. \(\pi\)
3. \(\dfrac{3\pi}{2}\)
4. \(\dfrac{\pi}{2}\)

A person sitting on the ground floor of a building notices through the window, of height \(1.5~\text{m}\), a ball dropped from the roof of the building crosses the window in \(0.1~\text{s}\). What is the velocity of the ball when it is at the topmost point of the window? \(\left(g = 10~\text{m/s}^2\right )\)

A parallel plate capacitor with cross-sectional area \(A\) and separation \(d\) has air between the plates. An insulating slab of the same area but the thickness of \(\dfrac{d}{2}\) is inserted between the plates as shown in the figure, having a dielectric constant, \(K=4.\) The ratio of the new capacitance to its original capacitance will be:

The mean free path \(l\) for a gas molecule depends upon the diameter, \(d\) of the molecule as:

The length of the string of a musical instrument is \(90\) cm and has a fundamental frequency of \(120\) Hz. Where should it be pressed to produce a fundamental frequency of \(180\) Hz?