In Young’s double slit experiment, the distance between slits and the screen is 1.0 m and monochromatic light of 600 nm is being used. A person standing near the slits is looking at the fringe pattern. When the separation between the slits is varied, the interference pattern disappears for a particular distance d₀ between the slits. If the angular resolution of the eye is $$({{{1}} \over {60}})^o$$, the value of d₀ is close to :

A hydrogen atom makes a transition from n = 2 to n = 1 and emits a photon. This photon strikes a doubly ionized lithium atom (z = 3) in excited state and completely removes the orbiting electron. The least quantum number for the excited state of the ion for the process is :

The potential (in volts) of a charge distribution is given by.

V(z) = 30 $$-$$ 5x² for $$\left| z \right|$$ $$ \le $$ 1 m.
V(z) = 35 $$-$$ 10 $$\left| z \right|$$ for $$\left| z \right|$$ $$ \ge $$1 m.

V(z) does not depend on x and y. If this potential is generated by a constant charge per unit volume $${\rho _0}$$ (in units of $${\varepsilon _0}$$) which is spread over a certain region, then choose the correct statement.

An audio signal consists of two distinct sounds : one a human speech signal in the frequency band of 200 Hz to 2700 Hz, while the other is a high frequency music signal in the frequency band of 10200 Hz to 15200 Hz. The ratio of the AM signal bandwidth required to send both the signals together to the AM signal bandwidth required to send just the human speech is :