Find the value of the angle of emergence from the prism given below for the incidence ray shown. The refractive index of the glass is \(\sqrt{3}\).

       

1. \(45^{\circ}\)
2. \(90^{\circ}\)
3. \(60^{\circ}\)
4. \(30^{\circ}\)$\mathrm{}$

A screw gauge gives the following readings when used to measure the diameter of a wire:
Main scale reading: \(0\) mm
Circular scale reading: \(52\) divisions 
Given that \(1\) mm on the main scale corresponds to \(100\) divisions on the circular scale, the diameter of the wire that can be inferred from the given data is:

A nucleus with mass number \(240\) breaks into fragments each of mass number \(120.\) The binding energy per nucleon of unfragmented nuclei is \(7.6~\text{MeV}\) while that of fragments is \(8.5~\text{MeV}.\) The total gain in the binding energy in the process is:

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? $\left(g=10\right)$ $m/s^2$

A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since:

The electron concentration in an \(\mathrm{n\text-}\)type semiconductor is the same as the hole concentration in a \(\mathrm{p\text{-}}\)type semiconductor. An external field (electric) is applied across each of them. Compare the currents in them.

A cup of coffee cools from \(90^{\circ}\text{C}\) $\mathrm{to}$ \(80^{\circ}\text{C}\) in \(t\) minutes, when the room temperature is \(20^{\circ}\text{C}.\)$\mathrm{}$ The time taken by a similar cup of coffee to cool from \(80^{\circ}\text{C}\) $\mathrm{to}$ \(60^{\circ}\text{C}\) at room temperature same at \(20^{\circ}\text{C}\) is:

In a potentiometer circuit, a cell of emf \(1.5~\text{V}\) gives a balance point at 36 cm length of wire. If another cell of emf 2.5 V replaces the first cell, then at what length of the wire, the balance point occur? 
1. 64 cm 
2. 62 cm 
3. 60 cm 
4. 21.6 cm