A small block slides down on a smooth inclined plane starting from rest at time \(t=0.\) Let \(S_n\) be the distance traveled by the block in the interval \(t=n-1\) to \(t=n.\) Then the ratio \(\dfrac{S_n}{S_{n +1}}\) is:
1. | \(\dfrac{2n+1}{2n-1}\) | 2. | \(\dfrac{2n}{2n-1}\) |
3. | \(\dfrac{2n-1}{2n}\) | 4. | \(\dfrac{2n-1}{2n+1}\) |
The velocity of a small ball of mass \(M\) and density \(d\), when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is \(d\over 2\) then the viscous force acting on the ball will be:
1. | \(\frac{3Mg}{2}\) | 2. | \(2Mg\) |
3. | \(\frac{Mg}{2}\) | 4. | \(Mg\) |
A thick current-carrying cable of radius '\(R\)' carries current \('I'\) uniformly distributed across its cross-section. The variation of magnetic field \(B(r)\) due to the cable with the distance '\(r\)' from the axis of the cable is represented by:
1. | |
2. | |
3. | 4. |
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. \(30^{\circ}\)
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:
1. | \(0.26\) cm | 2. | \(0.052\) cm |
3. | \(0.52\) cm | 4. | \(0.026\) cm |
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:
1. \(804~\text{MeV}\)
2. \(216~\text{MeV}\)
3. \(0.9~\text{MeV}\)
4. \(9.4~\text{MeV}\)
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?
1. | 12.3 kW | 2. | 7.0 kW |
3. | 10.2 kW | 4. | 8.1 kW |
A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since:
1. | a large aperture contributes to the quality and visibility of the images. |
2. | a large area of the objective ensures better light-gathering power. |
3. | a large aperture provides a better resolution. |
4. | all of the above. |
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.
1. | current in \(\mathrm{n\text-}\)type \(>\) current in \(\mathrm{p\text{-}}\)type. |
2. | no current will flow in \(\mathrm{p\text{-}}\)type, current will only flow in \(\mathrm{n\text-}\)type. |
3. | current in \(\mathrm{n\text-}\)type \(=\) current in \(\mathrm{p\text{-}}\)type. |
4. | current in \(\mathrm{p\text{-}}\)type \(>\) current in \(\mathrm{n\text-}\)type. |