In an experiment the angles are required to be measured using an instrument in which 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half a degree \(\left(=0.5^{\circ}\right)\), then the least count of the instrument is

The two lenses of an achromatic doublet should have

Consider the following vectors.

Choose the correct statement.

The small energy losses in transformers due to eddy currents can be reduced by

Two moles of a gas is expanded to double its volume by two different processes. One is isobaric and the other is isothermal. If \(W_1\) and \(W_2\) are the works done, respectively then

Two strings \(\mathrm{A}\) and \(\mathrm{B}\) produce beat of frequency \(\Delta f_1>0\). The tension in string \(\mathrm{A}\) is slightly increased and the beat frequency is found to be \(\Delta f_2>0\). If the original frequency of \(\mathrm{A}\) is \(f_0\) and \(\Delta f_2 < \Delta f_1\), then the frequency of \(\mathrm{B}\) is

A current carrying loop \(\mathrm{ABCD}\) has two circular arcs \(\mathrm{AD}\) and \(\mathrm{BC}\) with radius \(1 \mathrm{~cm}\) and \(2 \mathrm{~cm}\) respectively as shown in the figure. The two arcs \(\mathrm{AD}\) and \(\mathrm{BC}\) subtend a common angle \(30^{\circ}\) at the centre \(\mathrm{O}\). If the current flowing in the loop is \(\frac{1.2}{\pi} \mathrm{A}\), then the magnitude of net magnetic field at \(O\) is (Given \(\mu_0=4 \pi \times 10^{-7}\) )

The ratio of wavelengths of second line in Balmer series and the first line in Lyman series of hydrogen atom is

Two similar coils which are separated by \(2 \mathrm{~m}\) having radius of \(1 \mathrm{~m}\) and number of turns 80 have a common axis. Calculate the strength of magnetic field in microtesla at a point midway between them on their common axis when a current is \(0.2\)

The potential energy of an object is $U\left(x\right)=\left(5x^2-4x^3\right) \mathrm{J}$, where $x$ is the position in meter. The position at which the force becomes zero is

Monochromatic light of wavelength \(6000 Å\) incidents on a small angled prism. If the angle of the prism is \(6^{\circ}\), the refractive indices of the material of the prism for violet and red lights are respectively 1.52 and 1.48, then the angle of dispersion produced for this incident light is

Choose the correct statement from following.

Statement (I) : The slope of kinetic energy-displacement curve of a body in motion will be directly proportional to its acceleration. Statement (II) : From a height of \(15 \mathrm{~m}\) a ball is projected vertically upwards with a velocity of \(30 \mathrm{~m} / \mathrm{s}\). If the ball rises to the same height after hitting the ground, the loss of its energy on hitting the ground is \(30 \%\). Statement (III) : The velocity acquired by a body of mass ' \(m\) ' after travelling a fixed distance from rest under the action of a constant force is directly proportional to mass ' \(\mathrm{m}\) '. Which of the following is correct?