Two projectiles \(A\) and \(B\) are thrown with initial velocities of \(40\,m / s\) and \(60\,m / s\) at angles \(30^{\circ}\) and \(60^{\circ}\) with the horizontal respectively. The ratio of their ranges respectively is \(\left( g =10\,m / s ^2\right)\)

The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is

A particle of charge \(q\) and mass \(m\) is subjected to an electric field \(E = E _{0}\left(1- ax ^{2}\right)\) in the \(x-\)direction, where \(a\) and \(E _{0}\) are constants. Initially the particle was at rest at \(x=0 .\) Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is

The position-time graphs for two students \(A\) and \(B\) returning from the school to their homes are shown in figure \((A)\) \(A\) lives closer to the school \((B)\) \(B\) lives closer to the school \((C)\) \(A\) takes lesser time to reach home \((D)\) \(A\) travels faster than \(B\) \((E)\) \(B\) travels faster than \(A\) Choose the correct answer from the options given below :

A parallel beam of monochromatic light of wavelength \(5000 \mathring A\) is incident normally on a single narrow slit of width \(0.001 \mathrm{~mm}\). The light is focused by convex lens on screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of______________(degree).

Consider the equation \(H = \dfrac{x^p \epsilon^q E^r}{t^s}\), where \(H=\) magnetic field; \(E=\) electric field, \(\epsilon=\) permittivity, \(x=\) distance, \(t=\) time. The values of \(p, q, r\) and \(s\) respectively are:

Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m . They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process _________ J.

Given below are two statements : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\): A bar magnet dropped through a metallic cylindrical pipe takes more time to come down compared to a non-magnetic bar with same geometry and mass. Reason \(R\): For the magnetic bar, Eddy currents are produced in the metallic pipe which oppose the motion of the magnetic bar. In the light of the above statements, choose the correct answer from the options given below

Three rays of light, namely red (R), green (G) and blue (B) are incident on the face \(PQ\) of a right angled prism PQR as shown in figure. The refractive indices of the material of the prism for red, green and blue wavelength are \(1.27, 1.42\) and \(1.49\) respectively. The colour of the ray(s) emerging out of the face \(PR\) is:

A hemispherical glass body of radius \(10\, cm\) and refractive index \(1.5\) is silvered on its curved surface. A small air bubble is \(6\, cm\) below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen 

The resultant of these forces \(\overrightarrow{O P}, \overrightarrow{O Q}, \overrightarrow{O R}, \overrightarrow{O S}\) and \(\overrightarrow{{OT}}\) is approximately \(\ldots \ldots {N}\). [Take \(\sqrt{3}=1.7, \sqrt{2}=1.4\) Given \(\hat{{i}}\) and \(\hat{{j}}\) unit vectors along \({x}, {y}\) axis \(]\)