JEE (Advanced) 2015 Paper-1

Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies $$\omega_1$$ and $$\omega_2$$ and have total energies $$E_1$$ and $$E_2$$, respectively. The variations of their momenta p with positions x are shown in the figures. If $$\frac{a}{b} = n^2$$ and $$\frac{a}{R} = n$$, then the correct equation(s) is(are)

A ring of mass M and radius R is rotating with angular speed $$\omega$$ about a fixed vertical axis passing through its centre O with two point masses each of mass $$\frac{M}{8}$$ at rest at O. These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure. At some instant the angular speed of the system is $$\frac{8}{9}\omega$$ and one of the masses is at a distance of $$\frac{3}{5}R$$ from O. At this instant the distance of the other mass from O is

The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density $$\lambda$$ are kept parallel to each other. In their resulting electric field, point charges q and -q are kept in equilibrium between them. The point charges are confined to move in the x direction only. If they are given a small displacement about their equilibrium positions, then the correct statement(s) is(are)

Two identical glass rods $$S_1$$ and $$S_2$$ (refractive index = 1.5) have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light P is placed inside rod $$S_1$$ on its axis at a distance of 50 cm from the curved face, the light rays emanating from it are found to be parallel to the axis inside $$S_2$$. The distance d is

A conductor (shown in the figure) carrying constant current I is kept in the x-y plane in a uniform magnetic field $$\overrightarrow{B}$$. If F is the magnitude of the total magnetic force acting on the conductor, then the correct statement(s) is(are)

A containerof fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature T. Assuming The average energy per mole of the gas mixture is 2RT.the gases are ideal, the correct statement(s) is(are)

In an aluminum (Al) bar of square cross section, a square hole is drilled and is filled with iron (Fe) as shown in the figure. The electrical resistivities of Al and Fe are $$2.7 \times 10^{-8} Ω m$$ and $$1.0 \times 10^{-7} Ω m,$$ respectively. The electrical resistance between the two faces P and Q of the composite bar is

For photo-electric effect with incident photon wavelength $$\lambda$$, the stopping potential is $$V_0$$. Identify the correct variation(s) of $$V_0$$ with $$\lambda$$ and $$\frac{1}{\lambda}$$.

Match the nuclear processes given in column I with the appropriate option(s) in column II.

A particle of unit mass is moving along the x-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in column I (a and $$U_0$$ are constants). Match the potential energies in column I to the corresponding statement(s) in column II.