JEE Main 12th January 2019 Shift 1

In the figure shown, a circuit contains two identical resistors with resistance $$R = 5\Omega$$ and an inductance with $$L = 2$$ mH. An ideal battery of 15V is connected in the circuit. What will be the current through the battery long after the switch is closed?

A point source of light, S is placed at a distance L in front of the center of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance 2L as shown below. The distance over which the man can see the image of the light source in the mirror is:

A light wave is incident normally on a glass slab of refractive index 1.5. If 4% of light gets reflected and the amplitude of the electric field of the incident light is 30 V/m, then the amplitude of the electric field for the wave propagating in the glass medium will be:

What is the position and nature of image formed by lens combination shown in figure? ($$f_1$$, $$f_2$$ are focal lengths)

A particle A of mass m and charge q is accelerated by a potential difference of 50 V. Another particle B of mass 4m and charge q is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths $$\frac{\lambda_A}{\lambda_B}$$ is close to:

A particle of mass m moves in a circular orbit in a central potential field $$U(r) = \frac{1}{2}kr^2$$. If Bohr's quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number n as:

The output of the given logic circuit is:

A 100V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What is the modulation index?

The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 $$\mu$$m diameter of a wire is:

In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that, the variation $$\frac{dR}{dl}$$ of its resistance R with length l is $$\frac{dR}{dl} \propto \frac{1}{\sqrt{l}}$$. Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP?