JEE Main 2019 January 12 Shift 2 Paper & Solutions - JEE MCQ

A simple harmonic motion is represented by:

The amplitude and time period of the motion are:

In the given circuit diagram, the currents , I₁ =–0.3A, I₄ = 0.8 A and I₅ = 0.4 A, are flowing as shown. The currents I₂,I₃ and I₆,respectively, are :

A particle of mass 20 g is released with an initial velocity 5 m/s along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. When the particle reaches point B, its angular momentum about O will be : (Take g= 10 m/s²)

In the above circuit,     Current in L-R₁ path is I₁ and in C-R₂ path it is I₂. The voltage of A.C source is given by  volts. The phase difference  between I₁ and I₂ is :

A paramagnetic material has 10²⁸atoms/m³. Its magnetic susceptibility at temperature 350 K is 2.8 ×10^–4. Its susceptibility at 300 K is :

A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0ms^–1, at right angles to the horizontal component of the earth's magnetic field, of 0.3 × l0^–4Wb/m².The value of the induced emf in wire is :

In the figure, given that V_BB supply can vary from 0 to 5.0 V, V_CC = 5V, β_dc = 200, R_B = 100 kW, R_C=l kΩ and V_BE=1.0 V, The minimum base current and the input voltage at which the transistor will go to saturation, will be, respectively :

In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 μF.
All values in the circuit are in μF.

Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, T_A/T_B, is:

The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is I(x)'. Which one of the graphs represents the variation of I(x) with x correctlv?

When a certain photo sensistive surface is illuminated with monochromatic light of frequency n, the stopping potential for the photo current is - V₀/2. When the surface is illuminated by monochromatic light of frequency v/2, the stopping potential is -V₀. The threshold frequency for photoelectric emission is:

A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of 4 ×10^–4 A passes through it, its needle (pointer) deflects by one division. To use this galvanometer as a voltmeter of range 2.5 V, it should be connected to a resistance of:

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be:

Two particles A, B are moving on two concentric circles of radii R₁ and R₂ with equal angular speed ω. At t = 0, their positions and direction of motion are shown in the figure :

The relative velocity  is given by:

A plano-convex lens (focal length f₂, refractive index μ₂, radius of curvature R) fits exactly into a plano-concave lens (focal length f₁, refractive index μ₁, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be :

Let ℓ, r, c and v represent inductance, resistance, capacitance and voltage, respectively. The dimension of  in SI units will be:

In a radioactive decay chain, the initial nucleus is  . At the end there are 6 α-particles and 4 β-particles which are emitted. If the end nucleus, If , A and Z are given by :

The mean intensity of radiation on the surface of the Sun is about 108 W/m². The rms value of the corresponding magnetic field is closest to :

A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark.
The velocity of sound in air, obtained in the experiment, is close to:

An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K. The mean time between two successive collisions is 6 × 10^–8 s.If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to:

The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure: What is the value of current at t = 4s ?

A block kept on a rough inclined plane, as shown in the figure, remaias at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction betwreen the block and the plane is : [Take g = 10 m/s²]

An alpha - particle of mass m suffer s 1-dimensional elastic coolision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy.The mass of the nucleus is :-

A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume, with time, at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by :-

To double the coverging range of a TV transmittion tower, its height should be multiplied by :-

A parallel plate capacitor with plates of area 1m² each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge each plate is :-

In a Frank-Hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to :-