JEE Main 2019 (Online) 12th January Evening Slot

In the above circuit, C = \({{\sqrt 3 } \over 2}\)\(\mu\)F, R2 = 20 \(\Omega\), L = \({{\sqrt 3 } \over {10}}\) H and R1 = 10 \(\Omega\). Current in L-R1 path is I1 and in C-R2 path it is I2 . The voltage of A.C. source is given by, V = ...

In a radioactive decay chain, the initial nucleus is \({}_{90}^{232}\)Th. At the end there are 6 \(\alpha\)-particles and 4 \(\beta\)-particles which are emitted. If the end nucleus is \({}_Z^A\)X, A and Z are given by :

A parallel plate capacitor with plates of area 1 m2 each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is :
(Take \(\varepsilon\)0 = 8.85 \(\times\) 10\(-\)12 $...

In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 \(\mu\)F. All values in the circuit are in \(\mu\)F.

The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure :

When is the value of current at t = 4 s ?

An alpha-particle of mass m suffers 1-dimensional elastic collision 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

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

A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of 4 \(\times\) 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...

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

When a certain photosensitive surface is illuminated with monochromatic light of frequency v, the stopping
potential for the current is –V0/2. When the surface is illuminated by monochromatic light of frequency v/2, the stopping potential i...

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 :

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

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 closet to :

In the figure, given that VBB supply can vary from 0 to 5.0 V, VCC = 5V, \(\beta\)dc = 200, RB = 100 k\(\Omega\), RC = 1 k\(\Omega\) and VBE = 1.0 V. The minimum base current and the input voltage at which the transistor will go to satur...

A plano-convex lens (focal length f2, refractive index \(\mu\)2, radius of curvature R) fits exactly into a plano-concave lens (focal length f1, refractive index \(\mu\)1, radius of curvature R). Their plane surfaces are parallel to each ...

Formation of real image using a biconvex lens is shown below :

If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen ?

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, TA/TB, is ;

A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is \(\ell\)1, a...

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 \(\times\) 10–8 s. If the pressure is doubled and temperature is increased to 500 K, the mean time bet...

A block kept on a rough inclined plane, as shown in the figure, remains 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 stat...

A paramagnetic material has 1028 atoms/m3. Its magnetic susceptibility at temperature 350 K is 2.8 \(\times\) 10–4. Its susceptibility at 300 K is :

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 ...

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 :

A load of mass M kg is suspended from a steel wire of length 2m and radius 1.0 mm in Searle's apparatus
experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The...

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 correctly ?

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 reac...

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

The relative velocity $${\overrightarrow V _A} -...

A simple harmonic motion is represented by :
y = 5 (sin 3 \(\pi\) t + \(\sqrt 3\) cos 3 \(\pi\)t) cm
The amplitude and time period of the motion are :

Let \(\ell\), r, C and V represent inductance, resistance, capacitance and voltage, respectively. The dimension of \({\ell \over {rCV}}\) in SI units will be :

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 refe...