JEE Main 2022 (Online) 24th June Evening Shift

The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1, 2, 3, 4, 5, 7 and 9 is _____________.

A random variable X has the following probability distribution :

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In an examination, there are 10 true-false type questions. Out of 10, a student can guess the answer of 4 questions correctly with probability \({3 \over 4}\) and the remaining 6 questions correctly with probability \({1 \over 4}\). If the ...

The sum of all the real roots of the equation \(({e^{2x}} - 4)(6{e^{2x}} - 5{e^x} + 1) = 0\) is

The number of distinct real roots of the equation x7 \(-\) 7x \(-\) 2 = 0 is

Let x, y > 0. If x3y2 = 215, then the least value of 3x + 2y is

The sum of all the elements of the set \(\{ \alpha \in \{ 1,2,.....,100\} :HCF(\alpha ,24) = 1\}\) is __________.

Let the area of the triangle with vertices A(1, \(\alpha\)), B(\(\alpha\), 0) and C(0, \(\alpha\)) be 4 sq. units. If the points (\(\alpha\), \(-\)\(\alpha\)), (\(-\)\(\alpha\), \(\alpha\)) and (\(\alpha\)2, \(\beta\)) are collinear, then $...

The number of solutions of the equation \(\cos \left( {x + {\pi \over 3}} \right)\cos \left( {{\pi \over 3} - x} \right) = {1 \over 4}{\cos ^2}2x\), \(x \in [ - 3\pi ,3\pi ]\) is :

Let \(\widehat a\) and \(\widehat b\) be two unit vectors such that \(|(\widehat a + \widehat b) + 2(\widehat a \times \widehat b)| = 2\). If \(\theta\) \(\in\) (0, \(\pi\)) is the angle between \(\widehat a\) and \(\widehat b\), then among...

Given below are two statements :
Statement I : The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor.
Statement II : In ac circuit, the average power delivered by the source never becom...

In Bohr's atomic model of hydrogen, let K, P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level :

A sample contains 10\(-\)2 kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1 : 2. The ratio of the amounts of A and B after 16 s is \({x \over {100}}\). The value of x is ____...

If the charge on a capacitor is increased by 2 C, the energy stored in it increases by 44%. The original charge on the capacitor is (in C)

A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is

A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be :

An antenna is placed in a dielectric medium of dielectric constant 6.25. If the maximum size of that antenna is 5.0 mm, it can radiate a signal of minimum frequency of __________ GHz.
(Given \(\mu\)r = 1 for dielectric medium)

What will be the most suitable combination of three resistors A = 2\(\Omega\), B = 4\(\Omega\), C = 6\(\Omega\) so that \(\left( {{{22} \over 3}} \right)\)\(\Omega\) is equivalent resistance of combination?

A potentiometer wire of length 10 m and resistance 20 \(\Omega\) is connected in series with a 25 V battery and an external resistance 30 \(\Omega\). A cell of emf E in secondary circuit is balanced by 250 cm long potentiometer wire. The va...

The light of two different frequencies whose photons have energies 3.8 eV and 1.4 eV respectively, illuminate a metallic surface whose work function is 0.6 eV successively. The ratio of maximum speeds of emitted electrons for the two freque...

A circular coil of 1000 turns each with area 1m2 is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of 0.07T. The maximum voltage generation will be ___________ V.

An electric bulb is rated as 200 W. What will be the peak magnetic field at 4 m distance produced by the radiations coming from this bulb? Consider this bulb as a point source with 3.5% efficiency.

In the given circuit, the value of current IL will be ____________ mA. (When RL = 1k\(\Omega\))

Two identical charged particles each having a mass 10 g and charge 2.0 \(\times\) 10\(-\)7C are placed on a horizontal table with a separation of L between them such that they stay in limited equilibrium. If the coefficient of friction bet...

A long cylindrical volume contains a uniformly distributed charge of density \(\rho\). The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :

A ray of light is incident at an angle of incidence 60\(^\circ\) on the glass slab of refractive index \(\sqrt3\). After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray...

The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3R will be :

A Carnot engine takes 5000 kcal of heat from a reservoir at 727\(^\circ\)C and gives heat to a sink at 127\(^\circ\)C. The work done by the engine is

A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of 60 ms\(-\)1. What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail?
[Specific heat capacity of iron = 0...

A monoatomic gas performs a work of \({Q \over {4}}\) where Q is the heat supplied to it. The molar heat capacity of the gas will be ______________ R during this transformation. Where R is the gas constant.

An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to : [Use g = 10 ms$...

The soft-iron is a suitable material for making an electromagnet. This is because soft-iron has

A proton, a deutron and an \(\alpha\)-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :

A body is projected from the ground at an angle of 45\(^\circ\) with the horizontal. Its velocity after 2s is 20 ms\(-\)1. The maximum height reached by the body during its motion is __________ m. (use g = 10 ms\(-\)2)

Potential energy as a function of r is given by \(U = {A \over {{r^{10}}}} - {B \over {{r^5}}}\), where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :

In an experiment to verify Newton's law of cooling, a graph is plotted between the temperature difference (\(\Delta\)T) of the water and surroundings and time as shown in figure. The initial temperature of water is taken as 80\(^\circ\)C. T...

Two massless springs with spring constants 2 k and 9 k, carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will ...

Identify the pair of physical quantities that have same dimensions:

Two light beams of intensities in the ratio of 9 : 4 are allowed to interfere. The ratio of the intensity of maxima and minima will be :

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by \(y = (10\cos \pi x\sin {{2\pi t} \over T})\) cm
The amplitude...