JEE Main 2022 (Online) 26th June Evening Shift

Let r \(\in\) {p, q, \(\sim\)p, \(\sim\)q} be such that the logical statement
r \(\vee\) (\(\sim\)p) \(\Rightarrow\) (p \(\wedge\) q) \(\vee\) r
is a tautology. Then r is equal to :

If the system of equations
\(\alpha\)x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = \(\beta\)
has infinitely many solutions, then the ordered pair (\(\alpha\), \(\beta\)) is equal to :

Let \(X = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr 0 & 0 & 0 \cr } } \right],\,Y = \alpha I + \beta X + \gamma {X^2}\) and \(Z = {\alpha ^2}I - \alpha \beta X + ({\beta ^2} - \alpha \gamma ){X^2}\), \(\alpha\), $$\beta$...

The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is ___________.

If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is p, then 96 p is equal to _______________.

Let p and q be two real numbers such that p + q = 3 and p4 + q4 = 369. Then \({\left( {{1 \over p} + {1 \over q}} \right)^{ - 2}}\) is equal to _________.

If \(A = \sum\limits_{n = 1}^\infty {{1 \over {{{\left( {3 + {{( - 1)}^n}} \right)}^n}}}}\) and \(B = \sum\limits_{n = 1}^\infty {{{{{( - 1)}^n}} \over {{{\left( {3 + {{( - 1)}^n}} \right)}^n}}}}\), then \({A \over B}\) is equal to :

If a1 (> 0), a2, a3, a4, a5 are in a G.P., a2 + a4 = 2a3 + 1 and 3a2 + a3 = 2a4, then a2 + a4 + 2a5 is equal to ___________.

The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct v...

\(16\sin (20^\circ )\sin (40^\circ )\sin (80^\circ )\) is equal to :

A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process. The effective half-life of the nucleus will be:

The charge on capacitor of capacitance 15\(\mu\)F in the figure given below is :

A parallel plate capacitor with plate area A and plate separation d = 2 m has a capacitance of 4 \(\mu\)F. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant K = 3...

A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of 15 ms\(-\)1. The impulse imparted to the ball is ___________ Ns.

A sinusoidal wave y(t) = 40sin(10 \(\times\) 106 \(\pi\)t) is amplitude modulated by another sinusoidal wave x(t) = 20sin (1000 \(\pi\)t). The amplitude of minimum frequency component of modulated signal is :

The equivalent resistance between points A and B in the given network is :

A metal surface is illuminated by a radiation of wavelength 4500 \(\mathop A\limits^o\). The ejected photo-electron enters a constant magnetic field of 2 mT making an angle of 90\(^\circ\) with the magnetic field. If it starts revolving in...

The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength 6630 \(\mathop A\limits^o\) is 0.42 V. If the threshold frequency is x \(\times\) 1013 /s, where x is _________ (nearest integer).
(Given, ...

Two coils of self inductance L1 and L2 are connected in series combination having mutual inductance of the coils as M. The equivalent self inductance of the combination will be :

A metallic conductor of length 1 m rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity 5 rad s\(-\)1. If the horizontal component of earth's magnetic field is 0.2 \(\times\) 10\(-\)4 T, the...

Which is the correct ascending order of wavelengths?

The positive feedback is required by an amplifier to act an oscillator. The feedback here means :

Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5 \(\mu\)C are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be :

A small bulb is placed at the bottom of a tank containing water to a depth of \(\sqrt7\) m. The refractive index of water is \({4 \over 3}\). The area of the surface of water through which light from the bulb can emerge out is x\(\pi\) m2. ...

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of...

A flask contains argon and oxygen in the ratio of 3 : 2 in mass and the mixture is kept at 27\(^\circ\)C. The ratio of their average kinetic energy per molecule respectively will be :

A geyser heats water flowing at a rate of 2.0 kg per minute from 30\(^\circ\)C to 70\(^\circ\)C. If geyser operates on a gas burner, the rate of combustion of fuel will be ___________ g min\(-\)1.
[Heat of combustion = 8 \(\times\) 103 Jg$$...

A heat engine operates with the cold reservoir at temperature 324 K. The minimum temperature of the hot reservoir, if the heat engine takes 300 J heat from the hot reservoir and delivers 180 J heat to the cold reservoir per cycle, is _____...

In the arrangement shown in figure a1, a2, a3 and a4 are the accelerations of masses m1, m2, m3 and m4 respectively. Which of the following relation is true for this arrangement?

A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the 7th and 8th ball is __________ N...

A bar magnet having a magnetic moment of 2.0 \(\times\) 105 JT\(-\)1, is placed along the direction of uniform magnetic field of magnitude B
= 14 \(\times\) 10\(-\)5 T. The work done in rotating the magnet slowly through 60\(^\circ\) from...

Two 10 cm long, straight wires, each carrying a current of 5A are kept parallel to each other. If each wire experienced a force of 10\(-\)5 N, then separation between the wires is ____________ cm.

A ball is projected vertically upward with an initial velocity of 50 ms\(-\)1 at t = 0s. At t = 2s, another ball is projected vertically upward with same velocity. At t = __________ s, second ball will meet the first ball (g = 10 ms\(-\)2).

If p is the density and \(\eta\) is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number Re is :

A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is

The dimension of mutual inductance is :

A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling micro...

For a specific wavelength 670 nm of light coming from a galaxy moving with velocity v, the observed wavelength is 670.7 nm. The value of v is :

A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last for...

Arrange the four graphs in descending order of total work done; where W1, W2, W3 and W4 are the work done corresponding to figure a, b, c and d respectively.