JEE Main 2022 (Online) 25th June Morning Shift

Let \(x = 2t\), \(y = {{{t^2}} \over 3}\) be a conic. Let S be the focus and B be the point on the axis of the conic such that \(SA \bot BA\), where A is any point on the conic. If k is the ordinate of the centroid of the \(\Delta\)SAB, the...

The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is _____________.

Let A be a 3 \(\times\) 3 matrix having entries from the set {\(-\)1, 0, 1}. The number of all such matrices A having sum of all the entries equal to 5, is ___________.

Let E1 and E2 be two events such that the conditional probabilities \(P({E_1}|{E_2}) = {1 \over 2}\), \(P({E_2}|{E_1}) = {3 \over 4}\) and \(P({E_1} \cap {E_2}) = {1 \over 8}\). Then :

Let a, b and c be the length of sides of a triangle ABC such that \({{a + b} \over 7} = {{b + c} \over 8} = {{c + a} \over 9}\). If r and R are the radius of incircle and radius of circumcircle of the triangle ABC, respectively, then the va...

For a natural number n, let \({\alpha _n} = {19^n} - {12^n}\). Then, the value of \({{31{\alpha _9} - {\alpha _{10}}} \over {57{\alpha _8}}}\) is ___________.

The greatest integer less than or equal to the sum of first 100 terms of the sequence \({1 \over 3},{5 \over 9},{{19} \over {27}},{{65} \over {81}},\) ...... is equal to ___________.

The number of values of x in the interval \(\left( {{\pi \over 4},{{7\pi } \over 4}} \right)\) for which \(14\cos e{c^2}x - 2{\sin ^2}x = 21 - 4{\cos ^2}x\) holds, is ____________.

Let \(\overrightarrow a = {a_1}\widehat i + {a_2}\widehat j + {a_3}\widehat k\) \({a_i} > 0\), \(i = 1,2,3\) be a vector which makes equal angles with the coordinate axes OX, OY and OZ. Also, let the projection of \(\overrightarrow a\) on...

Let \(\theta\) be the angle between the vectors \(\overrightarrow a\) and \(\overrightarrow b\), where \(|\overrightarrow a | = 4,\) \(|\overrightarrow b | = 3\) and \(\theta \in \left( {{\pi \over 4},{\pi \over 3}} \right)\). Then $${...

Match List-I with List-II.

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:normal;}...

If wattless current flows in the AC circuit, then the circuit is :

The ratio for the speed of the electron in the 3rd orbit of He+ to the speed of the electron in the 3rd orbit of hydrogen atom will be :

The equivalent capacitance between points A and B in below shown figure will be __________ \(\mu\)F.

A signal of 100 THz frequency can be transmitted with maximum efficiency by :

A teacher in his physics laboratory allotted an experiment to determine the resistance (G) of a galvanometer. Students took the observations for \({1 \over 3}\) deflection in the galvanometer. Which of the below is true for measuring value ...

A resistor develops 300 J of thermal energy in 15 s, when a current of 2 A is passed through it. If the current increases to 3 A, the energy developed in 10 s is ____________ J.

The total current supplied to the circuit as shown in figure by the 5 V battery is ____________ A.

Given below are two statements :
Statement I : Davisson-Germer experiment establishes the wave nature of electrons.
Statement II : If electrons have wave nature, they can interfere and show diffraction.
In the light of the above statements ...

The current in a coil of self inductance 2.0 H is increasing according to I = 2 sin(t2) A. The amount of energy spent during the period when current changes from 0 to 2 A is ____________ J.

The electric field in an electromagnetic wave is given by E = 56.5 sin \(\omega\)(t \(-\) x/c) NC\(-\)1. Find the intensity of the wave if it is propagating along x-axis in the free space.
(Given : \(\varepsilon\)0 = 8.85 \(\times\) 10$$-$...

The photodiode is used to detect the optical signals. These diodes are preferably operated in reverse biased mode because :

In the figure, a very large plane sheet of positive charge is shown. P1 and P2 are two points at distance l and 2l from the charge distribution. If \(\sigma\) is the surface charge density, then the magnitude of electric fields E1 and E2 at...

A light wave travelling linearly in a medium of dielectric constant 4, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the ...

The difference of speed of light in the two media A and B (vA \(-\) vB) is 2.6 \(\times\) 107 m/s. If the refractive index of medium B is 1.47, then the ratio of refractive index of medium B to medium A is : (Given : speed of light in vacuu...

The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be : (Given g = acceleration due to gravity at the surface of earth).

The relation between root mean square speed (vrms) and most probable sped (vp) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :

A steam engine intakes 50 g of steam at 100\(^\circ\)C per minute and cools it down to 20\(^\circ\)C. If latent heat of vaporization of steam is 540 cal g\(-\)1, then the heat rejected by the steam engine per minute is __________ \(\times\)...

A force on an object of mass 100 g is \(\left( {10\widehat i + 5\widehat j} \right)\) N. The position of that object at t = 2 s is \(\left( {a\widehat i + b\widehat j} \right)\) m after starting from rest. The value of \({a \over b}\) will ...

A long straight wire with a circular cross-section having radius R, is carrying a steady current I. The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance r (r <...

The terminal velocity (vt) of the spherical rain drop depends on the radius (r) of the spherical rain drop as :

The velocity of upper layer of water in a river is 36 kmh\(-\)1. Shearing stress between horizontal layers of water is 10\(-\)3 Nm\(-\)2. Depth of the river is __________ m. (Co-efficient of viscosity of water is 10\(-\)2 Pa.s)

If force \(\overrightarrow F = 3\widehat i + 4\widehat j - 2\widehat k\) acts on a particle position vector \(2\widehat i + \widehat j + 2\widehat k\) then, the torque about the origin will be :

If \(Z = {{{A^2}{B^3}} \over {{C^4}}}\), then the relative error in Z will be :

\(\overrightarrow A\) is a vector quantity such that \(|\overrightarrow A |\) = non-zero constant. Which of the following expression is true for \(\overrightarrow A\) ?

Which of the following relations is true for two unit vector \(\widehat A\) and \(\widehat B\) making an angle \(\theta\) to each other?

The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is \(\pi\)/2 at point P and \(\pi\) at point Q. Then the difference between the resultant intensities ...

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm. The length of the open organ pipe is _____________ cm.

A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the m...

A 0.5 kg block moving at a speed of 12 ms\(-\)1 compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be _______________ Nm\(-\)1.