JEE Main 2022 (Online) 29th June Morning Shift

Let PQ be a focal chord of the parabola y2 = 4x such that it subtends an angle of \({\pi \over 2}\) at the point (3, 0). Let the line segment PQ be also a focal chord of the ellipse $$E:{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1...

Let b1b2b3b4 be a 4-element permutation with bi \(\in\) {1, 2, 3, ........, 100} for 1 \(\le\) i \(\le\) 4 and bi \(\ne\) bj for i \(\ne\) j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then ...

The probability that a randomly chosen 2 \(\times\) 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to :

Let \(\{ {a_n}\} _{n = 0}^\infty\) be a sequence such that \({a_0} = {a_1} = 0\) and \({a_{n + 2}} = 2{a_{n + 1}} - {a_n} + 1\) for all n \(\ge\) 0. Then, \(\sum\limits_{n = 2}^\infty {{{{a_n}} \over {{7^n}}}}\) is equal to:

Let a set A = A1 \(\cup\) A2 \(\cup\) ..... \(\cup\) Ak, where Ai \(\cap\) Aj = \(\phi\) for i \(\ne\) j, 1 \(\le\) j, j \(\le\) k. Define the relation R from A to A by R = {(x, y) : y \(\in\) Ai if and only if x \(\in\) Ai, 1 \(\le\) i $$\...

Let the mean and the variance of 5 observations x1, x2, x3, x4, x5 be \({24 \over 5}\) and \({194 \over 25}\) respectively. If the mean and variance of the first 4 observation are \({7 \over 2}\) and a respectively, then (4a + x5) is equal ...

The distance between the two points A and A' which lie on y = 2 such that both the line segments AB and A' B (where B is the point (2, 3)) subtend angle \({\pi \over 4}\) at the origin, is equal to :

The number of elements in the set \(S = \{ \theta \in [ - 4\pi ,4\pi ]:3{\cos ^2}2\theta + 6\cos 2\theta - 10{\cos ^2}\theta + 5 = 0\}\) is __________.

The number of solutions of the equation \(2\theta - {\cos ^2}\theta + \sqrt 2 = 0\) in R is equal to ___________.

Let \(\overrightarrow a = \alpha \widehat i + 3\widehat j - \widehat k\), \(\overrightarrow b = 3\widehat i - \beta \widehat j + 4\widehat k\) and \(\overrightarrow c = \widehat i + 2\widehat j - 2\widehat k\) where $$\alpha ,\,\beta \i...

For a series LCR circuit, I vs \(\omega\) curve is shown :
(a) To the left of \(\omega\)r, the circuit is mainly capacitive.
(b) To the left of \(\omega\)r, the circuit is mainly inductive.
(c) At \(\omega\)r, impedance of the circuit is eq...

The activity of a radioactive material is 2.56 \(\times\) 10\(-\)3 Ci. If the half life of the material is 5 days, after how many days the activity will become 2 \(\times\) 10\(-\)5 Ci ?

\(\sqrt {{d_1}}\) and \(\sqrt {{d_2}}\) are the impact parameters corresponding to scattering angles 60\(^\circ\) and 90\(^\circ\) respectively, when an \(\alpha\) particle is approaching a gold nucleus. For d1 = x d2, the value of x will...

A parallel plate capacitor filled with a medium of dielectric constant 10, is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant 15. Then the energy of capacitor will :

A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms\(-\)1 and 40 ms\(-\)1 respectively. The velocity of the third piece will ...

Only 2% of the optical source frequency is the available channel bandwidth for an optical communicating system operating at 1000 nm. If an audio signal requires a bandwidth of 8 kHz, how many channels can be accommodated for transmission :

The variation of applied potential and current flowing through a given wire is shown in figure. The length of wire is 31.4 cm. The diameter of wire is measured as 2.4 cm. The resistivity of the given wire is measured as x \(\times\) 10\(-\)...

For the network shown below, the value of VB \(-\) VA is ____________ V.

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R :
Assertion A : The photoelectric effect does not takes place, if the energy of the incident radiation is less than the work function of a...

The intensity of the light from a bulb incident on a surface is 0.22 W/m2. The amplitude of the magnetic field in this light-wave is ______________ \(\times\) 10\(-\)9 T.
(Given : Permittivity of vacuum \(\in\)0 = 8.85 \(\times\) 10\(-\)12 ...

A transistor is used in an amplifier circuit in common emitter mode. If the base current changes by 100 \(\mu\)A, it brings a change of 10 mA in collector current. If the load resistance is 2 k\(\Omega\) and input resistance is 1 k$$\Omega$...

A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength 1 \(\times\) 105 NC\(-\)1. If the charge on the particle is 40 \(\mu\)C and the initial velocity is 200 ms\(-\)1, how much distance...

A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30 cm and refractive index 1.5. The distance from the centre of the globe at which the beam of light can converge is _____________ mm.

The escape velocity of a body on a planet 'A' is 12 kms\(-\)1. The escape velocity of the body on another planet 'B', whose density is four times and radius is half of the planet 'A', is :

A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0\(^\circ\)C will be :
(Given gas constant R = 8.3 JK\(-\)...

In van der Waal equation \(\left[ {P + {a \over {{V^2}}}} \right]\) [V \(-\) b] = RT; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants \({a \over b}\) is dimensionally equal to :

Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same...

As per the given figure, two plates A and B of thermal conductivity K and 2 K are joined together to form a compound plate. The thickness of plates are 4.0 cm and 2.5 cm respectively and the area of cross-section is 120 cm2 for each plate. ...

300 cal. of heat is given to a heat engine and it rejects 225 cal. If source temperature is 227\(^\circ\)C, then the temperature of sink will be ______________ \(^\circ\)C.

At a certain place the angle of dip is 30\(^\circ\) and the horizontal component of earth's magnetic field is 0.5 G. The earth's total magnetic field (in G), at that certain place, is :

A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circula...

Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial velocity 'u' at t = 2 s. After a certain time, both balls meet 100 m above the ground....

A wire of length L is hanging from a fixed support. The length changes to L1 and L2 when masses 1 kg and 2 kg are suspended respectively from its free end. Then the value of L is equal to :

A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 kgs\(-\)1 and at a speed of 10 ms\(-\)1. Then, the initial acceleration of the block, in ms\(-\)2, ...

A spherical shell of 1 kg mass and radius R is rolling with angular speed \(\omega\) on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is \({a \over 3}\) R2\(\omega\). The value of a...

A body is performing simple harmonic with an amplitude of 10 cm. The velocity of the body was tripled by air jet when it is at 5 cm from its mean position. The new amplitude of vibration is \(\sqrt{x}\) cm. The value of x is _____________.

Two vectors \(\overrightarrow A\) and \(\overrightarrow B\) have equal magnitudes. If magnitude of \(\overrightarrow A\) + \(\overrightarrow B\) is equal to two times the magnitude of \(\overrightarrow A\) \(-\) \(\overrightarrow B\),...

Using Young's double slit experiment, a monochromatic light of wavelength 5000 \(\mathop A\limits^o\) produces fringes of fringe width 0.5 mm. If another monochromatic light of wavelength 6000 \(\mathop A\limits^o\) is used and the separa...

A longitudinal wave is represented by \(x = 10\sin 2\pi \left( {nt - {x \over \lambda }} \right)\) cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to :

A particle of mass 500 gm is moving in a straight line with velocity v = b x5/2. The work done by the net force during its displacement from x = 0 to x = 4 m is : (Take b = 0.25 m\(-\)3/2 s\(-\)1).