JEE Main 2022 (Online) 29th July Evening Shift

The number of natural numbers lying between 1012 and 23421 that can be formed using the digits \(2,3,4,5,6\) (repetition of digits is not allowed) and divisible by 55 is _________.

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then ...

The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number of trials in the binomial distribution is ____________.

Let \(\alpha, \beta(\alpha>\beta)\) be the roots of the quadratic equation \(x^{2}-x-4=0 .\) If \(P_{n}=\alpha^{n}-\beta^{n}\), \(n \in \mathrm{N}\), then \(\frac{P_{15} P_{16}-P_{14} P_{16}-P_{15}^{2}+P_{14} P_{15}}{P_{13} P_{14}}\) is equ...

$$ \begin{aligned} &\text { Let }\left\{a_{n}\right\}_{n=0}^{\infty} \text { be a sequence such that } a_{0}=a_{1}=0 \text { and } \\\\ &a_{n+2}=3 a_{n+1}-2 a_{n}+1, \forall n \geq 0 . \end{aligned} $$
Then $$a_{25} a_{23}-2 a_{25} a_{22}-2...

Let \(m_{1}, m_{2}\) be the slopes of two adjacent sides of a square of side a such that \(a^{2}+11 a+3\left(m_{1}^{2}+m_{2}^{2}\right)=220\). If one vertex of the square is \((10(\cos \alpha-\sin \alpha), 10(\sin \alpha+\cos \alpha))\), wh...

Let \(\mathrm{A}(\alpha,-2), \mathrm{B}(\alpha, 6)\) and \(\mathrm{C}\left(\frac{\alpha}{4},-2\right)\) be vertices of a \(\triangle \mathrm{ABC}\). If \(\left(5, \frac{\alpha}{4}\right)\) is the circumcentre of \(\triangle \mathrm{ABC}\), ...

The number of elements in the set \(S=\left\{x \in \mathbb{R}: 2 \cos \left(\frac{x^{2}+x}{6}\right)=4^{x}+4^{-x}\right\}\) is :

Let \(\vec{a}, \vec{b}, \vec{c}\) be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and
$$(\vec{a} \times \vec{b}) \cdot(\vec{b} \times \vec{c})+(\vec{b} \times \...

Let \(\vec{a}\) and \(\vec{b}\) be two vectors such that \(|\vec{a}+\vec{b}|^{2}=|\vec{a}|^{2}+2|\vec{b}|^{2}, \vec{a} \cdot \vec{b}=3\) and \(|\vec{a} \times \vec{b}|^{2}=75\). Then \(|\vec{a}|^{2}\) is equal to __________.

A circuit element \(\mathrm{X}\) when connected to an a.c. supply of peak voltage \(100 \mathrm{~V}\) gives a peak current of \(5 \mathrm{~A}\) which is in phase with the voltage. A second element \(\mathrm{Y}\) when connected to the same a...

A capacitor of capacitance 500 \(\mu\)F is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. The maximum current in LC circuit will be _______ A.

Read the following statements :
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the nucleus is independent of mass number.
(C) Density of the nucleus is directly proportional to the mass number.
(D) Dens...

Two radioactive materials A and B have decay constants \(25 \lambda\) and \(16 \lambda\) respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be "e" after a time $$\fr...

Two identical thin metal plates has charge \(q_{1}\) and \(q_{2}\) respectively such that \(q_{1}>q_{2}\). The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between the...

If momentum of a body is increased by 20%, then its kinetic energy increases by

A modulating signal \(2 \sin \left(6.28 \times 10^{6}\right) t\) is added to the carrier signal \(4 \sin \left(12.56 \times 10^{9}\right) t\) for amplitude modulation. The combined signal is passed through a non-linear square law device. Th...

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Alloys such as constantan and manganin are used in making standard resistance coils.
Reason R: Constantan and manganin have v...

A \(1 \mathrm{~m}\) long wire is broken into two unequal parts \(\mathrm{X}\) and \(\mathrm{Y}\). The \(\mathrm{X}\) part of the wire is streched into another wire W. Length of \(W\) is twice the length of \(X\) and the resistance of $$\mat...

An \(\alpha\) particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:

Nearly 10% of the power of a \(110 \mathrm{~W}\) light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of \(1 \mathrm{~m}\) from the bulb to a distance of \(5 \mathrm{~m}\) is $$...

A \(8 \mathrm{~V}\) Zener diode along with a series resistance \(\mathrm{R}\) is connected across a \(20 \mathrm{~V}\) supply (as shown in the figure). If the maximum Zener current is \(25 \mathrm{~mA}\), then the minimum value of R will be...

Two identical metallic spheres \(\mathrm{A}\) and \(\mathrm{B}\) when placed at certain distance in air repel each other with a force of \(\mathrm{F}\). Another identical uncharged sphere \(\mathrm{C}\) is first placed in contact with $$\ma...

Light enters from air into a given medium at an angle of \(45^{\circ}\) with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of
\(15^{\circ}\) from its original direction. The refractive in...

An object of mass \(1 \mathrm{~kg}\) is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) and radius of...

A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the ...

The root mean square speed of smoke particles of mass \(5 \times 10^{-17} \mathrm{~kg}\) in their Brownian motion in air at NTP is approximately. [Given \(\mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}\)]

Two bodies of masses \(m_{1}=5 \mathrm{~kg}\) and \(m_{2}=3 \mathrm{~kg}\) are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the i...

The vertical component of the earth's magnetic field is \(6 \times 10^{-5} \mathrm{~T}\) at any place where the angle of dip is \(37^{\circ}\). The earth's resultant magnetic field at that place will be \(\left(\right.\)Given $$\left.\tan 3...

A wire X of length \(50 \mathrm{~cm}\) carrying a current of \(2 \mathrm{~A}\) is placed parallel to a long wire \(\mathrm{Y}\) of length \(5 \mathrm{~m}\). The wire \(\mathrm{Y}\) carries a current of \(3 \mathrm{~A}\). The distance betwee...

A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach i...

A ball is released from a height h. If \(t_{1}\) and \(t_{2}\) be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between \(t_{1}\) and \(t_{2}\).

A tube of length \(50 \mathrm{~cm}\) is filled completely with an incompressible liquid of mass \(250 \mathrm{~g}\) and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity ...

A metal wire of length \(0.5 \mathrm{~m}\) and cross-sectional area \(10^{-4} \mathrm{~m}^{2}\) has breaking stress \(5 \times 10^{8} \,\mathrm{Nm}^{-2}\). A block of \(10 \mathrm{~kg}\) is attached at one end of the string and is rotating ...

The velocity of a small ball of mass \(0.3 \mathrm{~g}\) and density \(8 \mathrm{~g} / \mathrm{cc}\) when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $$1.3 \mathrm{~g} / \mat...

The speed of a transverse wave passing through a string of length \(50 \mathrm{~cm}\) and mass \(10 \mathrm{~g}\) is \(60 \mathrm{~ms}^{-1}\). The area of cross-section of the wire is \(2.0 \mathrm{~mm}^{2}\) and its Young's modulus is $$1....

The torque of a force \(5 \hat{i}+3 \hat{j}-7 \hat{k}\) about the origin is \(\tau\). If the force acts on a particle whose position vector is \(2 i+2 j+k\), then the value of \(\tau\) will be

The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is \(10 \mathrm{~s}\). If the metallic bob is immersed in water, then the new time period becomes \(5 \sqrt{x}\) s. The value of \(x\) will be ...

Match List I with List II.

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An unpolarised light beam of intensity \(2 I_{0}\) is passed through a polaroid P and then through another polaroid Q which is oriented in such a way that its passing axis makes an angle of \(30^{\circ}\) relative to that of P. The intensit...