JEE Main 2023 (Online) 31st January Morning Shift

Let 5 digit numbers be constructed using the digits \(0,2,3,4,7,9\) with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number 42923 is __________.

Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to ____________.

A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is :

The number of real roots of the equation \(\sqrt{x^{2}-4 x+3}+\sqrt{x^{2}-9}=\sqrt{4 x^{2}-14 x+6}\), is :

If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296 , respectively, then the sum of common ratios of all such GPs is

Let \(a_{1}, a_{2}, \ldots, a_{n}\) be in A.P. If \(a_{5}=2 a_{7}\) and \(a_{11}=18\), then
\(12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots+\frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)\) is equa...

Let \(\mathrm{R}\) be a relation on \(\mathrm{N} \times \mathbb{N}\) defined by \((a, b) ~\mathrm{R}~(c, d)\) if and only if \(a d(b-c)=b c(a-d)\). Then \(\mathrm{R}\) is

If the variance of the frequency distribution

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Let \(\vec{a}=2 \hat{i}+\hat{j}+\hat{k}\), and \(\vec{b}\) and \(\vec{c}\) be two nonzero vectors such that \(|\vec{a}+\vec{b}+\vec{c}|=|\vec{a}+\vec{b}-\vec{c}|\) and \(\vec{b} \cdot \vec{c}=0\). Consider the following two statements:
(A) ...

Let \(\vec{a}\) and \(\vec{b}\) be two vectors such that \(|\vec{a}|=\sqrt{14},|\vec{b}|=\sqrt{6}\) and \(|\vec{a} \times \vec{b}|=\sqrt{48}\). Then \((\vec{a} \cdot \vec{b})^{2}\) is equal to ___________.

If \(\mathrm{R}, \mathrm{X}_{\mathrm{L}}\), and \(\mathrm{X}_{\mathrm{C}}\) represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless :

An inductor of \(0.5 ~\mathrm{mH}\), a capacitor of \(20 ~\mu \mathrm{F}\) and resistance of \(20 ~\Omega\) are connected in series with a \(220 \mathrm{~V}\) ac source. If the current is in phase with the emf, the amplitude of current of t...

A free neutron decays into a proton but a free proton does not decay into neutron. This is because

For hydrogen atom, \(\lambda_{1}\) and \(\lambda_{2}\) are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of \(\lambda_{1}\) and \(\lambda_{2}\) is \(\frac{x}{32}\). The value of \(x\) is...

100 balls each of mass \(\mathrm{m}\) moving with speed \(v\) simultaneously strike a wall normally and reflected back with same speed, in time \(\mathrm{t ~s}\). The total force exerted by the balls on the wall is

The amplitude of \(15 \sin (1000 \pi \mathrm{t})\) is modulated by \(10 \sin (4 \pi \mathrm{t})\) signal. The amplitude modulated signal contains frequency (ies) of
A. \(500 \mathrm{~Hz}\)
B. \(2 \mathrm{~Hz}\)
C. \(250 \mathrm{~Hz}\)
D. $$...

The drift velocity of electrons for a conductor connected in an electrical circuit is \(\mathrm{V}_{\mathrm{d}}\). The conductor in now replaced by another conductor with same material and same length but double the area of cross section. T...

Two identical cells, when connected either in parallel or in series gives same current in an external resistance \(5 ~\Omega\). The internal resistance of each cell will be ___________ \(\Omega\).

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R
Assertion A : The beam of electrons show wave nature and exhibit interference and diffraction.
Reason R : Davisson Germer Experimentally v...

If a source of electromagnetic radiation having power \(15 \mathrm{~kW}\) produces \(10^{16}\) photons per second, the radiation belongs to a part of spectrum is.
(Take Planck constant \(h=6 \times 10^{-34} \mathrm{Js}\) )

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following
{Assume negligible air friction}

In a medium the speed of light wave decreases to \(0.2\) times to its speed in free space The ratio of relative permittivity to the refractive index of the medium is \(x: 1\). The value of \(x\) is _________.
(Given speed of light in free s...

The effect of increase in temperature on the number of electrons in conduction band (\(\mathrm{n_e}\)) and resistance of a semiconductor will be as:

Which of the following correctly represents the variation of electric potential \((\mathrm{V})\) of a charged spherical conductor of radius \((\mathrm{R})\) with radial distance \((\mathrm{r})\) from the center?

Expression for an electric field is given by \(\overrightarrow{\mathrm{E}}=4000 x^{2} \hat{i} \frac{\mathrm{V}}{\mathrm{m}}\). The electric flux through the cube of side \(20 \mathrm{~cm}\) when placed in electric field (as shown in the fig...

At a certain depth "d " below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height \(\mathrm{3 R}\) above earth surface. Where \(\mathrm{R}\) is Radius of earth (Take $$\mathrm{R}=6400 \mat...

The pressure of a gas changes linearly with volume from \(\mathrm{A}\) to \(\mathrm{B}\) as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be

The correct relation between \(\gamma = {{{c_p}} \over {{c_v}}}\) and temperature T is :

As shown in figure, a \(70 \mathrm{~kg}\) garden roller is pushed with a force of \(\vec{F}=200 \mathrm{~N}\) at an angle of \(30^{\circ}\) with horizontal. The normal reaction on the roller is
(Given \(\mathrm{g=10~m~s^{-2}}\))

A bar magnet with a magnetic moment \(5.0 \mathrm{Am}^{2}\) is placed in parallel position relative to a magnetic field of \(0.4 \mathrm{~T}\). The amount of required work done in turning the magnet from parallel to antiparallel position re...

A rod with circular cross-section area \(2 \mathrm{~cm}^{2}\) and length \(40 \mathrm{~cm}\) is wound uniformly with 400 turns of an insulated wire. If a current of \(0.4 \mathrm{~A}\) flows in the wire windings, the total magnetic flux pro...

The initial speed of a projectile fired from ground is \(\mathrm{u}\). At the highest point during its motion, the speed of projectile is \(\frac{\sqrt{3}}{2} u\). The time of flight of the projectile is :

The speed of a swimmer is \(4 \mathrm{~km} \mathrm{~h}^{-1}\) in still water. If the swimmer makes his strokes normal to the flow of river of width \(1 \mathrm{~km}\), he reaches a point \(750 \mathrm{~m}\) down the stream on the opposite b...

If 1000 droplets of water of surface tension \(0.07 \mathrm{~N} / \mathrm{m}\), having same radius \(1 \mathrm{~mm}\) each, combine to from a single drop. In the process the released surface energy is :-
$$\left( {\mathrm{Take}\,\pi = {{22...

A thin rod having a length of \(1 \mathrm{~m}\) and area of cross-section \(3 \times 10^{-6} \mathrm{~m}^{2}\) is suspended vertically from one end. The rod is cooled from \(210^{\circ} \mathrm{C}\) to \(160^{\circ} \mathrm{C}\). After cool...

A solid sphere of mass \(1 \mathrm{~kg}\) rolls without slipping on a plane surface. Its kinetic energy is \(7 \times 10^{-3} \mathrm{~J}\). The speed of the centre of mass of the sphere is __________ \(\operatorname{cm~s}^{-1}\)

The maximum potential energy of a block executing simple harmonic motion is \(25 \mathrm{~J}\). A is amplitude of oscillation. At \(\mathrm{A / 2}\), the kinetic energy of the block is

In the figure given below, a block of mass \(M=490 \mathrm{~g}\) placed on a frictionless table is connected with two springs having same spring constant \(\left(\mathrm{K}=2 \mathrm{~N} \mathrm{~m}^{-1}\right)\). If the block is horizontal...

Two polaroide \(\mathrm{A}\) and \(\mathrm{B}\) are placed in such a way that the pass-axis of polaroids are perpendicular to each other. Now, another polaroid \(\mathrm{C}\) is placed between \(\mathrm{A}\) and \(\mathrm{B}\) bisecting ang...

A lift of mass \(\mathrm{M}=500 \mathrm{~kg}\) is descending with speed of \(2 \mathrm{~ms}^{-1}\). Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of \(2 \mathrm{~ms}^{-2}\). The kinetic energy of ...