JEE Main 2023 (Online) 8th April Morning Shift

The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together, is :

Let the number of elements in sets \(A\) and \(B\) be five and two respectively. Then the number of subsets of \(A \times B\) each having at least 3 and at most 6 elements is :

In a bolt factory, machines \(A, B\) and \(C\) manufacture respectively \(20 \%, 30 \%\) and \(50 \%\) of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. If t...

Let \(\alpha, \beta, \gamma\) be the three roots of the equation \(x^{3}+b x+c=0\). If \(\beta \gamma=1=-\alpha\), then \(b^{3}+2 c^{3}-3 \alpha^{3}-6 \beta^{3}-8 \gamma^{3}\) is equal to :

Let \(S_{K}=\frac{1+2+\ldots+K}{K}\) and \(\sum_\limits{j=1}^{n} S_{j}^{2}=\frac{n}{A}\left(B n^{2}+C n+D\right)\), where \(A, B, C, D \in \mathbb{N}\) and \(A\) has least value. Then

Let \(A=\{0,3,4,6,7,8,9,10\}\) and \(R\) be the relation defined on \(A\) such that \(R=\{(x, y) \in A \times A: x-y\) is odd positive integer or \(x-y=2\}\). The minimum number of elements that must be added to the relation \(R\), so that ...

Let the mean and variance of 8 numbers \(x, y, 10,12,6,12,4,8\) be \(9\) and \(9.25\) respectively. If \(x > y\), then \(3 x-2 y\) is equal to _____________.

Let \(C(\alpha, \beta)\) be the circumcenter of the triangle formed by the lines
\(4 x+3 y=69\)
\(4 y-3 x=17\), and
\(x+7 y=61\).
Then \((\alpha-\beta)^{2}+\alpha+\beta\) is equal to :

If the points with position vectors \(\alpha \hat{i}+10 \hat{j}+13 \hat{k}, 6 \hat{i}+11 \hat{j}+11 \hat{k}, \frac{9}{2} \hat{i}+\beta \hat{j}-8 \hat{k}\) are collinear, then \((19 \alpha-6 \beta)^{2}\) is equal to :

Let \(\vec{a}=6 \hat{i}+9 \hat{j}+12 \hat{k}, \vec{b}=\alpha \hat{i}+11 \hat{j}-2 \hat{k}\) and \(\vec{c}\) be vectors such that \(\vec{a} \times \vec{c}=\vec{a} \times \vec{b}\). If $$\vec{a} \cdot \vec{c}=-12, \vec{c} \cdot(\hat{i}-2 \hat...

An oscillating LC circuit consists of a \(75 ~\mathrm{mH}\) inductor and a \(1.2 ~\mu \mathrm{F}\) capacitor. If the maximum charge to the capacitor is \(2.7 ~\mu \mathrm{C}\). The maximum current in the circuit will be ___________ $$\mathr...

For a nucleus \({ }_{\mathrm{A}}^{\mathrm{A}} \mathrm{X}\) having mass number \(\mathrm{A}\) and atomic number \(\mathrm{Z}\)
A. The surface energy per nucleon \(\left(b_{\mathrm{s}}\right)=-a_{1} A^{2 / 3}\).
B. The Coulomb contribution to...

A nucleus with mass number 242 and binding energy per nucleon as \(7.6~ \mathrm{MeV}\) breaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as \(8.1 ~\mathrm{MeV}\), the total gain in b...

In this figure the resistance of the coil of galvanometer G is \(2 ~\Omega\). The emf of the cell is \(4 \mathrm{~V}\). The ratio of potential difference across \(\mathrm{C}_{1}\) and \(\mathrm{C}_{2}\) is:

The momentum of a body is increased by \(50 \%\). The percentage increase in the kinetic energy of the body is ___________ \(\%\).

A TV transmitting antenna is \(98 \mathrm{~m}\) high and the receiving antenna is at the ground level. If the radius of the earth is \(6400 \mathrm{~km}\), the surface area covered by the transmitting antenna is approximately:

A current of \(2 \mathrm{~A}\) flows through a wire of cross-sectional area \(25.0 \mathrm{~mm}^{2}\). The number of free electrons in a cubic meter are \(2.0 \times 10^{28}\). The drift velocity of the electrons is __________ $$\times 10^{...

Proton \((\mathrm{P})\) and electron (e) will have same de-Broglie wavelength when the ratio of their momentum is (assume, \(\mathrm{m}_{\mathrm{p}}=1849 \mathrm{~m}_{\mathrm{e}}\) ):

Certain galvanometers have a fixed core made of non magnetic metallic material. The function of this metallic material is

For the logic circuit shown, the output waveform at \(\mathrm{Y}\) is:

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius \(\mathrm{R}\), with distance \(r\) from the centre O is represented by:

An electric dipole of dipole moment is \(6.0 \times 10^{-6} ~\mathrm{C m}\) placed in a uniform electric field of \(1.5 \times 10^{3} ~\mathrm{NC}^{-1}\) in such a way that dipole moment is along electric field. The work done in rotating di...

In a reflecting telescope, a secondary mirror is used to:

Two vertical parallel mirrors A and B are separated by \(10 \mathrm{~cm}\). A point object \(\mathrm{O}\) is placed at a distance of \(2 \mathrm{~cm}\) from mirror \(\mathrm{A}\). The distance of the second nearest image behind mirror A fro...

Given below are two statements:
Statement I: If \(\mathrm{E}\) be the total energy of a satellite moving around the earth, then its potential energy will be \(\frac{E}{2}\).
Statement II: The kinetic energy of a satellite revolving in an or...

The weight of a body on the earth is \(400 \mathrm{~N}\). Then weight of the body when taken to a depth half of the radius of the earth will be:

Given below are two statements:
Statement I: If heat is added to a system, its temperature must increase.
Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.
In the light of the above sta...

At any instant the velocity of a particle of mass \(500 \mathrm{~g}\) is \(\left(2 t \hat{i}+3 t^{2} \hat{j}\right) \mathrm{ms}^{-1}\). If the force acting on the particle at \(t=1 \mathrm{~s}\) is \((\hat{i}+x \hat{j}) \mathrm{N}\). Then t...

The magnetic intensity at the center of a long current carrying solenoid is found to be \(1.6 \times 10^{3} \mathrm{Am}^{-1}\). If the number of turns is 8 per cm, then the current flowing through the solenoid is __________ A.

A charge particle moving in magnetic field B, has the components of velocity along B as well as perpendicular to B. The path of the charge particle will be

Two projectiles A and B are thrown with initial velocities of \(40 \mathrm{~m} / \mathrm{s}\) and \(60 \mathrm{~m} / \mathrm{s}\) at angles \(30^{\circ}\) and \(60^{\circ}\) with the horizontal respectively. The ratio of their ranges respec...

An air bubble of volume \(1 \mathrm{~cm}^{3}\) rises from the bottom of a lake \(40 \mathrm{~m}\) deep to the surface at a temperature of \(12^{\circ} \mathrm{C}\). The atmospheric pressure is \(1 \times 10^{5} \mathrm{~Pa}\) the density of...

An aluminium rod with Young's modulus \(Y=7.0 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}\) undergoes elastic strain of \(0.04 \%\). The energy per unit volume stored in the rod in SI unit is:

An air bubble of diameter \(6 \mathrm{~mm}\) rises steadily through a solution of density \(1750 \mathrm{~kg} / \mathrm{m}^{3}\) at the rate of \(0.35 \mathrm{~cm} / \mathrm{s}\). The co-efficient of viscosity of the solution (neglect densi...

The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is \(\frac{1}{x} \mathrm{MR}^{2}\), where \(\mathrm{R}\) is the radius and \(M\) is the mass of the semicircular ...

Dimension of \(\frac{1}{\mu_{0} \in_{0}}\) should be equal to

A cylindrical wire of mass \((0.4 \pm 0.01) \mathrm{g}\) has length \((8 \pm 0.04) \mathrm{cm}\) and radius \((6 \pm 0.03) \mathrm{mm}\). The maximum error in its density will be:

Two forces having magnitude \(A\) and \(\frac{A}{2}\) are perpendicular to each other. The magnitude of their resultant is:

The engine of a train moving with speed \(10 \mathrm{~ms}^{-1}\) towards a platform sounds a whistle at frequency \(400 \mathrm{~Hz}\). The frequency heard by a passenger inside the train is: (neglect air speed. Speed of sound in air $$=330...

An organ pipe \(40 \mathrm{~cm}\) long is open at both ends. The speed of sound in air is \(360 \mathrm{~ms}^{-1}\). The frequency of the second harmonic is ___________ \(\mathrm{Hz}\).