JEE Main 2023 (Online) 11th April Morning Shift

In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sits on the allotted seat, is _________.

Let \(S=\left\{M=\left[a_{i j}\right], a_{i j} \in\{0,1,2\}, 1 \leq i, j \leq 2\right\}\) be a sample space and \(A=\{M \in S: M\) is invertible \(\}\) be an event. Then \(P(A)\) is equal to :

If \(a\) and \(b\) are the roots of the equation \(x^{2}-7 x-1=0\), then the value of \(\frac{a^{21}+b^{21}+a^{17}+b^{17}}{a^{19}+b^{19}}\) is equal to _____________.

Let \(x_{1}, x_{2}, \ldots, x_{100}\) be in an arithmetic progression, with \(x_{1}=2\) and their mean equal to 200 . If \(y_{i}=i\left(x_{i}-i\right), 1 \leq i \leq 100\), then the mean of \(y_{1}, y_{2}, \ldots, y_{100}\) is :

Let \(S=109+\frac{108}{5}+\frac{107}{5^{2}}+\ldots .+\frac{2}{5^{107}}+\frac{1}{5^{108}}\). Then the value of \(\left(16 S-(25)^{-54}\right)\) is equal to ___________.

An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?

Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 fr...

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

For any vector \(\vec{a}=a_{1} \hat{i}+a_{2} \hat{j}+a_{3} \hat{k}\), with \(10\left|a_{i}\right|<1, i=1,2,3\), consider the following statements :
(A): $$\max \left\{\left|a_{1}\right|,\left|a_{2}\right|,\left|a_{3}\right|\right\} \leq|\ve...

Let \(\vec{a}\) be a non-zero vector parallel to the line of intersection of the two planes described by \(\hat{i}+\hat{j}, \hat{i}+\hat{k}\) and \(\hat{i}-\hat{j}, \hat{j}-\hat{k}\). If \(\theta\) is the angle between the vector $$\vec{a}$...

As per the given graph, choose the correct representation for curve \(\mathrm{A}\) and curve B.
Where \(\mathrm{X}_{\mathrm{C}}=\) reactance of pure capacitive circuit connected with A.C. source
\(\mathrm{X}_{\mathrm{L}}=\) reactance of pu...

Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If \(\lambda_{A}\) and \(\lambda_{B}\) are decay constants of A and B respectively, then choose the correct relation ...

A parallel plate capacitor of capacitance \(2 \mathrm{~F}\) is charged to a potential \(\mathrm{V}\), The energy stored in the capacitor is \(E_{1}\). The capacitor is now connected to another uncharged identical capacitor in parallel combi...

An average force of \(125 \mathrm{~N}\) is applied on a machine gun firing bullets each of mass \(10 \mathrm{~g}\) at the speed of \(250 \mathrm{~m} / \mathrm{s}\) to keep it in position. The number of bullets fired per second by the machin...

A coin placed on a rotating table just slips when it is placed at a distance of \(1 \mathrm{~cm}\) from the center. If the angular velocity of the table in halved, it will just slip when placed at a distance of _________ from the centre :

A transmitting antenna is kept on the surface of the earth. The minimum height of receiving antenna required to receive the signal in line of sight at \(4 \mathrm{~km}\) distance from it is \(x \times 10^{-2} \mathrm{~m}\). The value of $$x...

Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:

The current sensitivity of moving coil galvanometer is increased by \(25 \%\). This increase is achieved only by changing in the number of turns of coils and area of cross section of the wire while keeping the resistance of galvanometer coi...

In the circuit diagram shown in figure given below, the current flowing through resistance \(3 ~\Omega\) is \(\frac{x}{3} A\).
The value of \(x\) is ___________

A metallic surface is illuminated with radiation of wavelength \(\lambda\), the stopping potential is \(V_{0}\). If the same surface is illuminated with radiation of wavelength \(2 \lambda\). the stopping potential becomes $$\frac{V_{o}}{4}...

A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is $$x \times 10^{15} \mathrm{~H...

The magnetic field B crossing normally a square metallic plate of area \(4 \mathrm{~m}^{2}\) is changing with time as shown in figure. The magnitude of induced emf in the plate during \(\mathrm{t}=2 s\) to \(\mathrm{t}=4 s\), is __________ ...

The electric field in an electromagnetic wave is given as
\(\overrightarrow{\mathrm{E}}=20 \sin \omega\left(\mathrm{t}-\frac{x}{\mathrm{c}}\right) \overrightarrow{\mathrm{j}} \mathrm{NC}^{-1}\)
where \(\omega\) and \(c\) are angular frequen...

The logic performed by the circuit shown in figure is equivalent to :

As shown in the figure, a configuration of two equal point charges \(\left(q_{0}=+2 \mu \mathrm{C}\right)\) is placed on an inclined plane. Mass of each point charge is \(20 \mathrm{~g}\). Assume that there is no friction between charge and...

The critical angle for a denser-rarer interface is \(45^{\circ}\). The speed of light in rarer medium is \(3 \times 10^{8} \mathrm{~m} / \mathrm{s}\). The speed of light in the denser medium is:

The radius of curvature of each surface of a convex lens having refractive index 1.8 is \(20 \mathrm{~cm}\). The lens is now immersed in a liquid of refractive index 1.5 . The ratio of power of lens in air to its power in the liquid will be...

The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are \(\rho\) and \(\rho / 3\) respectively. The ratio of acceleration due to gravity at their surfaces \(\left(g_{A}: g_{B}\right)\) will be:

\(1 \mathrm{~kg}\) of water at \(100^{\circ} \mathrm{C}\) is converted into steam at \(100^{\circ} \mathrm{C}\) by boiling at atmospheric pressure. The volume of water changes from \(1.00 \times 10^{-3} \mathrm{~m}^{3}\) as a liquid to $$1....

On a temperature scale '\(\mathrm{X}\)', the boiling point of water is \(65^{\circ} \mathrm{X}\) and the freezing point is \(-15^{\circ} \mathrm{X}\). Assume that the \(\mathrm{X}\) scale is linear. The equivalent temperature corresponding ...

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafloride (polyatomic). Arrange these on the...

The free space inside a current carrying toroid is filled with a material of susceptibility \(2 \times 10^{-2}\). The percentage increase in the value of magnetic field inside the toroid will be

A projectile fired at \(30^{\circ}\) to the ground is observed to be at same height at time \(3 \mathrm{~s}\) and \(5 \mathrm{~s}\) after projection, during its flight. The speed of projection of the projectile is ___________ $$\mathrm{m} ~...

From the \(\mathrm{v}-t\) graph shown, the ratio of distance to displacement in \(25 \mathrm{~s}\) of motion is:

The length of a wire becomes \(l_{1}\) and \(l_{2}\) when \(100 \mathrm{~N}\) and \(120 \mathrm{~N}\) tensions are applied respectively. If \(10 ~l_{2}=11~ l_{1}\), the natural length of wire will be \(\frac{1}{x} ~l_{1}\). Here the value o...

A solid sphere of mass \(500 \mathrm{~g}\) and radius \(5 \mathrm{~cm}\) is rotated about one of its diameter with angular speed of \(10 ~\mathrm{rad} ~\mathrm{s}^{-1}\). If the moment of inertia of the sphere about its tangent is $$x \time...

The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement \((x)\) starting from mean position to extreme position (A) is given by

Given below are two statements :
Statements I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances.
Statements II : \(\mathrm{Au} < \mathrm{Parsec} (\mathrm{Pc}) < \mathrm{ly}\)
In the lig...

The equation of wave is given by
\(\mathrm{Y}=10^{-2} \sin 2 \pi(160 t-0.5 x+\pi / 4)\)
where \(x\) and \(Y\) are in \(\mathrm{m}\) and \(\mathrm{t}\) in \(s\). The speed of the wave is ________ \(\mathrm{km} ~\mathrm{h}^{-1}\).

A force \(\vec{F}=(2+3 x) \hat{i}\) acts on a particle in the \(x\) direction where F is in newton and \(x\) is in meter. The work done by this force during a displacement from \(x=0\) to \(x=4 \mathrm{~m}\), is __________ J.