JEE Main 2023 (Online) 13th April Evening Shift

Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits \(1,2,3,4,5\) with repetition, is _________.

The random variable \(\mathrm{X}\) follows binomial distribution \(\mathrm{B}(\mathrm{n}, \mathrm{p})\), for which the difference of the mean and the variance is 1 . If \(2 \mathrm{P}(\mathrm{X}=2)=3 \mathrm{P}(\mathrm{X}=1)\), then $$n^{2}...

Let \(\alpha, \beta\) be the roots of the equation \(x^{2}-\sqrt{2} x+2=0\). Then \(\alpha^{14}+\beta^{14}\) is equal to

Let \([\alpha]\) denote the greatest integer \(\leq \alpha\). Then \([\sqrt{1}]+[\sqrt{2}]+[\sqrt{3}]+\ldots+[\sqrt{120}]\) is equal to __________

Let a\(_1\), a\(_2\), a\(_3\), .... be a G.P. of increasing positive numbers. Let the sum of its 6th and 8th terms be 2 and the product of its 3rd and 5th terms be \(\frac{1}{9}\). Then \(6(a_2+a_4)(a_4+a_6)\) is equal to

Let \(\mathrm{A}=\{-4,-3,-2,0,1,3,4\}\) and \(\mathrm{R}=\left\{(a, b) \in \mathrm{A} \times \mathrm{A}: b=|a|\right.\) or \(\left.b^{2}=a+1\right\}\) be a relation on \(\mathrm{A}\). Then the minimum number of elements, that must be added ...

The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 were wrongly read as 45 and 50 respectively. Then the correct variance is _________

Let \((\alpha, \beta)\) be the centroid of the triangle formed by the lines \(15 x-y=82,6 x-5 y=-4\) and \(9 x+4 y=17\). Then \(\alpha+2 \beta\) and \(2 \alpha-\beta\) are the roots of the equation :

Let \(|\vec{a}|=2,|\vec{b}|=3\) and the angle between the vectors \(\vec{a}\) and \(\vec{b}\) be \(\frac{\pi}{4}\). Then \(|(\vec{a}+2 \vec{b}) \times(2 \vec{a}-3 \vec{b})|^{2}\) is equal to :

Let for a triangle \(\mathrm{ABC}\),
\(\overrightarrow{\mathrm{AB}}=-2 \hat{i}+\hat{j}+3 \hat{k}\)
\(\overrightarrow{\mathrm{CB}}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}\)
$$\overrightarrow{\mathrm{CA}}=4 \hat{i}+3 \hat{j}+\delta \hat{k...

Given below are two statements:
Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor.
Statement II : An AC circuit containing a pure capacitor or a pure inductor consumes high power due...

Given below are two statements: one is labelled as Assertion \(\mathbf{A}\) and the other is labelled as Reason \(\mathbf{R}\)
Assertion A : The binding energy per nucleon is practically independent of the atomic number for nuclei of mass n...

In the network shown below, the charge accumulated in the capacitor in steady state will be:

In the circuit shown, the energy stored in the capacitor is \(n ~\mu \mathrm{J}\). The value of \(n\) is __________

A vehicle of mass \(200 \mathrm{~kg}\) is moving along a levelled curved road of radius \(70 \mathrm{~m}\) with angular velocity of \(0.2 ~\mathrm{rad} / \mathrm{s}\). The centripetal force acting on the vehicle is:

To radiate EM signal of wavelength \(\lambda\) with high efficiency, the antennas should have a minimum size equal to:

Given below are two statements:
Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface.
Statement II : Above the threshold frequency...

An atom absorbs a photon of wavelength \(500 \mathrm{~nm}\) and emits another photon of wavelength \(600 \mathrm{~nm}\). The net energy absorbed by the atom in this process is \(n \times 10^{-4} ~\mathrm{eV}\). The value of n is __________....

An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area \(24 \mathrm{~cm}^{2}\). The two ends of the wire are connected to a resistor. The total resistance in the circuit is $$12 ~\Omega...

In an electromagnetic wave, at an instant and at particular position, the electric field is along the negative \(z\)-axis and magnetic field is along the positive \(x\)-axis. Then the direction of propagation of electromagnetic wave is:

The output from NAND gate having inputs A and B given below will be,

A \(10 ~\mu \mathrm{C}\) charge is divided into two parts and placed at \(1 \mathrm{~cm}\) distance so that the repulsive force between them is maximum. The charges of the two parts are:

Three point charges \(\mathrm{q},-2 \mathrm{q}\) and \(2 \mathrm{q}\) are placed on $x$-axis at a distance \(x=0, x=\frac{3}{4} R\) and \(x=R\) respectively from origin as shown. If \(\mathrm{q}=2 \times 10^{-6} \mathrm{C}\) and $$\mathrm{R...

A bi convex lens of focal length \(10 \mathrm{~cm}\) is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is ____________ D.

Given below are two statements:
Statement I : For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases.
Statement II : Escape velocity is independent of the radius of the p...

Two planets A and B of radii \(\mathrm{R}\) and 1.5 R have densities \(\rho\) and \(\rho / 2\) respectively. The ratio of acceleration due to gravity at the surface of \(\mathrm{B}\) to \(\mathrm{A}\) is:

The initial pressure and volume of an ideal gas are P\(_0\) and V\(_0\). The final pressure of the gas when the gas is suddenly compressed to volume \(\frac{V_0}{4}\) will be :
(Given \(\gamma\) = ratio of specific heats at constant pressur...

The mean free path of molecules of a certain gas at STP is \(1500 \mathrm{~d}\), where \(\mathrm{d}\) is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at \(373 \mathrm{~K}\) ...

Two plates \(\mathrm{A}\) and \(\mathrm{B}\) have thermal conductivities \(84 ~\mathrm{Wm}^{-1} \mathrm{~K}^{-1}\) and \(126 ~\mathrm{Wm}^{-1} \mathrm{~K}^{-1}\) respectively. They have same surface area and same thickness. They are placed ...

An electron is moving along the positive \(\mathrm{x}\)-axis. If the uniform magnetic field is applied parallel to the negative z-axis, then
A. The electron will experience magnetic force along positive y-axis
B. The electron will experienc...

A straight wire \(\mathrm{AB}\) of mass \(40 \mathrm{~g}\) and length \(50 \mathrm{~cm}\) is suspended by a pair of flexible leads in uniform magnetic field of magnitude \(0.40 \mathrm{~T}\) as shown in the figure. The magnitude of the curr...

The distance travelled by an object in time \(t\) is given by \(s=(2.5) t^{2}\). The instantaneous speed of the object at \(\mathrm{t}=5 \mathrm{~s}\) will be:

A passenger sitting in a train A moving at \(90 \mathrm{~km} / \mathrm{h}\) observes another train \(\mathrm{B}\) moving in the opposite direction for \(8 \mathrm{~s}\). If the velocity of the train B is \(54 \mathrm{~km} / \mathrm{h}\), th...

Given below are two statements: one is labelled as Assertion \(\mathbf{A}\) and the other is labelled as Reason \(\mathbf{R}\)
Assertion A : A spherical body of radius \((5 \pm 0.1) \mathrm{mm}\) having a particular density is falling throu...

A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52.5 N. The angular acceleration of the cylinder will be _________ rad s\(^{-2}\).

A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is :

In the equation \(\left[X+\frac{a}{Y^{2}}\right][Y-b]=\mathrm{R} T, X\) is pressure, \(Y\) is volume, \(\mathrm{R}\) is universal gas constant and \(T\) is temperature. The physical quantity equivalent to the ratio \(\frac{a}{b}\) is:

In a Young's double slits experiment, the ratio of amplitude of light coming from slits is \(2: 1\). The ratio of the maximum to minimum intensity in the interference pattern is:

In an experiment with sonometer when a mass of \(180 \mathrm{~g}\) is attached to the string, it vibrates with fundamental frequency of \(30 \mathrm{~Hz}\). When a mass \(\mathrm{m}\) is attached, the string vibrates with fundamental freque...

A car accelerates from rest to \(u \mathrm{~m} / \mathrm{s}\). The energy spent in this process is E J. The energy required to accelerate the car from \(u \mathrm{~m} / \mathrm{s}\) to \(2 \mathrm{u} \mathrm{m} / \mathrm{s}\) is $$\mathrm{n...