JEE Main 2023 (Online) 6th April Evening Shift

For the system of equations
\(x+y+z=6\)
\(x+2 y+\alpha z=10\)
\(x+3 y+5 z=\beta\), which one of the following is NOT true?

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is :

The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is __________.

Three dice are rolled. If the probability of getting different numbers on the three dice is \(\frac{p}{q}\), where \(p\) and \(q\) are co-prime, then \(q-p\) is equal to :

If \(\operatorname{gcd}~(\mathrm{m}, \mathrm{n})=1\) and \(1^{2}-2^{2}+3^{2}-4^{2}+\ldots . .+(2021)^{2}-(2022)^{2}+(2023)^{2}=1012 ~m^{2} n\) then \(m^{2}-n^{2}\) is equal to :

If
\((20)^{19}+2(21)(20)^{18}+3(21)^{2}(20)^{17}+\ldots+20(21)^{19}=k(20)^{19}\),
then \(k\) is equal to ___________.

If the mean and variance of the frequency distribution

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The value of \(\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}\) is __________.

Let the vectors \(\vec{a}, \vec{b}, \vec{c}\) represent three coterminous edges of a parallelopiped of volume V. Then the volume of the parallelopiped, whose coterminous edges are represented by \(\vec{a}, \vec{b}+\vec{c}\) and $$\vec{a}+2 ...

The sum of all values of \(\alpha\), for which the points whose position vectors are \(\hat{i}-2 \hat{j}+3 \hat{k}, 2 \hat{i}-3 \hat{j}+4 \hat{k},(\alpha+1) \hat{i}+2 \hat{k}\) and \(9 \hat{i}+(\alpha-8) \hat{j}+6 \hat{k}\) are coplanar, is...

A capacitor of capacitance \(150.0 ~\mu \mathrm{F}\) is connected to an alternating source of emf given by \(\mathrm{E}=36 \sin (120 \pi \mathrm{t}) \mathrm{V}\). The maximum value of current in the circuit is approximately equal to :

A small particle of mass \(m\) moves in such a way that its potential energy \(U=\frac{1}{2} m ~\omega^{2} r^{2}\) where \(\omega\) is constant and \(r\) is the distance of the particle from origin. Assuming Bohr's quantization of momentum ...

Experimentally it is found that \(12.8 ~\mathrm{eV}\) energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is \(\frac{9}{x} \times 10^{-10} \mathrm{~m}\). The...

As shown in the figure, two parallel plate capacitors having equal plate area of \(200 \mathrm{~cm}^{2}\) are joined in such a way that \(a \neq b\). The equivalent capacitance of the combination is \(x \in_{0} \mathrm{~F}\). The value of $...

As shown in the figure, a particle is moving with constant speed \(\pi ~\mathrm{m} / \mathrm{s}\). Considering its motion from \(\mathrm{A}\) to \(\mathrm{B}\), the magnitude of the average velocity is :

A child of mass \(5 \mathrm{~kg}\) is going round a merry-go-round that makes 1 rotation in \(3.14 \mathrm{~s}\). The radius of the merry-go-round is \(2 \mathrm{~m}\). The centrifugal force on the child will be

For an amplitude modulated wave the minimum amplitude is \(3 \mathrm{~V}\), while the modulation index is \(60 \%\). The maximum amplitude of the modulated wave is:

Figure shows a part of an electric circuit. The potentials at points \(a, b\) and \(c\) are \(30 \mathrm{~V}, 12 \mathrm{~V}\) and \(2 \mathrm{~V}\) respectively. The current through the \(20 ~\Omega\) resistor will be,

A student is provided with a variable voltage source \(\mathrm{V}\), a test resistor \(R_{T}=10 ~\Omega\), two identical galvanometers \(G_{1}\) and \(G_{2}\) and two additional resistors, \(R_{1}=10 ~M \Omega\) and \(R_{2}=0.001 ~\Omega\)....

As shown in the figure, the voltmeter reads \(2 \mathrm{~V}\) across \(5 ~\Omega\) resistor. The resistance of the voltmeter is _________ \(\Omega\).

The work functions of Aluminium and Gold are \(4.1 ~\mathrm{eV}\) and and \(5.1 ~\mathrm{eV}\) respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is

Two concentric circular coils with radii \(1 \mathrm{~cm}\) and \(1000 \mathrm{~cm}\), and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be ___________ $...

The energy density associated with electric field \(\vec{E}\) and magnetic field \(\vec{B}\) of an electromagnetic wave in free space is given by \(\left(\epsilon_{0}-\right.\) permittivity of free space, \(\mu_{0}-\) permeability of free s...

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: Diffusion current in a p-n junction is greater than the drift current in magnitude if the junction is forward biased.
Reason R...

A dipole comprises of two charged particles of identical magnitude \(q\) and opposite in nature. The mass 'm' of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance...

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The phase difference of two light waves change if they travel through different media having same thickness, but different ind...

A 2 meter long scale with least count of \(0.2 \mathrm{~cm}\) is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at $$80 \mathrm{...

The weight of a body on the surface of the earth is \(100 \mathrm{~N}\). The gravitational force on it when taken at a height, from the surface of earth, equal to one-fourth the radius of the earth is:

Choose the incorrect statement from the following:

The temperature of an ideal gas is increased from \(200 \mathrm{~K}\) to \(800 \mathrm{~K}\). If r.m.s. speed of gas at \(200 \mathrm{~K}\) is \(v_{0}\). Then, r.m.s. speed of the gas at \(800 \mathrm{~K}\) will be:

A body cools in 7 minutes from \(60^{\circ} \mathrm{C}\) to \(40^{\circ} \mathrm{C}\). The temperature of the surrounding is \(10^{\circ} \mathrm{C}\). The temperature of the body after the next 7 minutes will be:

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

A proton with a kinetic energy of \(2.0 ~\mathrm{eV}\) moves into a region of uniform magnetic field of magnitude \(\frac{\pi}{2} \times 10^{-3} \mathrm{~T}\). The angle between the direction of magnetic field and velocity of proton is $$60...

A particle starts with an initial velocity of \(10.0 \mathrm{~ms}^{-1}\) along \(x\)-direction and accelerates uniformly at the rate of \(2.0 \mathrm{~ms}^{-2}\). The time taken by the particle to reach the velocity of $$60.0 \mathrm{~ms}^{...

Given below are two statements: one is labelled as Assertion \(\mathbf{A}\) and the other is labelled as Reason \(\mathbf{R}\)
Assertion A: When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principle is o...

A metal block of mass \(\mathrm{m}\) is suspended from a rigid support through a metal wire of diameter \(14 \mathrm{~mm}\). The tensile stress developed in the wire under equilibrium state is \(7 \times 10^{5} \mathrm{Nm}^{-2}\). The value...

A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is \(\sqrt{\frac{2}{x}}\). The...

A simple pendulum with length \(100 \mathrm{~cm}\) and bob of mass \(250 \mathrm{~g}\) is executing S.H.M. of amplitude \(10 \mathrm{~cm}\). The maximum tension in the string is found to be \(\frac{x}{40} \mathrm{~N}\). The value of \(x\) i...

A beam of light consisting of two wavelengths \(7000~\mathop A\limits^o\) and \(5500~\mathop A\limits^o\) is used to obtain interference pattern in Young's double slit experiment. The distance between the slits is \(2.5 \mathrm{~mm}\) and...

A body is dropped on ground from a height '\(h_{1}\)' and after hitting the ground, it rebounds to a height '\(h_{2}\)'. If the ratio of velocities of the body just before and after hitting ground is 4 , then percentage loss in kinetic ener...