JEE Main 2023 (Online) 8th April Evening Shift

If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which \(\mathrm{C}\) and \(\mathrm{S}\) do not come together, is \((6 !) \mathrm{k}\), then \(\mathrm{k}\) is equal to :

If the probability that the random variable \(\mathrm{X}\) takes values \(x\) is given by \(\mathrm{P}(\mathrm{X}=x)=\mathrm{k}(x+1) 3^{-x}, x=0,1,2,3, \ldots\), where \(\mathrm{k}\) is a constant, then \(\mathrm{P}(\mathrm{X} \geq 2)\) is ...

Let m and \(\mathrm{n}\) be the numbers of real roots of the quadratic equations \(x^{2}-12 x+[x]+31=0\) and \(x^{2}-5|x+2|-4=0\) respectively, where \([x]\) denotes the greatest integer \(\leq x\). Then $$\mathrm{m}^{2}+\mathrm{mn}+\mathr...

Let \(\mathrm{a}_{\mathrm{n}}\) be the \(\mathrm{n}^{\text {th }}\) term of the series \(5+8+14+23+35+50+\ldots\) and \(\mathrm{S}_{\mathrm{n}}=\sum_\limits{k=1}^{n} a_{k}\). Then \(\mathrm{S}_{30}-a_{40}\) is equal to :

Let \(0 < z < y < x\) be three real numbers such that \(\frac{1}{x}, \frac{1}{y}, \frac{1}{z}\) are in an arithmetic progression and \(x, \sqrt{2} y, z\) are in a geometric progression. If \(x y+y z+z x=\frac{3}{\sqrt{2}} x y z\) , then $$3...

Let \(\mathrm{A}=\{1,2,3,4,5,6,7\}\). Then the relation \(\mathrm{R}=\{(x, y) \in \mathrm{A} \times \mathrm{A}: x+y=7\}\) is :

Let the mean and variance of 12 observations be \(\frac{9}{2}\) and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is \(\frac{m}{n}\), wh...

The value of \(36\left(4 \cos ^{2} 9^{\circ}-1\right)\left(4 \cos ^{2} 27^{\circ}-1\right)\left(4 \cos ^{2} 81^{\circ}-1\right)\left(4 \cos ^{2} 243^{\circ}-1\right)\) is :

Let the vectors \(\vec{u}_{1}=\hat{i}+\hat{j}+a \hat{k}, \vec{u}_{2}=\hat{i}+b \hat{j}+\hat{k}\) and \(\vec{u}_{3}=c \hat{i}+\hat{j}+\hat{k}\) be coplanar. If the vectors $$\vec{v}_{1}=(a+b) \hat{i}+c \hat{j}+c \hat{k}, \vec{v}_{2}=a \hat{i...

The area of the quadrilateral \(\mathrm{ABCD}\) with vertices \(\mathrm{A}(2,1,1), \mathrm{B}(1,2,5), \mathrm{C}(-2,-3,5)\) and \(\mathrm{D}(1,-6,-7)\) is equal to :

A series combination of resistor of resistance \(100 ~\Omega\), inductor of inductance \(1 ~\mathrm{H}\) and capacitor of capacitance \(6.25 ~\mu \mathrm{F}\) is connected to an ac source. The quality factor of the circuit will be _________...

A radio active material is reduced to \(1 / 8\) of its original amount in 3 days. If \(8 \times 10^{-3} \mathrm{~kg}\) of the material is left after 5 days the initial amount of the material is

The waves emitted when a metal target is bombarded with high energy electrons are

The ratio of wavelength of spectral lines \(\mathrm{H}_{\alpha}\) and \(\mathrm{H}_{\beta}\) in the Balmer series is \(\frac{x}{20}\). The value of \(x\) is _________.

A \(600 ~\mathrm{pF}\) capacitor is charged by \(200 \mathrm{~V}\) supply. It is then disconnected from the supply and is connected to another uncharged \(600 ~\mathrm{pF}\) capacitor. Electrostatic energy lost in the process is ___________...

The power radiated from a linear antenna of length \(l\) is proportional to
(Given, \(\lambda=\) Wavelength of wave):

The equivalent resistance between A and B as shown in figure is:

The number density of free electrons in copper is nearly \(8 \times 10^{28} \mathrm{~m}^{-3}\). A copper wire has its area of cross section \(=2 \times 10^{-6} \mathrm{~m}^{2}\) and is carrying a current of \(3.2 \mathrm{~A}\). The drift sp...

In photo electric effect
A. The photocurrent is proportional to the intensity of the incident radiation
B. Maximum Kinetic energy with which photoelectrons are emitted depends on the intensity of incident light.
C. Max. K.E with which photo...

An emf of \(0.08 \mathrm{~V}\) is induced in a metal rod of length \(10 \mathrm{~cm}\) held normal to a uniform magnetic field of \(0.4 \mathrm{~T}\), when moves with a velocity of:

For a given transistor amplifier circuit in \(\mathrm{CE}\) configuration \(\mathrm{V}_{\mathrm{CC}}=1 \mathrm{~V}, \mathrm{R}_{\mathrm{C}}=1 ~\mathrm{k} \Omega, \mathrm{R}_{\mathrm{b}}=100 ~\mathrm{k} \Omega\) and \(\beta=100\). Value of b...

Electric potential at a point '\(\mathrm{P}\)' due to a point charge of \(5 \times 10^{-9} \mathrm{C}\) is \(50 \mathrm{~V}\). The distance of '\(\mathrm{P}\)' from the point charge is:
(Assume, $$\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10...

Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature \(30 \mathrm{~cm}\). The centre of curvature of surface is towards denser medium and a point object is placed...

The acceleration due to gravity at height \(h\) above the earth if \(h << \mathrm{R}\) (Radius of earth) is given by

The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new ang...

The temperature at which the kinetic energy of oxygen molecules becomes double than its value at \(27^{\circ} \mathrm{C}\) is

Work done by a Carnot engine operating between temperatures \(127^{\circ} \mathrm{C}\) and \(27^{\circ} \mathrm{C}\) is \(2 \mathrm{~kJ}\). The amount of heat transferred to the engine by the reservoir is :

A steel rod of length \(1 \mathrm{~m}\) and cross sectional area \(10^{-4} \mathrm{~m}^{2}\) is heated from \(0^{\circ} \mathrm{C}\) to \(200^{\circ} \mathrm{C}\) without being allowed to extend or bend. The compressive tension produced in ...

Given below are two statements: one is labelled as Assertion \(\mathbf{A}\) and the other is labelled as Reason \(\mathbf{R}\)
Assertion A : Electromagnets are made of soft iron.
Reason R : Soft iron has high permeability and low retentivit...

The ratio of magnetic field at the centre of a current carrying coil of radius \(r\) to the magnetic field at distance \(r\) from the centre of coil on its axis is \(\sqrt{x}: 1\). The value of \(x\) is __________

The trajectory of projectile, projected from the ground is given by \(y=x-\frac{x^{2}}{20}\). Where \(x\) and \(y\) are measured in meter. The maximum height attained by the projectile will be.

Given below are two statements
Statement I : Area under velocity- time graph gives the distance travelled by the body in a given time.
Statement II : Area under acceleration- time graph is equal to the change in velocity- in the given time....

A hydraulic automobile lift is designed to lift vehicles of mass \(5000 \mathrm{~kg}\). The area of cross section of the cylinder carrying the load is \(250 \mathrm{~cm}^{2}\). The maximum pressure the smaller piston would have to bear is $...

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity \(3 \mathrm{~m} / \mathrm{s}\) (as shown in figure). Maximum height with respect to the initial position covered by it will be __________ cm.

For particle P revolving round the centre O with radius of circular path \(\mathrm{r}\) and angular velocity \(\omega\), as shown in below figure, the projection of OP on the \(x\)-axis at time \(t\) is

Match List I with List II

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The width of fringe is \(2 \mathrm{~mm}\) on the screen in a double slits experiment for the light of wavelength of \(400 \mathrm{~nm}\). The width of the fringe for the light of wavelength 600 \(\mathrm{nm}\) will be:

A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be _________ cm.

A bullet of mass \(0.1 \mathrm{~kg}\) moving horizontally with speed \(400 \mathrm{~ms}^{-1}\) hits a wooden block of mass \(3.9 \mathrm{~kg}\) kept on a horizontal rough surface. The bullet gets embedded into the block and moves $$20 \math...

A body of mass \(5 \mathrm{~kg}\) is moving with a momentum of \(10 \mathrm{~kg} \mathrm{~ms}^{-1}\). Now a force of \(2 \mathrm{~N}\) acts on the body in the direction of its motion for \(5 \mathrm{~s}\). The increase in the Kinetic energy...