JEE Main 2024 (Online) 6th April Evening Shift

From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable \(X\) denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If va...

In a triangle \(\mathrm{ABC}, \mathrm{BC}=7, \mathrm{AC}=8, \mathrm{AB}=\alpha \in \mathrm{N}\) and \(\cos \mathrm{A}=\frac{2}{3}\). If \(49 \cos (3 \mathrm{C})+42=\frac{\mathrm{m}}{\mathrm{n}}\), where \(\operatorname{gcd}(m, n)=1\), then ...

Let \(\alpha, \beta\) be roots of \(x^2+\sqrt{2} x-8=0\). If \(\mathrm{U}_{\mathrm{n}}=\alpha^{\mathrm{n}}+\beta^{\mathrm{n}}\), then \(\frac{\mathrm{U}_{10}+\sqrt{2} \mathrm{U}_9}{2 \mathrm{U}_8}\) is equal to ________.

Let \(A B C\) be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle \(A B C\) and the same process is repeated infinitely many times. If \(\mathrm{P}\) is the sum of perimeters and $$...

A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took ...

If \(\mathrm{S}(x)=(1+x)+2(1+x)^2+3(1+x)^3+\cdots+60(1+x)^{60}, x \neq 0\), and \((60)^2 \mathrm{~S}(60)=\mathrm{a}(\mathrm{b})^{\mathrm{b}}+\mathrm{b}\), where \(a, b \in N\), then \((a+b)\) equal to _________.

Let \(\mathrm{A}=\{1,2,3,4,5\}\). Let \(\mathrm{R}\) be a relation on \(\mathrm{A}\) defined by \(x \mathrm{R} y\) if and only if \(4 x \leq 5 \mathrm{y}\). Let \(\mathrm{m}\) be the number of elements in \(\mathrm{R}\) and \(\mathrm{n}\) b...

If the locus of the point, whose distances from the point \((2,1)\) and \((1,3)\) are in the ratio \(5: 4\), is \(a x^2+b y^2+c x y+d x+e y+170=0\), then the value of \(a^2+2 b+3 c+4 d+e\) is equal to :

Let \(\vec{a}=2 \hat{i}+\hat{j}-\hat{k}, \vec{b}=((\vec{a} \times(\hat{i}+\hat{j})) \times \hat{i}) \times \hat{i}\). Then the square of the projection of \(\vec{a}\) on \(\vec{b}\) is:

Let \(\overrightarrow{\mathrm{a}}=6 \hat{i}+\hat{j}-\hat{k}\) and \(\overrightarrow{\mathrm{b}}=\hat{i}+\hat{j}\). If \(\overrightarrow{\mathrm{c}}\) is a is vector such that $$|\overrightarrow{\mathrm{c}}| \geq 6, \overrightarrow{\mathrm{a...

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is \(2.5 \mathrm{~nF}\). If resistance of \(200 \Omega\) and \(100 \mathrm{~mH}\) inductor is being used in the given circuit. The f...

The longest wavelength associated with Paschen series is : (Given \(\mathrm{R}_{\mathrm{H}}=1.097 \times 10^7 \mathrm{SI}\) unit)

A capacitor of \(10 \mu \mathrm{F}\) capacitance whose plates are separated by \(10 \mathrm{~mm}\) through air and each plate has area \(4 \mathrm{~cm}^2\) is now filled equally with two dielectric media of \(K_1=2, K_2=3\) respectively as ...

A car of \(800 \mathrm{~kg}\) is taking turn on a banked road of radius \(300 \mathrm{~m}\) and angle of banking \(30^{\circ}\). If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: $...

The number of electrons flowing per second in the filament of a \(110 \mathrm{~W}\) bulb operating at \(220 \mathrm{~V}\) is : (Given \(\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\))

In the given figure an ammeter A consists of a \(240 \Omega\) coil connected in parallel to a \(10 \Omega\) shunt. The reading of the ammeter is ________ \(\mathrm{mA}\).

When UV light of wavelength \(300 \mathrm{~nm}\) is incident on the metal surface having work function \(2.13 \mathrm{~eV}\), electron emission takes place. The stopping potential is :
(Given hc \(=1240 \mathrm{~eV} \mathrm{~nm}\) )

In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at \(10.2 \mathrm{~V}\). The wavelength of light emitted by hydrogen atom when excited to the first excitation level is ________ nm. (Given hc $...

In a coil, the current changes from \(-2 \mathrm{~A}\) to \(+2 \mathrm{~A}\) in \(0.2 \mathrm{~s}\) and induces an emf of \(0.1 \mathrm{~V}\). The self inductance of the coil is :

In the given electromagnetic wave \(\mathrm{E}_{\mathrm{y}}=600 \sin (\omega t-\mathrm{kx}) \mathrm{Vm}^{-1}\), intensity of the associated light beam is (in \(\mathrm{W} / \mathrm{m}^2\) : (Given $$\epsilon_0=9 \times 10^{-12} \mathrm{C}^2...

The acceptor level of a p-type semiconductor is \(6 \mathrm{~eV}\). The maximum wavelength of light which can create a hole would be : Given \(\mathrm{hc}=1242 \mathrm{~eV} \mathrm{~nm}\).

Two identical conducting spheres P and S with charge Q on each, repel each other with a force \(16 \mathrm{~N}\). A third identical uncharged conducting sphere \(\mathrm{R}\) is successively brought in contact with the two spheres. The new ...

For the thin convex lens, the radii of curvature are at \(15 \mathrm{~cm}\) and \(30 \mathrm{~cm}\) respectively. The focal length the lens is \(20 \mathrm{~cm}\). The refractive index of the material is :

Assuming the earth to be a sphere of uniform mass density, a body weighed \(300 \mathrm{~N}\) on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?

Given below are two statements:
Statement (I) : Dimensions of specific heat is \([\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}]\).
Statement (II) : Dimensions of gas constant is $$[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}...

Energy of 10 non rigid diatomic molecules at temperature \(\mathrm{T}\) is :

A total of \(48 \mathrm{~J}\) heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by \(2^{\circ} \mathrm{C}\). The work done by the gas is:
Given, $$\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm...

A body of weight \(200 \mathrm{~N}\) is suspended from a tree branch through a chain of mass \(10 \mathrm{~kg}\). The branch pulls the chain by a force equal to (if \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\)) :

Match List I with List II:

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A coil having 100 turns, area of \(5 \times 10^{-3} \mathrm{~m}^2\), carrying current of \(1 \mathrm{~mA}\) is placed in uniform magnetic field of \(0.20 \mathrm{~T}\) such a way that plane of coil is perpendicular to the magnetic field. Th...

A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in \(t_1\). If it is projected vertically downwards from the same point with the same speed, it reaches the ground in \(t_2\). Time required...

A particle moves in a straight line so that its displacement \(x\) at any time \(t\) is given by \(x^2=1+t^2\). Its acceleration at any time \(\mathrm{t}\) is \(x^{-\mathrm{n}}\) where \(\mathrm{n}=\) _________.

Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : \(\mathrm{R}=\) Radius of bubble, \(\mathrm{S}=\) Surface tension of bubble)

A wire of cross sectional area A, modulus of elasticity \(2 \times 10^{11} \mathrm{~Nm}^{-2}\) and length \(2 \mathrm{~m}\) is stretched between two vertical rigid supports. When a mass of \(2 \mathrm{~kg}\) is suspended at the middle it sa...

Three balls of masses \(2 \mathrm{~kg}, 4 \mathrm{~kg}\) and \(6 \mathrm{~kg}\) respectively are arranged at centre of the edges of an equilateral triangle of side \(2 \mathrm{~m}\). The moment of inertia of the system about an axis through...

In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its \(4^{\text {th }}\) division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 ma...

In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division \(=49 \mathrm{~MSD} ; 20\) divisions on main scale in each \(\mathrm{cm}\)
For mark on paper
$$\text ...

Two coherent monochromatic light beams of intensities I and \(4 \mathrm{~I}\) are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is \(x \mathrm{~I}\). The value of \(x\) is __________.

Two open organ pipes of lengths \(60 \mathrm{~cm}\) and \(90 \mathrm{~cm}\) resonate at \(6^{\text {th }}\) and \(5^{\text {th }}\) harmonics respectively. The difference of frequencies for the given modes is _________ \(\mathrm{Hz}\). (Vel...

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be :