JEE Main 2024 (Online) 9th April Evening Shift

Consider the circle \(C: x^2+y^2=4\) and the parabola \(P: y^2=8 x\). If the set of all values of \(\alpha\), for which three chords of the circle \(C\) on three distinct lines passing through the point \((\alpha, 0)\) are bisected by the p...

The number of integers, between 100 and 1000 having the sum of their digits equals to 14 , is __________.

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the \(i^{\text {th }}\) roll than the number obtained in the \((i-1)^{\text {th }}\) roll, \(i=2,3\), is equal to

Two vertices of a triangle \(\mathrm{ABC}\) are \(\mathrm{A}(3,-1)\) and \(\mathrm{B}(-2,3)\), and its orthocentre is \(\mathrm{P}(1,1)\). If the coordinates of the point \(\mathrm{C}\) are \((\alpha, \beta)\) and the centre of the of the c...

Let \(\alpha, \beta ; \alpha>\beta\), be the roots of the equation \(x^2-\sqrt{2} x-\sqrt{3}=0\). Let \(\mathrm{P}_n=\alpha^n-\beta^n, n \in \mathrm{N}\). Then $$(11 \sqrt{3}-10 \sqrt{2}) \mathrm{P}_{10}+(11 \sqrt{2}+10) \mathrm{P}_{11}-11 ...

Let \(a, a r, a r^2\), ............ be an infinite G.P. If \(\sum_\limits{n=0}^{\infty} a r^n=57\) and \(\sum_\limits{n=0}^{\infty} a^3 r^{3 n}=9747\), then \(a+18 r\) is equal to

If \(\left(\frac{1}{\alpha+1}+\frac{1}{\alpha+2}+\ldots . .+\frac{1}{\alpha+1012}\right)-\left(\frac{1}{2 \cdot 1}+\frac{1}{4 \cdot 3}+\frac{1}{6 \cdot 5}+\ldots \ldots+\frac{1}{2024 \cdot 2023}\right)=\frac{1}{2024}\), then \(\alpha\) is e...

If the variance of the frequency distribution

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Between the following two statements:
Statement I : Let \(\vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}\) and \(\vec{b}=2 \hat{i}+\hat{j}-\hat{k}\). Then the vector \(\vec{r}\) satisfying \(\vec{a} \times \vec{r}=\vec{a} \times \vec{b}\) and $$\vec{a...

Let \(\vec{a}=2 \hat{i}+\alpha \hat{j}+\hat{k}, \vec{b}=-\hat{i}+\hat{k}, \vec{c}=\beta \hat{j}-\hat{k}\), where \(\alpha\) and \(\beta\) are integers and \(\alpha \beta=-6\). Let the values of the ordered pair \((\alpha, \beta)\), for whic...

A capacitor of reactance \(4 \sqrt{3} \Omega\) and a resistor of resistance \(4 \Omega\) are connected in series with an ac source of peak value \(8 \sqrt{2} \mathrm{~V}\). The power dissipation in the circuit is __________ W.

A hydrogen atom in ground state is given an energy of \(10.2 \mathrm{~eV}\). How many spectral lines will be emitted due to transition of electrons?

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of \(2: 1\). After disintegration they will move :

The energy released in the fusion of \(2 \mathrm{~kg}\) of hydrogen deep in the sun is \(E_H\) and the energy released in the fission of \(2 \mathrm{~kg}\) of \({ }^{235} \mathrm{U}\) is \(E_U\). The ratio \(\frac{E_H}{E_U}\) is approximate...

At room temperature \((27^{\circ} \mathrm{C})\), the resistance of a heating element is \(50 \Omega\). The temperature coefficient of the material is \(2.4 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}\). The temperature of the element, when it...

To determine the resistance (R) of a wire, a circuit is designed below. The \(V\)-\(I\) characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of $R$ is _________ \(\Omega\)...

The effective resistance between \(A\) and \(B\), if resistance of each resistor is \(R\), will be :

UV light of \(4.13 \mathrm{~eV}\) is incident on a photosensitive metal surface having work function \(3.13 \mathrm{~eV}\). The maximum kinetic energy of ejected photoelectrons will be:

A square loop of side \(15 \mathrm{~cm}\) being moved towards right at a constant speed of \(2\mathrm{~cm} / \mathrm{s}\) as shown in figure. The front edge enters the \(50 \mathrm{~cm}\) wide magnetic field at \(t=0\). The value of induced...

The magnetic field in a plane electromagnetic wave is \(\mathrm{B}_{\mathrm{y}}=\left(3.5 \times 10^{-7}\right) \sin \left(1.5 \times 10^3 x+0.5 \times 10^{11} t\right) \mathrm{T}\). The corresponding electric field will be :

The \(I\)-\(V\) characteristics of an electronic device shown in the figure. The device is :

In the truth table of the above circuit the value of X and Y are :

Five charges \(+q,+5 q,-2 q,+3 q\) and \(-4 q\) are situated as shown in the figure. The electric flux due to this configuration through the surface \(S\) is :

An electric field \(\vec{E}=(2 x \hat{i}) N C^{-1}\) exists in space. A cube of side \(2 \mathrm{~m}\) is placed in the space as per figure given below. The electric flux through the cube is ______ \(\mathrm{Nm}^2 / \mathrm{C}\).

The following figure represents two biconvex lenses \(L_1\) and \(L_2\) having focal length \(10 \mathrm{~cm}\) and \(15 \mathrm{~cm}\) respectively. The distance between \(L_1\) & \(L_2\) is :

A satellite of \(10^3 \mathrm{~kg}\) mass is revolving in circular orbit of radius \(2 R\). If \(\frac{10^4 R}{6} \mathrm{~J}\) energy is supplied to the satellite, it would revolve in a new circular orbit of radius
(use $$g=10 \mathrm{~m} ...

The temperature of a gas is \(-78^{\circ} \mathrm{C}\) and the average translational kinetic energy of its molecules is \(\mathrm{K}\). The temperature at which the average translational kinetic energy of the molecules of the same gas becom...

A real gas within a closed chamber at \(27^{\circ} \mathrm{C}\) undergoes the cyclic process as shown in figure. The gas obeys \(P V^3=R T\) equation for the path \(A\) to \(B\). The net work done in the complete cycle is (assuming $$R=8 \m...

A \(1 \mathrm{~kg}\) mass is suspended from the ceiling by a rope of length \(4 \mathrm{~m}\). A horizontal force '\(F\)' is applied at the mid point of the rope so that the rope makes an angle of \(45^{\circ}\) with respect to the vertical...

A proton and a deutron \((q=+\mathrm{e}, m=2.0 \mathrm{u})\) having same kinetic energies enter a region of uniform magnetic field \(\vec{B}\), moving perpendicular to \(\vec{B}\). The ratio of the radius \(r_d\) of deutron path to the radi...

A straight magnetic strip has a magnetic moment of \(44 \mathrm{~Am}^2\). If the strip is bent in a semicircular shape, its magnetic moment will be ________ \(\mathrm{Am}^2\).
(given \(\pi=\frac{22}{7}\))

Two cars are travelling towards each other at speed of \(20 \mathrm{~m} \mathrm{~s}^{-1}\) each. When the cars are \(300 \mathrm{~m}\) apart, both the drivers apply brakes and the cars retard at the rate of $$2 \mathrm{~m} \mathrm{~s}^{-2}$...

A spherical ball of radius \(1 \times 10^{-4} \mathrm{~m}\) and density \(10^5 \mathrm{~kg} / \mathrm{m}^3\) falls freely under gravity through a distance \(h\) before entering a tank of water, If after entering in water the velocity of the...

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

A circular disc reaches from top to bottom of an inclined plane of length \(l\). When it slips down the plane, if takes \(t \mathrm{~s}\). When it rolls down the plane then it takes \(\left(\frac{\alpha}{2}\right)^{1 / 2} t \mathrm{~s}\), w...

A particle of mass \(0.50 \mathrm{~kg}\) executes simple harmonic motion under force \(F=-50(\mathrm{Nm}^{-1}) x\). The time period of oscillation is \(\frac{x}{35} s\). The value of \(x\) is _________.
(Given \(\pi=\frac{22}{7}\))

The de-Broglie wavelength associated with a particle of mass \(m\) and energy \(E\) is \(h / \sqrt{2 m E}\). The dimensional formula for Planck's constant is :

The resultant of two vectors \(\vec{A}\) and \(\vec{B}\) is perpendicular to \(\vec{A}\) and its magnitude is half that of \(\vec{B}\). The angle between vectors \(\vec{A}\) and \(\vec{B}\) is _________\(^\circ\).

Monochromatic light of wavelength \(500 \mathrm{~nm}\) is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index \(=1.5\)), th...

A force \((3 x^2+2 x-5) \mathrm{N}\) displaces a body from \(x=2 \mathrm{~m}\) to \(x=4 \mathrm{~m}\). Work done by this force is ________ J.