JEE Main 2024 (Online) 30th January Evening Shift

Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn is white, is

The number of real solutions of the equation \(x\left(x^2+3|x|+5|x-1|+6|x-2|\right)=0\) is _________.

Let \(a\) and \(b\) be be two distinct positive real numbers. Let \(11^{\text {th }}\) term of a GP, whose first term is \(a\) and third term is \(b\), is equal to \(p^{\text {th }}\) term of another GP, whose first term is \(a\) and fifth ...

Let \(S_n\) be the sum to \(n\)-terms of an arithmetic progression \(3,7,11\),
If \(40<\left(\frac{6}{n(n+1)} \sum_\limits{k=1}^n S_k\right)<42\), then \(n\) equals ________.

The number of symmetric relations defined on the set \(\{1,2,3,4\}\) which are not reflexive is _________.

The variance \(\sigma^2\) of the data

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-bre...

If \(x^2-y^2+2 h x y+2 g x+2 f y+c=0\) is the locus of a point, which moves such that it is always equidistant from the lines \(x+2 y+7=0\) and \(2 x-y+8=0\), then the value of \(g+c+h-f\) equals

For \(\alpha, \beta \in(0, \pi / 2)\), let \(3 \sin (\alpha+\beta)=2 \sin (\alpha-\beta)\) and a real number \(k\) be such that \(\tan \alpha=k \tan \beta\). Then, the value of \(k\) is equal to

Let \(\vec{a}=\hat{i}+\alpha \hat{j}+\beta \hat{k}, \alpha, \beta \in \mathbb{R}\). Let a vector \(\vec{b}\) be such that the angle between \(\vec{a}\) and \(\vec{b}\) is \(\frac{\pi}{4}\) and \(|\vec{b}|^2=6\). If $$\vec{a} \cdot \vec{b}=3...

Let \(\vec{a}\) and \(\vec{b}\) be two vectors such that \(|\vec{b}|=1\) and \(|\vec{b} \times \vec{a}|=2\). Then \(|(\vec{b} \times \vec{a})-\vec{b}|^2\) is equal to

An alternating voltage \(V(t)=220 \sin 100 \pi t\) volt is applied to a purely resistive load of \(50 \Omega\). The time taken for the current to rise from half of the peak value to the peak value is:

A power transmission line feeds input power at \(2.3 \mathrm{~kV}\) to a step down transformer with its primary winding having 3000 turns. The output power is delivered at \(230 \mathrm{~V}\) by the transformer. The current in the primary o...

An electron revolving in \(n^{\text {th }}\) Bohr orbit has magnetic moment \(\mu_n\). If \(\mu_n \propto n^x\), the value of \(x\) is

In a nuclear fission reaction of an isotope of mass \(M\), three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect \(\Delta M\) will be :

When a potential difference \(V\) is applied across a wire of resistance \(R\), it dissipates energy at a rate \(W\). If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the energy dis...

Two resistance of \(100 \Omega\) and \(200 \Omega\) are connected in series with a battery of \(4 \mathrm{~V}\) and negligible internal resistance. A voltmeter is used to measure voltage across \(100 \Omega\) resistance, which gives reading...

For the photoelectric effect, the maximum kinetic energy \(\left(E_k\right)\) of the photoelectrons is plotted against the frequency \((v)\) of the incident photons as shown in figure. The slope of the graph gives

If the total energy transferred to a surface in time \(\mathrm{t}\) is \(6.48 \times 10^5 \mathrm{~J}\), then the magnitude of the total momentum delivered to this surface for complete absorption will be:

Match List I with List II

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:normal;}
...

In the given circuit, the voltage across load resistance (R\(_L\)) is :

A particle of charge '\(-q\)' and mass '\(m\)' moves in a circle of radius '\(r\)' around an infinitely long line charge of linear charge density '\(+\lambda\)'. Then time period will be given as :
(Consider \(k\) as Coulomb's constant)

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of \(37^{\circ}\) with each other. When suspended in a liquid of density \(0.7 \mathrm{~g} / \mathrm{cm}^3\), the angle remains same. If dens...

In an experiment to measure the focal length \((f)\) of a convex lens, the magnitude of object distance \((x)\) and the image distance \((y)\) are measured with reference to the focal point of the lens. The \(y\)-\(x\) plot is shown in figu...

Escape velocity of a body from earth is \(11.2 \mathrm{~km} / \mathrm{s}\). If the radius of a planet be onethird the radius of earth and mass be one-sixth that of earth, the escape velocity from the planet is :

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is \(4 m\), then the time period of small oscillations will be __________ s. [take $$g=\pi^2...

Choose the correct statement for processes A & B shown in figure.

A block of ice at \(-10^{\circ} \mathrm{C}\) is slowly heated and converted to steam at \(100^{\circ} \mathrm{C}\). Which of the following curves represent the phenomenon qualitatively:

If three moles of monoatomic gas \(\left(\gamma=\frac{5}{3}\right)\) is mixed with two moles of a diatomic gas \(\left(\gamma=\frac{7}{5}\right)\), the value of adiabatic exponent \(\gamma\) for the mixture is

A block of mass \(m\) is placed on a surface having vertical crossection given by \(y=x^2 / 4\). If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is:

Three blocks \(A, B\) and \(C\) are pulled on a horizontal smooth surface by a force of \(80 \mathrm{~N}\) as shown in figure



The tensions T\(_1\) and T\(_2\) in the string are respectively :

The current of \(5 \mathrm{~A}\) flows in a square loop of sides \(1 \mathrm{~m}\) is placed in air. The magnetic field at the centre of the loop is \(X \sqrt{2} \times 10^{-7} T\). The value of \(X\) is _________.

Projectiles A and B are thrown at angles of \(45^{\circ}\) and \(60^{\circ}\) with vertical respectively from top of a \(400 \mathrm{~m}\) high tower. If their ranges and times of flight are same, the ratio of their speeds of projection $$v...

A big drop is formed by coalescing 1000 small identical drops of water. If \(E_1\) be the total surface energy of 1000 small drops of water and \(E_2\) be the surface energy of single big drop of water, then \(E_1: E_2\) is \(x: 1\) where $...

Two discs of moment of inertia \(I_1=4 \mathrm{~kg} \mathrm{~m}^2\) and \(I_2=2 \mathrm{~kg} \mathrm{~m}^2\), about their central axes & normal to their planes, rotating with angular speeds \(10 \mathrm{~rad} / \mathrm{s}\) & $$4 \mathrm{~r...

If 50 Vernier divisions are equal to 49 main scale divisions of a traveling microscope and one smallest reading of main scale is \(0.5 \mathrm{~mm}\), the Vernier constant of traveling microscope is

If mass is written as \(m=k \mathrm{c}^{\mathrm{P}} G^{-1 / 2} h^{1 / 2}\) then the value of \(P\) will be : (Constants have their usual meaning with $k a$ dimensionless constant)

A vector has magnitude same as that of \(\vec{A}=3 \hat{i}+4 \hat{j}\) and is parallel to \(\vec{B}=4 \hat{i}+3 \hat{j}\). The \(x\) and \(y\) components of this vector in first quadrant are \(x\) and 3 respectively where \(x=\) _________.

A beam of unpolarised light of intensity \(I_0\) is passed through a polaroid \(A\) and then through another polaroid \(B\) which is oriented so that its principal plane makes an angle of \(45^{\circ}\) relative to that of \(A\). The intens...

A point source is emitting sound waves of intensity \(16 \times 10^{-8} \mathrm{~Wm}^{-2}\) at the origin. The difference in intensity (magnitude only) at two points located at a distances of \(2 m\) and \(4 m\) from the origin respectively...

A block of mass \(1 \mathrm{~kg}\) is pushed up a surface inclined to horizontal at an angle of \(60^{\circ}\) by a force of \(10 \mathrm{~N}\) parallel to the inclined surface as shown in figure. When the block is pushed up by $$10 \mathrm...