JEE Main 2024 (Online) 27th January Evening Shift

An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives all white balls and the second draw gives all black balls, is :

If \(\alpha, \beta\) are the roots of the equation, \(x^2-x-1=0\) and \(S_n=2023 \alpha^n+2024 \beta^n\), then :

\(\text { The } 20^{\text {th }} \text { term from the end of the progression } 20,19 \frac{1}{4}, 18 \frac{1}{2}, 17 \frac{3}{4}, \ldots,-129 \frac{1}{4} \text { is : }\)

Let \(A\) and \(B\) be two finite sets with \(m\) and \(n\) elements respectively. The total number of subsets of the set \(A\) is 56 more than the total number of subsets of \(B\). Then the distance of the point \(P(m, n)\) from the point ...

The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in place of 12 . If \(\mu\) and \(\sigma^2\) denote the mean and variance of the correc...

Let \(\mathrm{R}\) be the interior region between the lines \(3 x-y+1=0\) and \(x+2 y-5=0\) containing the origin. The set of all values of \(a\), for which the points \(\left(a^2, a+1\right)\) lie in \(R\), is :

If the sum of squares of all real values of \(\alpha\), for which the lines \(2 x-y+3=0,6 x+3 y+1=0\) and \(\alpha x+2 y-2=0\) do not form a triangle is \(p\), then the greatest integer less than or equal to \(p\) is _________.

If \(2 \tan ^2 \theta-5 \sec \theta=1\) has exactly 7 solutions in the interval \(\left[0, \frac{n \pi}{2}\right]\), for the least value of \(n \in \mathbf{N}\), then \(\sum_\limits{k=1}^n \frac{k}{2^k}\) is equal to:

Let the position vectors of the vertices \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) of a triangle be \(2 \hat{i}+2 \hat{j}+\hat{k}, \hat{i}+2 \hat{j}+2 \hat{k}\) and \(2 \hat{i}+\hat{j}+2 \hat{k}\) respectively. Let \(l_1, l_2\) and $$l_...

The position vectors of the vertices \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) of a triangle are \(2 \hat{i}-3 \hat{j}+3 \hat{k}, 2 \hat{i}+2 \hat{j}+3 \hat{k}\) and \(-\hat{i}+\hat{j}+3 \hat{k}\) respectively. Let \(l\) denotes the len...

Primary side of a transformer is connected to \(230 \mathrm{~V}, 50 \mathrm{~Hz}\) supply. Turns ratio of primary to secondary winding is \(10: 1\). Load resistance connected to secondary side is \(46 \Omega\). The power consumed in it is :

A series LCR circuit with \(\mathrm{L}=\frac{100}{\pi} \mathrm{mH}, \mathrm{C}=\frac{10^{-3}}{\pi} \mathrm{F}\) and \(\mathrm{R}=10 \Omega\), is connected across an ac source of \(220 \mathrm{~V}, 50 \mathrm{~Hz}\) supply. The power factor ...

The atomic mass of \({ }_6 \mathrm{C}^{12}\) is \(12.000000 \mathrm{~u}\) and that of \({ }_6 \mathrm{C}^{13}\) is \(13.003354 \mathrm{~u}\). The required energy to remove a neutron from \({ }_6 \mathrm{C}^{13}\), if mass of neutron is $$1....

If Rydberg's constant is \(R\), the longest wavelength of radiation in Paschen series will be \(\frac{\alpha}{7 R}\), where \(\alpha=\) ________.

Three voltmeters, all having different internal resistances are joined as shown in figure. When some potential difference is applied across \(A\) and \(B\), their readings are \(V_1, V_2\) and \(V_3\). Choose the correct option.

A current of \(200 \mu \mathrm{A}\) deflects the coil of a moving coil galvanometer through \(60^{\circ}\). The current to cause deflection through \(\frac{\pi}{10}\) radian is :

Wheatstone bridge principle is used to measure the specific resistance \(\left(S_1\right)\) of given wire, having length \(L\), radius \(r\). If \(X\) is the resistance of wire, then specific resistance is ; $$S_1=X\left(\frac{\pi r^2}{L}\r...

The threshold frequency of a metal with work function \(6.63 \mathrm{~eV}\) is :

An object is placed in a medium of refractive index 3 . An electromagnetic wave of intensity \(6 \times 10^8 \mathrm{~W} / \mathrm{m}^2\) falls normally on the object and it is absorbed completely. The radiation pressure on the object would...

The truth table of the given circuit diagram is :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Work done by electric field on moving a positive charge on an equipotential surface is always zero.
Reason (R) : Elec...

Two charges of \(-4 \mu \mathrm{C}\) and \(+4 \mu \mathrm{C}\) are placed at the points \(\mathrm{A}(1,0,4) \mathrm{m}\) and \(\mathrm{B}(2,-1,5) \mathrm{m}\) located in an electric field $$\overrightarrow{\mathrm{E}}=0.20 \hat{i} \mathrm{~...

The electric potential at the surface of an atomic nucleus \((z=50)\) of radius \(9 \times 10^{-13} \mathrm{~cm}\) is __________ \(\times 10^6 \mathrm{~V}\).

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit a...

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of \(\frac{\mathrm{Cp}}{\mathrm{Cv}}\) for the gas is :

The equation of state of a real gas is given by \(\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}\), where \(\mathrm{P}, \mathrm{V}\) and \(\mathrm{T}\) are pressure, volume and temperature respect...

The total kinetic energy of 1 mole of oxygen at \(27^{\circ} \mathrm{C}\) is :
[Use universal gas constant \((R)=8.31 \mathrm{~J} /\) mole K]

Given below are two statements :
Statement (I) : The limiting force of static friction depends on the area of contact and independent of materials.
Statement (II) : The limiting force of kinetic friction is independent of the area of contac...

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii \(R_1=2 \pi \mathrm{m}\) and \(R_2=4 \pi \mathrm{m}\), carrying current \(\mathrm{I}=4 \mathrm{~A}\) as per figure given below is $$\alpha \times 10^{...

A body falling under gravity covers two points \(A\) and \(B\) separated by \(80 \mathrm{~m}\) in \(2 \mathrm{~s}\). The distance of upper point A from the starting point is _________ \(\mathrm{m}\) (use \(\mathrm{g}=10 \mathrm{~ms}^{-2}\))...

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The property of body, by virtue of which it tends to regain its original shape when the external force is removed, is...

The reading of pressure metre attached with a closed pipe is \(4.5 \times 10^4 \mathrm{~N} / \mathrm{m}^2\). On opening the valve, water starts flowing and the reading of pressure metre falls to $$2.0 \times 10^4 \mathrm{~N} / \mathrm{m}^2$...

A heavy iron bar of weight \(12 \mathrm{~kg}\) is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle \(60^{\circ}\) with the horizontal, the weight experienced by the man is :

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is \(\frac{7}{x}\), where \(x\) is _________.

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more tha...

When a polaroid sheet is rotated between two crossed polaroids then the transmitted light intensity will be maximum for a rotation of :

A parallel beam of monochromatic light of wavelength 5000 \(\mathop A\limits^o\) is incident normally on a single narrow slit of width \(0.001 \mathrm{~mm}\). The light is focused by convex lens on screen, placed on its focal plane. The fir...

A closed organ pipe \(150 \mathrm{~cm}\) long gives 7 beats per second with an open organ pipe of length \(350 \mathrm{~cm}\), both vibrating in fundamental mode. The velocity of sound is __________ \(\mathrm{m} / \mathrm{s}\).

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle \((\theta)\) of thread deflection in the extreme position will be :

A bullet is fired into a fixed target looses one third of its velocity after travelling \(4 \mathrm{~cm}\). It penetrates further \(\mathrm{D} \times 10^{-3} \mathrm{~m}\) before coming to rest. The value of \(\mathrm{D}\) is :