JEE Main 2023 (Online) 1st February Evening Shift

Number of integral solutions to the equation \(x+y+z=21\), where \(x \ge 1,y\ge3,z\ge4\), is equal to ____________.

The total number of six digit numbers, formed using the digits 4, 5, 9 only and divisible by 6, is ____________.

Two dice are thrown independently. Let \(\mathrm{A}\) be the event that the number appeared on the \(1^{\text {st }}\) die is less than the number appeared on the \(2^{\text {nd }}\) die, \(\mathrm{B}\) be the event that the number appeared...

The number of integral values of k, for which one root of the equation \(2x^2-8x+k=0\) lies in the interval (1, 2) and its other root lies in the interval (2, 3), is :

The sum \(\sum\limits_{n = 1}^\infty {{{2{n^2} + 3n + 4} \over {(2n)!}}}\) is equal to :

The sum of the common terms of the following three arithmetic progressions.
\(3,7,11,15, \ldots ., 399\),
\(2,5,8,11, \ldots ., 359\) and
\(2,7,12,17, \ldots ., 197\),
is equal to _____________.

Let \(P(S)\) denote the power set of \(S=\{1,2,3, \ldots ., 10\}\). Define the relations \(R_{1}\) and \(R_{2}\) on \(P(S)\) as \(\mathrm{AR}_{1} \mathrm{~B}\) if $$\left(\mathrm{A} \cap \mathrm{B}^{\mathrm{c}}\right) \cup\left(\mathrm{B} \...

Let \(9=x_{1} < x_{2} < \ldots < x_{7}\) be in an A.P. with common difference d. If the standard deviation of \(x_{1}, x_{2}..., x_{7}\) is 4 and the mean is \(\bar{x}\), then \(\bar{x}+x_{6}\) is equal to :

Let \(\vec{a}=5 \hat{i}-\hat{j}-3 \hat{k}\) and \(\vec{b}=\hat{i}+3 \hat{j}+5 \hat{k}\) be two vectors. Then which one of the following statements is TRUE ?

Let \(\vec{a}=2 \hat{i}-7 \hat{j}+5 \hat{k}, \vec{b}=\hat{i}+\hat{k}\) and \(\vec{c}=\hat{i}+2 \hat{j}-3 \hat{k}\) be three given vectors. If \(\overrightarrow{\mathrm{r}}\) is a vector such that $$\vec{r} \times \vec{a}=\vec{c} \times \vec...

A square shaped coil of area \(70 \mathrm{~cm}^{2}\) having 600 turns rotates in a magnetic field of \(0.4 ~\mathrm{wbm}^{-2}\), about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If ...

An electron of a hydrogen like atom, having \(Z=4\), jumps from \(4^{\text {th }}\) energy state to \(2^{\text {nd }}\) energy state. The energy released in this process, will be :
(Given Rch = \(13.6~\mathrm{eV}\))
Where R = Rydberg consta...

Nucleus A having \(Z=17\) and equal number of protons and neutrons has \(1.2 ~\mathrm{MeV}\) binding energy per nucleon.
Another nucleus \(\mathrm{B}\) of \(Z=12\) has total 26 nucleons and \(1.8 ~\mathrm{MeV}\) binding energy per nucleons....

Given below are two statements: One is labeled as Assertion A and the other is labeled as Reason R.
Assertion A : Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same rad...

In an amplitude modulation, a modulating signal having amplitude of X Volt is superimposed with a carrier signal of amplitude Y Volt in first case. Then, in second case, the same modulating signal is superimposed with different carrier sign...

Given below are two statements : One is labelled as Assertion \(\mathbf{A}\) and the other is labelled as Reason \(\mathbf{R}\).
Assertion A : For measuring the potential difference across a resistance of \(600 \Omega\), the voltmeter with ...

Equivalent resistance between the adjacent corners of a regular n-sided polygon of uniform wire of resistance R would be :

In the given circuit, the value of \(\left| {{{{\mathrm{I_1}} + {\mathrm{I_3}}} \over {{\mathrm{I_2}}}}} \right|\) is _____________

The threshold frequency of a metal is \(f_{0}\). When the light of frequency \(2 f_{0}\) is incident on the metal plate, the maximum velocity of photoelectrons is \(v_{1}\). When the frequency of incident radiation is increased to $$5 \math...

A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed :
A. By changing the magnitude of the magnetic field within the coil.
B. By chan...

The ratio of average electric energy density and total average energy density of electromagnetic wave is :

Choose the correct statement about Zener diode :

A cubical volume is bounded by the surfaces \(\mathrm{x}=0, x=\mathrm{a}, y=0, y=\mathrm{a}, \mathrm{z}=0, z=\mathrm{a}\). The electric field in the region is given by \(\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} x \hat{i}\). Where $$\mathr...

Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is _______________.

The escape velocities of two planets \(\mathrm{A}\) and \(\mathrm{B}\) are in the ratio \(1: 2\). If the ratio of their radii respectively is \(1: 3\), then the ratio of acceleration due to gravity of planet A to the acceleration of gravity...

For a body projected at an angle with the horizontal from the ground, choose the correct statement.

A Carnot engine operating between two reservoirs has efficiency \(\frac{1}{3}\). When the temperature of cold reservoir raised by x, its efficiency decreases to \(\frac{1}{6}\). The value of x, if the temperature of hot reservoir is $$99^\c...

For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure.

The temperature corresponding to the point '\(\mathrm{K}\)' is :

As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle \(30^\circ\), with horizontal. For \(\mu_s=0.25\), the block will just start to move for the value of F : [Given $$g=10~\ma...

Figures (a), (b), (c) and (d) show variation of force with time.

The impulse is highest in figure.

As shown in the figure, a long straight conductor with semicircular arc of radius \(\frac{\pi}{10}\)m is carrying current \(\mathrm{I=3A}\). The magnitude of the magnetic field, at the center O of the arc is :
(The permeability of the vacuu...

For a train engine moving with speed of \(20 \mathrm{~ms}^{-1}\), the driver must apply brakes at a distance of 500 \(\mathrm{m}\) before the station for the train to come to rest at the station. If the brakes were applied at half of this d...

The Young's modulus of a steel wire of length \(6 \mathrm{~m}\) and cross-sectional area \(3 \mathrm{~mm}^{2}\), is \(2 \times 10^{11}~\mathrm{N} / \mathrm{m}^{2}\). The wire is suspended from its support on a given planet. A block of mass ...

The surface of water in a water tank of cross section area \(750 \mathrm{~cm}^{2}\) on the top of a house is \(h \mathrm{~m}\) above the tap level. The speed of water coming out through the tap of cross section area \(500 \mathrm{~mm}^{2}\)...

Moment of inertia of a disc of mass '\(M\)' and radius '\(R\)' about any of its diameter is \(\frac{M R^{2}}{4}\). The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be, $$\frac{...

Choose the correct length (L) versus square of the time period (\(\mathrm{T}^{2}\)) graph for a simple pendulum executing simple harmonic motion.

If the velocity of light \(\mathrm{c}\), universal gravitational constant \(\mathrm{G}\) and Planck's constant \(\mathrm{h}\) are chosen as fundamental quantities. The dimensions of mass in the new system is :

As shown in the figure, in Young's double slit experiment, a thin plate of thickness \(t=10 \mu \mathrm{m}\) and refractive index \(\mu=1.2\) is inserted infront of slit \(S_{1}\). The experiment is conducted in air \((\mu=1)\) and uses a m...

A block is fastened to a horizontal spring. The block is pulled to a distance \(x=10 \mathrm{~cm}\) from its equilibrium position (at \(x=0\)) on a frictionless surface from rest. The energy of the block at \(x=5\) \(\mathrm{cm}\) is $$0.25...

A force \(\mathrm{F}=\left(5+3 y^{2}\right)\) acts on a particle in the \(y\)-direction, where \(\mathrm{F}\) is in newton and \(y\) is in meter. The work done by the force during a displacement from \(y=2 \mathrm{~m}\) to $$y=5 \mathrm{~m}...