JEE Main 2023 (Online) 24th January Evening Shift

The number of square matrices of order 5 with entries from the set {0, 1}, such that the sum of all the elements in each row is 1 and the sum of all the elements in each column is also 1, is :

Three urns A, B and C contain 4 red, 6 black; 5 red, 5 black; and \(\lambda\) red, 4 black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn...

The number of real solutions of the equation \(3\left( {{x^2} + {1 \over {{x^2}}}} \right) - 2\left( {x + {1 \over x}} \right) + 5 = 0\), is

If \({{{1^3} + {2^3} + {3^3}\, + \,...\,up\,to\,n\,terms} \over {1\,.\,3 + 2\,.\,5 + 3\,.\,7\, + \,...\,up\,to\,n\,terms}} = {9 \over 5}\), then the value of \(n\) is

The minimum number of elements that must be added to the relation R = {(a, b), (b, c), (b, d)} on the set {a, b, c, d} so that it is an equivalence relation, is __________.

Let the six numbers \(\mathrm{a_1,a_2,a_3,a_4,a_5,a_6}\), be in A.P. and \(\mathrm{a_1+a_3=10}\). If the mean of these six numbers is \(\frac{19}{2}\) and their variance is \(\sigma^2\), then 8\(\sigma^2\) is equal to :

The equations of the sides AB, BC and CA of a triangle ABC are : \(2x+y=0,x+py=21a,(a\pm0)\) and \(x-y=3\) respectively. Let P(2, a) be the centroid of \(\Delta\)ABC. Then (BC)\(^2\) is equal to ___________.

Let \(\mathrm{S = \{ \theta \in [0,2\pi ):\tan (\pi \cos \theta ) + \tan (\pi \sin \theta ) = 0\}}\). Then \(\sum\limits_{\theta \in S} {{{\sin }^2}\left( {\theta + {\pi \over 4}} \right)}\) is equal to __________.

Let \(\overrightarrow \alpha = 4\widehat i + 3\widehat j + 5\widehat k\) and \(\overrightarrow \beta = \widehat i + 2\widehat j - 4\widehat k\). Let \({\overrightarrow \beta _1}\) be parallel to \(\overrightarrow \alpha\) and $${\ove...

Let $$\overrightarrow a = \widehat i + 2\widehat j + \lambda \widehat k,\overrightarrow b = 3\widehat i - 5\widehat j - \lambda \widehat k,\overrightarrow a \,.\,\overrightarrow c = 7,2\overrightarrow b \,.\,\overrightarrow c + 43 = 0,\...

A photon is emitted in transition from n = 4 to n = 1 level in hydrogen atom. The corresponding wavelength for this transition is (given, h = 4 \(\times\) 10\(^{-15}\) eVs) :

The energy released per fission of nucleus of \(^{240}\)X is 200 MeV. The energy released if all the atoms in 120g of pure \(^{240}\)X undergo fission is ____________ \(\times\) 10\(^{25}\) MeV.
(Given \(\mathrm{N_A=6\times10^{23}}\))

A parallel plate capacitor with air between the plate has a capacitance of 15pF. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant 3.5. Then the capacitance becomes $$\f...

A body of mass 200g is tied to a spring of spring constant 12.5 N/m, while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed 5 rad/s. Then th...

Match List I with List II

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A cell of emf 90 V is connected across series combination of two resistors each of 100\(\Omega\) resistance. A voltmeter of resistance 400\(\Omega\) is used to measure the potential difference across each resistor. The reading of the voltme...

If a copper wire is stretched to increase its length by 20%. The percentage increase in resistance of the wire is __________%.

An \(\alpha\)-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavelength:

A metallic rod of length 'L' is rotated with an angular speed of '\(\omega\)' normal to a uniform magnetic field 'B' about an axis passing through one end of rod as shown in figure. The induced emf will be :

Three identical resistors with resistance R = 12\(\Omega\) and two identical inductors with self inductance L = 5 mH are connected to an ideal battery with emf of 12 V as shown in figure. The current through the battery long after the switc...

The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by
\(\mathrm{{E_x} = {E_o}\sin (kz - \omega t)}\)
\(\mathrm{{B_y} = {B_o}\sin (kz - \omega t)}\)
Then the correct relation between...

The logic gate equivalent to the given circuit diagram is :

The electric potential at the centre of two concentric half rings of radii R\(_1\) and R\(_2\), having same linear charge density \(\lambda\) is :

When a beam of white light is allowed to pass through convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called :

A convex lens of refractive index 1.5 and focal length 18cm in air is immersed in water. The change in focal length of the lens will be ___________ cm.
(Given refractive index of water \(=\frac{4}{3}\))

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : A pendulum clock when taken to Mount Everest becomes fast.
Reason R : The value of g (acceleration due to gravity) is less a...

If the distance of the earth from Sun is 1.5 \(\times\) 10\(^6\) km. Then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is :

Given below are two statements:
Statement I : Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.
Statement II : Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from earth's...

Let \(\gamma_1\) be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and \(\gamma_2\) be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid...

In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; \(\mathrm{T_3 > T_2 > T_1}\) as :

A long solenoid is formed by winding 70 turns cm\(^{-1}\). If 2.0 A current flows, then the magnetic field produced inside the solenoid is ____________ (\(\mu_0=4\pi\times10^{-7}\) TmA\(^{-1}\))

A single turn current loop in the shape of a right angle triangle with sides 5 cm, 12 cm, 13 cm is carrying a current of 2 A. The loop is in a uniform magnetic field of magnitude 0.75 T whose direction is parallel to the current in the 13 c...

The velocity time graph of a body moving in a straight line is shown in the figure.

The ratio of displacement to distance travelled by the body in time 0 to 10s is :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Steel is used in the construction of buildings and bridges.
Reason R : Steel is more elastic and its elastic limit is high.
I...

The frequency (\(\nu\)) of an oscillating liquid drop may depend upon radius (\(r\)) of the drop, density (\(\rho\)) of liquid and the surface tension (s) of the liquid as \(\nu=r^a\rho^b s^c\). The values of a, b and c respectively are

A Spherical ball of radius 1mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. Viscous force on the ball when it attains constant velocity is \(3696\times10^{-x}\) N. The value of $$...

A uniform solid cylinder with radius R and length L has moment of inertia I\(_1\), about the axis of the cylinder. A concentric solid cylinder of radius \(R'=\frac{R}{2}\) and length \(L'=\frac{L}{2}\) is carved out of the original cylinder...

A mass m attached to free end of a spring executes SHM with a period of 1s. If the mass is increased by 3 kg the period of the oscillation increases by one second, the value of mass m is ___________ kg.

If two vectors \(\overrightarrow P = \widehat i + 2m\widehat j + m\widehat k\) and \(\overrightarrow Q = 4\widehat i - 2\widehat j + m\widehat k\) are perpendicular to each other. Then, the value of m will be :

A body of mass 1kg begins to move under the action of a time dependent force \(\overrightarrow F = \left( {t\widehat i + 3{t^2}\,\widehat j} \right)\) N, where \(\widehat i\) and \(\widehat j\) are the unit vectors along \(x\) and \(y\) ax...