JEE Main 2023 (Online) 25th January Morning Shift

Let \(x,y,z > 1\) and \(A = \left[ {\matrix{ 1 & {{{\log }_x}y} & {{{\log }_x}z} \cr {{{\log }_y}x} & 2 & {{{\log }_y}z} \cr {{{\log }_z}x} & {{{\log }_z}y} & 3 \cr } } \right]\). Then \(\mathrm{|adj~(adj~A^2)|}\) is equal ...

Let S\(_1\) and S\(_2\) be respectively the sets of all \(a \in \mathbb{R} - \{ 0\}\) for which the system of linear equations
\(ax + 2ay - 3az = 1\)
\((2a + 1)x + (2a + 3)y + (a + 1)z = 2\)
\((3a + 5)x + (a + 5)y + (a + 2)z = 3\)
has uniq...

Let \(\mathrm{A_1,A_2,A_3}\) be the three A.P. with the same common difference d and having their first terms as \(\mathrm{A,A+1,A+2}\), respectively. Let a, b, c be the \(\mathrm{7^{th},9^{th},17^{th}}\) terms of \(\mathrm{A_1,A_2,A_3}\), ...

The distance of the point \((6,-2\sqrt2)\) from the common tangent \(\mathrm{y=mx+c,m > 0}\), of the curves \(x=2y^2\) and \(x=1+y^2\) is :

Let \(x\) and \(y\) be distinct integers where \(1 \le x \le 25\) and \(1 \le y \le 25\). Then, the number of ways of choosing \(x\) and \(y\), such that \(x+y\) is divisible by 5, is ____________.

Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space \(S = \left\{ {x \in \mathbb{Z}:x(66 - x) \ge {5 \over 9}M} \right\}\) and the event $$\mathrm{A = \{ x \in S:x\,is\,a\,multiple\,...

Let S = {1, 2, 3, 5, 7, 10, 11}. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is _____________.

The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12. If the new mean of the marks is 10.2, then their new variance is equal to :

The vector \(\overrightarrow a = - \widehat i + 2\widehat j + \widehat k\) is rotated through a right angle, passing through the y-axis in its way and the resulting vector is \(\overrightarrow b\). Then the projection of $$3\overrightarr...

Let \(\overrightarrow a\), \(\overrightarrow b\) and \(\overrightarrow c\) be three non zero vectors such that \(\overrightarrow b\) . \(\overrightarrow c\) = 0 and $$\overrightarrow a \times (\overrightarrow b \times \overrightarrow...

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes \(x\) times its initial resonant frequency \(\omega_0\). The value of \(x\) is :

An LCR series circuit of capacitance 62.5 nF and resistance of 50 \(\Omega\), is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is __________ mH.
(Take $$\pi^2...

The ratio of the density of oxygen nucleus (\(_8^{16}O\)) and helium nucleus (\(_2^{4}\mathrm{He}\)) is

The wavelength of the radiation emitted is \(\lambda_0\) when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydroge...

A parallel plate capacitor has plate area 40 cm\(^2\) and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5. The capacitance of the system is :

A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take g = 10 m/s\(^2\)...

A message signal of frequency 5 kHz is used to modulate a carrier signal of frequency 2 MHz. The bandwidth for amplitude modulation is :

A uniform metallic wire carries a current 2 A, when 3.4 V battery is connected across it. The mass of uniform metallic wire is 8.92 \(\times\) 10\(^{-3}\) kg, density is 8.92 \(\times\) 10\(^{3}\) kg/m\(^3\) and resistivity is 1.7 $$\times$...

In the given circuit, the equivalent resistance between the terminal A and B is __________ \(\Omega\).

Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of \(\lambda_0\). IF the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would...

An electromagnetic wave is transporting energy in the negative \(z\) direction. At a certain point and certain time the direction of electric field of the wave is along positive \(y\) direction. What will be the direction of the magnetic fi...

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Photodiodes are used in forward bias usually for measuring the light intensity.
Reason R : For a p-n junction diode, at appl...

A uniform electric field of 10 N/C is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each plate is 10 cm. The angle...

A ray of light is incident from air on a glass plate having thickness \(\sqrt3\) cm and refractive index \(\sqrt2\). The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray...

Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the parti...

The root mean square velocity of molecules of gas is

A Carnot engine with efficiency 50% takes heat from a source at 600 K. In order to increase the efficiency to 70%, keeping the temperature of sink same, the new temperature of the source will be :

A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2 m long and 0.2 m in diameter. The magnetic intensity at the center of the solenoid when a current of 2 A flows through it is :

Match List I with List II

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...

A car travels a distance of '\(x\)' with speed \(v_1\) and then same distance '\(x\)' with speed \(v_2\) in the same direction. The average speed of the car is :

Match List I with List II

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.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
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...

A bowl filled with very hot soup cools from 98\(^\circ\)C to 86\(^\circ\)C in 2 minutes when the room temperature is 22\(^\circ\)C. How long it will take to cool from 75\(^\circ\)C to 69\(^\circ\)C?

As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45\(^\circ\) with the load axis. The length ...

An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and length 1 m pivoted at its end C on a vertical wall as shown in figure. It is supported by a cable AB such that the system is in equilibrium. The tension in ...

\(\mathrm{I_{CM}}\) is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. \(\mathrm{I_{AB}}\) is it's moment of inertia about an axis AB perpendicular to plane and ...

T is the time period of simple pendulum on the earth's surface. Its time period becomes \(x\) T when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of \(x\) will be :

If \(\overrightarrow P = 3\widehat i + \sqrt 3 \widehat j + 2\widehat k\) and \(\overrightarrow Q = 4\widehat i + \sqrt 3 \widehat j + 2.5\widehat k\) then, the unit vector in the direction of $$\overrightarrow P \times \overrightarrow Q...

In Young's double slits experiment, the position of 5\(\mathrm{^{th}}\) bright fringe from the central maximum is 5 cm. The distance between slits and screen is 1 m and wavelength of used monochromatic light is 600 nm. The separation betwee...

The distance between two consecutive points with phase difference of 60\(^\circ\) in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave is travelling is __________ km/s

An object of mass 'm' initially at rest on a smooth horizontal plane starts moving under the action of force F = 2N. In the process of its linear motion, the angle \(\theta\) (as shown in figure) between the direction of force and horizonta...