JEE Main 2021 (Online) 25th February Evening Shift

If for the matrix, \(A = \left[ {\matrix{ 1 & { - \alpha } \cr \alpha & \beta \cr } } \right]\), \(A{A^T} = {I_2}\), then the value of \({\alpha ^4} + {\beta ^4}\) is :

Let A be a 3 \(\times\) 3 matrix with det(A) = 4. Let Ri denote the ith row of A. If a matrix B is obtained by performing the operation R2 \(\to\) 2R2 + 5R3 on 2A, then det(B) is equal to :

The shortest distance between the line x \(-\) y = 1 and the curve x2 = 2y is :

A line is a common tangent to the circle (x \(-\) 3)2 + y2 = 9 and the parabola y2 = 4x. If the two points of contact (a, b) and (c, d) are distinct and lie in the first quadrant, then 2(a + c) is equal to _________.

Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen element of A leaves remainder 2 when divided by 5 is :

In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are 35%, 20% and 10% respectively. A per...

Let \(\alpha\) and \(\beta\) be the roots of x2 \(-\) 6x \(-\) 2 = 0. If an = \(\alpha\)n \(-\) \(\beta\)n for n \(\ge\) 1, then the value of \({{{a_{10}} - 2{a_8}} \over {3{a_9}}}\) is :

The minimum value of \(f(x) = {a^{{a^x}}} + {a^{1 - {a^x}}}\), where a, \(x \in R\) and a > 0, is equal to :

If 0 < x, y < \(\pi\) and cosx + cosy \(-\) cos(x + y) = \({3 \over 2}\), then sinx + cosy is equal to :

Let \(\overrightarrow a = \widehat i + \alpha \widehat j + 3\widehat k\) and \(\overrightarrow b = 3\widehat i - \alpha \widehat j + \widehat k\). If the area of the parallelogram whose adjacent sides are represented by the vectors $$\ove...

Match List I with List II.



List I

List II




(a)
Rectifier
(i)
Used either for stepping up or stepping down the a.c. voltage


(b)
Stabilizer
(ii)
Used to convert a.c. voltage i...

An LCR circuit contains resistance of 110\(\Omega\) and a supply of 220 V at 300 rad/s angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by 45\(^\circ\). If on the other hand, only inductor ...

The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from n = 2 to n = 1 state is :

An electron with kinetic energy K1 enters between parallel plates of a capacitor at an angle '\(\alpha\)' with the plates. It leaves the plates at angle '\(\beta\)' with kinetic energy K2. Then the ratio of kinetic energies K1 : K2 will be ...

Two particles having masses 4 g and 16 g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n : 2. The value of n will be ___________.

If a message signal of frequency 'fm' is amplitude modulated with a carrier signal of frequency 'fc' and radiated through an antenna, the wavelength of the corresponding signal in air is :

A current of 6A enters one corner P of an equilateral triangle PQR having 3 wires of resistance 2\(\Omega\) each and leaves by the corner R. The currents i1 in ampere is _________.

The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength 491 nm is 0.710 V. When the incident wavelength is changed to a new value, the stopping potential is 1.43 V. The new wavelength is...

An electron of mass me and a proton of mass mp = 1836 me are moving with the same speed. The ratio of their de Broglie wavelength \({{{}^\lambda electron} \over {{}^\lambda proton}}\) will be :

The peak electric field produced by the radiation coming from the 8W bulb at a distance of 10 m is \({x \over {10}}\sqrt {{{{\mu _0}c} \over \pi }} {V \over m}\). The efficiency of the bulb is 10% and it is a point source. The value of x is...

The wavelength of an X-ray beam is 10\(\mathop A\limits^o\). The mass of a fictitious particle having the same energy as that of the X-ray photons is \({x \over 3}h\) kg. The value of x is __________. (h = Planck's constant)

For extrinsic semiconductors; when doping level is increased;

The truth table for the following logic circuit is :

A charge 'q' is placed at one corner of a cube as shown in figure. The flux of electrostatic field \(\overrightarrow E\) through the shaded area is :

Two identical conducting spheres with negligible volume have 2.1 nC and \(-\)0.1 nC charges, respectively. They are brought into contact and then separated by a distance of 0.5 m. The electrostatic force acting between the spheres is ______...

Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.20 m. The charge on each of the sphere is \({a \over {21}} \times {10^{ - 8}}\)C. The va...

The initial velocity vi required to project a body vertically upward from the surface of the earth to reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity ve such that $${v_i} = \sqrt {{x \...

A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by 52K, its efficiency is doubled. The temperature in Kelvin of the source will be __________.

Given below are two statements :Statement I : In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution.Statement II : In a diatomic molecule, the rotational energy at a given temperature equals the t...

Thermodynamic process is shown below on a P-V diagram for one mole of an ideal gas. If V2 = 2V1 then the ratio of temperature T2/T1 is :

In a ferromagnetic material, below the curie temperature, a domain is defined as :

A stone is dropped from the top of a building. When it crosses a point 5 m below the top, another stone starts to fall from a point 25 m below the top. Both stones reach the bottom of building simultaneously. The height of the building is :

A sphere of radius 'a' and mass 'm' rolls along a horizontal plane with constant speed v0. It encounters an inclined plane at angle \(\theta\) and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?

Two identical springs of spring constant '2k' are attached to a block of mass m and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of o...

Y = A sin(\(\omega\)t + \(\phi\)0) is the time-displacement equation of a SHM. At t = 0 the displacement of the particle is \(Y = {A \over 2}\) and it is moving along negative x-direction. Then the initial phase angle \(\phi\)0 will be:

The point A moves with a uniform speed along the circumference of a circle of radius 0.36 m and covers 30\(^\circ\) in 0.1 s. The perpendicular projection 'P' from 'A' on the diameter MN represents the simple harmonic motion of 'P'. The res...

If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity \({1 \over {4\pi {\varepsilon _0}}}{{|e{|^2}} \over {hc}}\) has dimensions of :

If \(\overrightarrow P \times \overrightarrow Q = \overrightarrow Q \times \overrightarrow P\), the angle between \(\overrightarrow P\) and \(\overrightarrow Q\) is \(\theta\)(0\(^\circ\) < \(\theta\) < 360\(^\circ\)). The value of '$...

Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter 0.1 \(\mu\)m. If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that:

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4%, will be __________%.