JEE Main 2021 (Online) 24th February Evening Shift

The negation of the statement \(\sim p \wedge (p \vee q)\) is :

Let A and B be 3 \(\times\) 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations (A2B2 \(-\) B2A2) X = O, where X is a 3 \(\times\) 1 column matrix of unknown variables and O is...

For the system of linear equations:\(x - 2y = 1,x - y + kz = - 2,ky + 4z = 6,k \in R\),consider the following statements :(A) The system has unique solution if \(k \ne 2,k \ne - 2\).(B) The system has unique solution if k = \(-\)2(C) The ...

If P is a point on the parabola y = x2 + 4 which is closest to the straight line y = 4x \(-\) 1, then the co-ordinates of P are :

The students S1, S2, ....., S10 are to be divided into 3 groups A, B and C such that each group has at least one student and the group C has at most 3 students. Then the total number of possibilities of forming such groups is ___________.

The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5} have exactly two elements in their intersection, is :

Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a, c), (2, b) and (a, b) be \(\left( {{{10} \over 3},{7 \over 3}} \right)\). If \(\alpha\), \(\beta\) are the roots of the equation $$a{x^2} + bx + 1 ...

The number of the real roots of the equation \({(x + 1)^2} + |x - 5| = {{27} \over 4}\) is ________.

The sum of first four terms of a geometric progression (G. P.) is \({{65} \over {12}}\) and the sum of their respective reciprocals is \({{65} \over {18}}\). If the product of first three terms of the G.P. is 1, and the third term is $$\alp...

If the variance of 10 natural numbers 1, 1, 1, ....., 1, k is less than 10, then the maximum possible value of k is ________.

A series L-C-R circuit is designed to resonate at an angular frequency \(\omega\)0 = 105 rad/s. The circuit draws 16W power from 120V source at resonance. The value of resistance 'R' in the circuit is _________ \(\Omega\).

According to Bohr atomic model, in which of the following transitions will the frequency be maximum?

Two solids A and B of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic energies (K.E.)A : (K.E.)B will be \({{A \over 1}}\), so the value of A will be ________.

A circular hole of radius \(\left( {{a \over 2}} \right)\) is cut out of a circular disc of radius 'a' as shown in figure. The centroid of the remaining circular portion with respect to point 'O' will be :

A signal of 0.1 kW is transmitted in a cable. The attenuation of cable is \(-\)5 dB per km and cable length is 20 km. The power received at receiver is 10\(-\)x W. The value of x is ________.[Gain in $$dB = 10{\log _{10}}\left( {{{{P_o}} \o...

A cylindrical wire of radius 0.5 mm and conductivity 5 \(\times\) 107 S/m is subjected to an electric field of 10 mV/m. The expected value of current in the wire will be x3\(\pi\) mA. The value of x is _________.

An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be :

The de-Broglie wavelength of a proton and \(\alpha\)-particle are equal. The ratio of their velocities is :

Figure shows a circuit that contains four identical resistors with resistance R = 2.0\(\Omega\), two identical inductors with inductance L = 2.0 mH and an ideal battery with emf E = 9V. The current 'i' just after the switch 'S' is closed wi...

An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be _________ \(\times\) 10\(-\)2 cm.

Match List - I with List - II.



List I

List II




(a)
Source of microwave frequency
(i)
Radioactive decay of nucleus


(b)
Source of infrared frequency
(ii)
Magnetron


(...

Zener breakdown occurs in a p \(-\) n junction having p and n both :

Given below are two statements :Statement I : PN junction diodes can be used to function as transistor, simply by connecting two diodes, back to back, which acts as the base terminal.Statement II : In the study of transistor, the amplificat...

The logic circuit shown above is equivalent to :

Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance x (x << d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion...

A point charge of +12\(\mu\)C is at a distance 6 cm vertically above the centre of a square of side 12 cm as shown in figure. The magnitude of the electric flux through the square will be __________ \(\times\) 103 Nm2/C.

A body weights 49N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator?[Use \(g = {{GM} \over {{R^2}}}\) = 9.8 ms\(-\)2 and radius of earth, R = 6400 km.]

If one mole of an ideal gas at (P1, V1) is allowed to expand reversibly and isothermally (A to B) its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is ...

The root mean square speed of molecules of a given mass of a gas at 27\(^\circ\)C and 1 atmosphere pressure is 200 ms\(-\)1. The root mean square speed of molecules of the gas at 127\(^\circ\)C and 2 atmosphere pressure is $${{x \over {\sqr...

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules :

A particle is projected with velocity v0 along x-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. ma = \(-\) \(\alpha\)x2. The distance at which the particle stops :

A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains :

A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be ________ cm.

A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is _______ \(\times\) 10\(-\)1 kg ...

In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant k, the frequency of oscillation of given ...

When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is :

The period of oscillation of a simple pendulum is \(T = 2\pi \sqrt {{L \over g}}\). Measured value of 'L' is 1.0 m from meter scale having a minimum division of 1 mm and time of one complete oscillation is 1.95 s measured from stopwatch of...

If the source of light used in a Young's double slit experiment is changed from red to violet :

Which of the following equations represents a travelling wave?

Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having frequency of 676 Hz. The beat frequency heard by each driver will be ___________ Hz. [Velocity of sound in air is 340 m/s.]