JEE Main 2021 (Online) 24th February Morning Shift

Let P = \(\left[ {\matrix{ 3 & { - 1} & { - 2} \cr 2 & 0 & \alpha \cr 3 & { - 5} & 0 \cr } } \right]\), where \(\alpha\) \(\in\) R. Suppose Q = [ qij] is a matrix satisfying PQ = kl3 for some non-zero k \(\in\) R. If ...

The locus of the mid-point of the line segment joining the focus of the parabola y2 = 4ax to a
moving point of the parabola, is another parabola whose directrix is :

A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at
least 2 Indians and double the number of foreigners as Indians. Then the number of ways,
the committee can be formed, is :

Let Bi (i = 1, 2, 3) be three independent events in a sample space. The probability that only B1 occur is \(\alpha\), only B2 occurs is \(\beta\) and only B3 occurs is \(\gamma\). Let p be the probability that none of the events Bi occur...

An ordinary dice is rolled for a certain number of times. If the probability of getting an odd
number 2 times is equal to the probability of getting an even number 3 times, then the
probability of getting an odd number for odd number of tim...

Let p and q be two positive numbers such that p + q = 2 and p4+q4 = 272. Then p and q are
roots of the equation :

Let  A = {n \(\in\) N: n is a 3-digit number}
       B = {9k + 2: k \(\in\) N}
and C = {9k + \(l\): k \(\in\) N} for some \(l ( 0 < l < 9)\)
If the sum of all the elements of the set A \(\cap\) (B \(\cup\) C) is 274 \(\times\) 4...

A man is walking on a straight line. The arithmetic mean
of the reciprocals of the intercepts of this line on the
coordinate axes is \({1 \over 4}\). Three stones A, B and C are placed at the points
(1, 1), (2, 2) and (4, 4) respectively. T...

If
\({e^{\left( {{{\cos }^2}x + {{\cos }^4}x + {{\cos }^6}x + ...\infty } \right){{\log }_e}2}}\)
satisfies the equation t2 - 9t + 8 = 0, then the value of
$${{2\sin x} \over {\sin x + \sqrt 3 \cos x}}\left( {0 < x < {\pi \over 2}} \right)...

Let three vectors \(\overrightarrow a ,\overrightarrow b\) and \(\overrightarrow c\) be such that \(\overrightarrow c\) is coplanar with \(\overrightarrow a\) and \(\overrightarrow b\),
\(\overrightarrow a .\overrightarrow c\) ...

A common transistor radio set requires 12 V (D.C.) for its operation. The D.C. source is constructed by using a transformer and a rectifier circuit, which are operated at 220 V (A.C.) on standard domestic A.C. supply. The number of turns of...

A resonance circuit having inductance and resistance 2 \(\times\) 10\(-\)4 H and 6.28\(\Omega\) respectively oscillates at 10 MHz frequency. The value of quality factor of this resonator is ___________. [\(\pi\) = 3.14]

In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked A, B, C, D and E.The transitions A, B and C respectively represent :

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be :

A ball with a speed of 9 m/s collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of 30\(^\circ\) with the original direction. The ratio of velocities of the balls after collision is x...

An audio signal vm = 20 sin 2\(\pi\)(1500t) amplitude modulates a carrier vc = 80 sin 2\(\pi\)(100,000t).The value of percent modulation is _________.

A cell E1 of emf 6V and internal resistance 2\(\Omega\) is connected with another cell E2 of emf 4V and internal resistance 8\(\Omega\) (as shown in the figure). The potential difference across points X and Y is :

A current through a wire depends on time as i = \(\alpha\)0t + \(\beta\)t2where \(\alpha\)0 = 20 A/s and \(\beta\) = 8 As\(-\)2. Find the charge crossed through a section of the wire in 15 s.

Given below are two statements : Statement I : Two photons having equal linear momenta have equal wavelengths.Statement II : If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease.In the light ...

An electromagnetic wave of frequency 5 GHz, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are 2. Its velocity in this medium is ____________ \(\times\) 107 m/s.

If an emitter current is changed by 4 mA, the collector current changes by 3.5 mA. The value of \(\beta\) will be :

In connection with the circuit drawn below, the value of current flowing through 2 k\(\Omega\) resistor is _________ \(\times\) 10\(-\)4 A.

A cube of side 'a' has point charges +Q located at each of its vertices except at the origin where the charge is \(-\)Q. The electric field at the centre of cube is :

The focal length f is related to the radius of curvature r of the spherical convex mirror by :

Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revolution is :

Consider two satellites S1 and S2 with periods of revolution 1 hr. and 8 hr. respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite S1 to the angular velocity of satellite S2 is :

Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be :

n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes.A \(\to\) B : Isothermal expansion at temperature T so that the volume is doubled from V1 to V2 = 2V1 and pressure charges from P1 ...

Match List I with List II.



List I

List II




(a)
Isothermal
(i)
Pressure constant


(b)
Isochoric
(ii)
Temperature constant


(c)
Adiabatic
(iii)
Volume cons...

Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is '\(\alpha\)'. The metal sheet is heated uniformly, by a small temperature \(\Delta\)T, so that i...

An inclined plane is bent in such a way that the vertical cross-section is given by \(y = {{{x^2}} \over 4}\) where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of frict...

The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be _________ N. [g = 10 ms$$...

If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph?

If Y, K and \(\eta\) are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

A hydraulic press can lift 100 kg when a mass 'm' is placed on the smaller piston. It can lift ___________ kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the ...

Moment of inertia (M. I.) of four bodies, having same mass and radius, are reported as; I1 = M.I. of thin circular ring about its diameter,I2 = M.I. of circular disc about an axis perpendicular to disc and going through the centre,I3 = M.I....

In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When t...

The work done by a gas molecule in an isolated system is given by, \(W = \alpha {\beta ^2}{e^{ - {{{x^2}} \over {\alpha kT}}}}\), where x is the displacement, k is the Boltzmann constant and T is the temperature. \(\alpha\) and \(\beta\) ar...

An unpolarised light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as 100 Lumens. Now, if the analyzer is rotated around the horizontal axis (direction ...

In a Young's double slit experiment, the width of the one of the slit is three times the other slit. The amplitude of the light coming from a slit is proportional to the slit-width. Find the ratio of the maximum to the minimum intensity in ...