JEE Main 2021 (Online) 22th July Evening Shift

Let \(A = \left[ {\matrix{ 0 & 1 & 0 \cr 1 & 0 & 0 \cr 0 & 0 & 1 \cr } } \right]\). Then the number of 3 \(\times\) 3 matrices B with entries from the set {1, 2, 3, 4, 5} and satisfying AB = BA is ____________.

If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers greater than 10,000 is equal to _____________.

Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 \(\times\) 2 matrices. The probability that such formed matrix have all different entries and are non-singular, is :

Let [x] denote the greatest integer less than or equal to x. Then, the values of x\(\in\)R satisfying the equation \({[{e^x}]^2} + [{e^x} + 1] - 3 = 0\) lie in the interval :

Let Sn denote the sum of first n-terms of an arithmetic progression. If S10 = 530, S5 = 140, then S20 \(-\) S6 is equal to:

The sum of all the elements in the set {n\(\in\) {1, 2, ....., 100} | H.C.F. of n and 2040 is 1} is equal to _____________.

Consider the following frequency distribution :
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The number of solutions of sin7x + cos7x = 1, x\(\in\) [0, 4\(\pi\)] is equal to

Let a vector \({\overrightarrow a }\) be coplanar with vectors \(\overrightarrow b = 2\widehat i + \widehat j + \widehat k\) and \(\overrightarrow c = \widehat i - \widehat j + \widehat k\). If \({\overrightarrow a}\) is perpendicular to ...

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

In a circuit consisting of a capacitance and a generator with alternating emf Eg = Eg0 sin\(\omega\)t, VC and IC are the voltage and current. Correct phasor diagram for such circuit is

Match List - I with List - II



List - I

List - II




(a)
\(\omega L > {1 \over {\omega C}}\)
(i)
Current is in phase with emf


(b)
\(\omega L = {1 \over {\omega C}}\)
(ii)
Curre...

A nucleus with mass number 184 initially at rest emits an \(\alpha\)-particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the \(\alpha\)-particle.

A bullet of '4 g' mass is fired from a gun of mass 4 kg. If the bullet moves with the muzzle speed of 50 ms\(-\)1, the impulse imparted to the gun and velocity of recoil of gun are :

The position of the centre of mass of a uniform semi-circular wire of radius 'R' placed in x-y plane with its centre at the origin and the line joining its ends as x-axis is given by \(\left( {0,{{xR} \over \pi }} \right)\). Then, the value...

What should be the height of transmitting antenna and the population covered if the television telecast is to cover a radius of 150 km? The average population density around the tower is 2000/km2 and the value of Re = 6.5 \(\times\) 106 m.

A Copper (Cu) rod of length 25 cm and cross-sectional area 3 mm2 is joined with a similar Aluminium (Al) rod as shown in figure. Find the resistance of the combination between the ends A and B.(Take Resistivity of Copper = 1.7 \(\times\) 10...

In an electric circuit, a cell of certain emf provides a potential difference of 1.25 V across a load resistance of 5\(\Omega\). However, it provides a potential difference of 1 V across a load resistance of 2\(\Omega\). The emf of the cell...

An electron of mass me and a proton of mass mp are accelerated through the same potential difference. The ratio of the de-Broglie wavelength associated with the electron to that with the proton is

Intensity of sunlight is observed as 0.092 Wm\(-\)2 at a point in free space. What will be the peak value of magnetic field at the point?(\({\varepsilon _0} = 8.85 \times {10^{ - 12}}{C^2}{N^{ - 1}}{m^{ - 2}}\))

Consider a situation in which reserve biased current of a particular P-N junction increases when it is exposed to a light of wavelength \(\le\) 621 nm. During this process, enhancement in carrier concentration takes place due to generation ...

In a given circuit diagram, a 5 V zener diode along with a series resistance is connected across a 50 V power supply. The minimum value of the resistance required, if the maximum zener current is 90 mA will be __________ \(\Omega\).

An electric dipole is placed on x-axis in proximity to a line charge of linear charge density 3.0 \(\times\) 10\(-\)6 C/m. Line charge is placed on z-axis and positive and negative charge of dipole is at a distance of 10 mm and 12 mm from t...

The total charge enclosed in an incremental volume of 2 \(\times\) 10\(-\)9 m3 located at the origin is ___________ nC, if electric flux density of its field is found asD = e\(-\)x sin y \(\widehat i\) \(-\) e\(-\)x cos y \(\widehat j\) + 2...

A ray of light passes from a denser medium to a rarer medium at an angle of incidence i. The reflected and refracted rays make an angle of 90\(^\circ\) with each other. The angle of reflection and refraction are respectively r and r'. The c...

A ray of light passing through a prism (\(\mu\) = \(\sqrt 3\)) suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is _____________ (in degrees).

A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height h is ___________ s.

What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T?

The area of cross-section of a railway track is 0.01 m2. The temperature variation is 10\(^\circ\)C. Coefficient of liner expansion of material of track is 10\(-\)5/\(^\circ\)C. The energy stored per meter in the track is ____________ J/m.(...

Choose the correct option

Statement I : The ferromagnetic property depends on temperature. At high temperature, ferromagnet becomes paramagnet.Statement II : At high temperature, the domain wall area of a ferromagnetic substance increases.In the light of the above s...

In 5 minutes, a body cools from 75\(^\circ\)C to 65\(^\circ\)C at room temperature of 25\(^\circ\)C. The temperature of body at the end of next 5 minutes is _________\(^\circ\) C.

Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter.The correct statement for this situation...

The centre of a wheel rolling on a plane surface moves with a speed v0. A particle on the rim of the wheel at the same level as the centre will be moving at a speed \(\sqrt x {v_0}\). Then the value of x is _____________.

T0 is the time period of a simple pendulum at a place. if the length of the pendulum is reduced to \({1 \over {16}}\) times of its initial value, the modified time period is :

Three students S1, S2 and S3 perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations ar...

What will be the projection of vector \(\overrightarrow A = \widehat i + \widehat j + \widehat k\) on vector \(\overrightarrow B = \widehat i + \widehat j\) ?

Three particles P, Q and R are moving along the vectors \(\overrightarrow A = \widehat i + \widehat j\), \(\overrightarrow B = \widehat j + \widehat k\) and \(\overrightarrow C = - \widehat i + \widehat j\) respectively. They strike on ...

The motion of a mass on a spring, with spring constant K is as shown in figure.The equation of motion is given by x(t) = A sin\(\omega\)t + B cos\(\omega\)t with \(\omega\) = \(\sqrt {{K \over m}}\)Suppose that at time t = 0, the position ...

A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the work done by the porter in lowering the suitcase.(take g = 9.8 ms\(-\)2)