JEE Main 2021 (Online) 26th August Evening Shift

Let A be a 3 \(\times\) 3 real matrix. If det(2Adj(2 Adj(Adj(2A)))) = 241, then the value of det(A2) equal __________.

A fair die is tossed until six is obtained on it. Let x be the number of required tosses, then the conditional probability P(x \(\ge\) 5 | x > 2) is :

Two fair dice are thrown. The numbers on them are taken as \(\lambda\) and \(\mu\), and a system of linear equationsx + y + z = 5x + 2y + 3z = \(\mu\) x + 3y + \(\lambda\)z = 1is constructed. If p is the probability that the system has a un...

Let \(\lambda\) \(\ne\) 0 be in R. If \(\alpha\) and \(\beta\) are the roots of the equation x2 \(-\) x + 2\(\lambda\) = 0, and \(\alpha\) and \(\gamma\) are the roots of equation 3x2 \(-\) 10x + 27\(\lambda\) = 0, then $${{\beta \gamma } \...

The sum of all 3-digit numbers less than or equal to 500, that are formed without using the digit "1" and they all are multiple of 11, is _____________.

Let a1, a2, ......., a10 be an AP with common difference \(-\) 3 and b1, b2, ........., b10 be a GP with common ratio 2. Let ck = ak + bk, k = 1, 2, ......, 10. If c2 = 12 and c3 = 13, then \(\sum\limits_{k = 1}^{10} {{c_k}}\) is equal to ...

Let the mean and variance of four numbers 3, 7, x and y(x > y) be 5 and 10 respectively. Then the mean of four numbers 3 + 2x, 7 + 2y, x + y and x \(-\) y is ______________.

The value of $$2\sin \left( {{\pi \over 8}} \right)\sin \left( {{{2\pi } \over 8}} \right)\sin \left( {{{3\pi } \over 8}} \right)\sin \left( {{{5\pi } \over 8}} \right)\sin \left( {{{6\pi } \over 8}} \right)\sin \left( {{{7\pi } \over 8}} ...

A hall has a square floor of dimension 10 m \(\times\) 10 m (see the figure) and vertical walls. If the angle GPH between the diagonals AG and BH is \({\cos ^{ - 1}}{1 \over 5}\), then the height of the hall (in meters) is :

If the projection of the vector \(\widehat i + 2\widehat j + \widehat k\) on the sum of the two vectors \(2\widehat i + 4\widehat j - 5\widehat k\) and \(- \lambda \widehat i + 2\widehat j + 3\widehat k\) is 1, then \(\lambda\) is equal to...

In the given circuit the AC source has \(\omega\) = 100 rad s-1. Considering the inductor and capacitor to be ideal, what will be the current I flowing through the circuit?

At time t = 0, a material is composed of two radioactive atoms A and B, where NA(0) = 2NB(0). The decay constant of both kind of radioactive atoms is \(\lambda\). However, A disintegrates to B and B disintegrates to C. Which of the followin...

A parallel plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant K1 and K2 of same area A/2 and thickness d/2 are inserted in the space between the plates. The capacitance of the ...

A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that \(r = {L \over {\sqrt 2 }}\). The speed of particle will be :

A transmitting antenna at top of a tower has a height of 50 m and the height of receiving antenna is 80 m. What is range of communication for Line of Sight (LoS) mode?[use radius of earth = 6400 km]

If you are provided a set of resistances 2\(\Omega\), 4\(\Omega\), 6\(\Omega\) and 8\(\Omega\). Connect these resistances so as to obtain an equivalent resistance of \({{46} \over 3}\)\(\Omega\).

An electric bulb of 500 watt at 100 volt is used in a circuit having a 200 V supply. Calculate the resistance R to be connected in series with the bulb so that the power delivered by the bulb is 500 W.

The de-Broglie wavelength of a particle having kinetic energy E is \(\lambda\). How much extra energy must be given to this particle so that the de-Broglie wavelength reduces to 75% of the initial value?

If the maximum value of accelerating potential provided by a ratio frequency oscillator is 12 kV. The number of revolution made by a proton in a cyclotron to achieve one sixth of the speed of light is ...............[mp = 1.67 \(\times\) 10...

A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s\(-\)1 in a uniform horizontal magnetic field of 3.0 \(\times\) 10\(-\)2 T. The maximum emf induced the coil will be ........

A light beam is described by \(E = 800\sin \omega \left( {t - {x \over c}} \right)\). An electron is allowed to move normal to the propagation of light beam with a speed of 3 \(\times\) 107 ms\(-\)1. What is the maximum magnetic force exert...

Four NOR gates are connected as shown in figure. The truth table for the given figure is :

For the given circuit, the power across Zener diode is .............. mW.

The two thin coaxial rings, each of radius 'a' and having charges +Q and \(-\)Q respectively are separated by a distance of 's'. The potential difference between the centres of the two rings is :

An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal length 15 cm is placed on other side of lens at 8 cm as shown in the figure. Image of object coincides with the object.When the convex mirror is removed...

The temperature of equal masses of three different liquids x, y and z are 10\(^\circ\)C, 20\(^\circ\)C and 30\(^\circ\)C respectively. The temperature of mixture when x is mixed with y is 16\(^\circ\)C and that when y is mixed with z is 26$...

A cylindrical container of volume 4.0 \(\times\) 10\(-\)3 m3 contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400 K. The pressure of the mixture of gases is :[Take gas constant as 8.3 J...

A refrigerator consumes an average 35W power to operate between temperature \(-\)10\(^\circ\)C to 25\(^\circ\)C. If there is no loss of energy then how much average heat per second does it transfer?

The coefficient of static friction between two blocks is 0.5 and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is .................. N. (take g = 10 ms-2)

A coil in the shape of an equilateral triangle of side 10 cm lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field 20 mT. The torque acting on the coil when a current of 0.2 A is passed t...

A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :

Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is \({{24} \over \pi } \times {10^2}\) Nm-2. What is the minimum radius of the wire ? (Take g = 10 ms-2)

The solid cylinder of length 80 cm and mass M has a radius of 20 cm. Calculate the density of the material used if the moment of inertia of the cylinder about an axis CD parallel to AB as shown in figure is 2.7 kg m2.

Two simple harmonic motions are represented by the equations \({x_1} = 5\sin \left( {2\pi t + {\pi \over 4}} \right)\) and \({x_2} = 5\sqrt 2 (\sin 2\pi t + \cos 2\pi t)\). The amplitude of second motion is ................ times the ampli...

Match List - I with List - II Choose the most appropriate answer from the options given below :

If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is :

The acceleration due to gravity is found upto an accuracy of 4% on a planet. The energy supplied to a simple pendulum to known mass 'm' to undertake oscillations of time period T is being estimated. If time period is measured to an accuracy...

The angle between vector \(\left( {\overrightarrow A } \right)\) and \(\left( {\overrightarrow A - \overrightarrow B } \right)\) is :

A source of light is placed in front of a screen. Intensity of light on the screen is I. Two Polaroids P1 and P2 are so placed in between the source of light and screen that the intensity of light on screen is I/2. P2 should be rotated by a...

Two waves are simultaneously passing through a string and their equations are : y1 = A1 sin k(x \(-\) vt), y2 = A2 sin k(x \(-\) vt + x0). Given amplitudes A1 = 12 mm and A2 = 5 mm, x0 = 3.5 cm and wave number k = 6.28 cm\(-\)1. The amplitu...