JEE Main 2021 (Online) 26th February Evening Shift

If the matrix \(A = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 2 & 0 \cr 3 & 0 & { - 1} \cr } } \right]\) satisfies the equation $${A^{20}} + \alpha {A^{19}} + \beta A = \left[ {\matrix{
1 & 0 & 0 \cr
0 & 4 & 0 \cr
0 &...

A natural number has prime factorization given by n = 2x3y5z, where y and z are such that y + z = 5 and y\(-\)1 + z\(-\)1 = \({5 \over 6}\), y > z. Then the number of odd divisions of n, including 1, is :

A seven digit number is formed using digits 3, 3, 4, 4, 4, 5, 5. The probability, that number so formed is divisible by 2, is :

The triangle of maximum area that can be inscribed in a given circle of radius 'r' is :

Let \(\alpha\) and \(\beta\) be two real numbers such that \(\alpha\) + \(\beta\) = 1 and \(\alpha\)\(\beta\) = \(-\)1. Let pn = (\(\alpha\))n + (\(\beta\))n, pn\(-\)1 = 11 and pn+1 = 29 for some integer n \(\ge\) 1. Then, the value of p$...

If the arithmetic mean and geometric mean of the pth and qth terms of the sequence \(-\)16, 8, \(-\)4, 2, ...... satisfy the equation 4x2 \(-\) 9x + 5 = 0, then p + q is equal to __________.

The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is _________.

The sum of the series \(\sum\limits_{n = 1}^\infty {{{{n^2} + 6n + 10} \over {(2n + 1)!}}}\) is equal to :

Let X1, X2, ......., X18 be eighteen observations such that \(\sum\limits_{i = 1}^{18} {({X_i} - } \alpha ) = 36\) and \(\sum\limits_{i = 1}^{18} {({X_i} - } \beta {)^2} = 90\), where \(\alpha\) and \(\beta\) are distinct real numbers. If t...

If vectors \(\overrightarrow {{a_1}} = x\widehat i - \widehat j + \widehat k\) and \(\overrightarrow {{a_2}} = \widehat i + y\widehat j + z\widehat k\) are collinear, then a possible unit vector parallel to the vector $$x\widehat i + y\wi...

Find the peak current and resonant frequency of the following circuit (as shown in figure).

A radioactive sample is undergoing \(\alpha\) decay. At any time t1, its activity is A and another time t2, the activity is \({A \over 5}\). What is the average life time for the sample?

If the highest frequency modulating a carrier is 5 kHz, then the number of AM broadcast stations accommodated in a 90 kHz bandwidth are _________.

A wire of 1\(\Omega\) has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in resistance to the nearest integer is :

The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 1 state will be :

Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective ...

An aeroplane, with its wings spread 10 m, is flying at a speed of 180 km/h in a horizontal direction. The total intensity of earth's field at that part is 2.5 \(\times\) 10\(-\)4 Wb/m2 and the angle of dip is 60\(^\circ\). The emf induced b...

Draw the output signal Y in the given combination of gates.

The zener diode has a Vz = 30V. The current passing through the diode for the following circuit is ________ mA.

27 similar drops of mercury are maintained at 10V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is __________ times that of a smaller drop.

Given below are two statements: Statement I : An electric dipole is placed at the center of a hollow sphere. The flux of the electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.Statement II : ...

An inclined plane making an angle of 30\(^\circ\) with the horizontal is placed in a uniform horizontal electric field \(200{N \over C}\) as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest at a he...

A point source of light S, placed at a distance 60cm in front of the centre of a plane mirror of width 50 cm, hangs vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 1.2 m from it (s...

Given below are two statements : one is labeled as Assertion A and the other is labeled as Reason R.Assertion A : For a simple microscope, the angular size of the object equals the angular size of the image.Reason R : Magnification is achie...

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors \(\overrightarrow a\), \(\overrightarrow b\) and \(\overrightarrow c\) respectively. Then choose the correct relation for these vectors.

In the reported figure of earth, the value of acceleration due to gravity is same at point A and C but it is smaller than that of its value at point B (surface of the earth). The value of OA : AB will be x : y. The value of x is ________.

The volume V of a given mass of monoatomic gas changes with temperature T according to the relation \(V = K{T^{{2 \over 3}}}\). The workdone when temperature changes by 90K will be xR. The value of x is _________. [R = universal gas constan...

The internal energy (U), pressure (P) and volume (V) of an ideal gas are related as U \(=\) 3PV + 4. The gas is :

1 mole of rigid diatomic gas performs a work of \({Q \over 5}\) when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is \({xR \over 8}\). The value of x is _________. [R = universal gas constant]

Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on the mass B as shown in the figure. If the mass A starts moving away from mass B with acceleration 'a', then the acceleration of mass B will be :

The trajectory of a projectile in a vertical plane is y = \(\alpha\)x \(-\) \(\beta\)x2, where \(\alpha\) and \(\beta\) are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of proje...

A scooter accelerates from rest for time t1 at constant rate a1 and then retards at constant rate a2 for time t2 and comes to rest. The correct value of \({{{t_1}} \over {{t_2}}}\) wil be :

The length of metallic wire is l1 when tension in it is T1. It is l2 when the tension is T2. The original length of the wire will be :

A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of inertia about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a d...

Given below are two statements :Statement I : A second's pendulum has a time period of 1 second.Statement II : It takes precisely one second to move between the two extreme positions.In the light of the above statements, choose the correct ...

A particle executes S.H.M. with amplitude 'a', and time period 'T'. The displacement of the particle when its speed is half of maximum speed is \({{\sqrt x a} \over 2}\). The value of x is __________.

Time period of a simple pendulum is T. The time taken to complete \({5 \over 8}\) oscillations starting from mean position is \({\alpha \over \beta }T\). The value of \(\alpha\) is _________.

A particle executes S.H.M., the graph of velocity as a function of displacement is :

If 'C' and 'V' represent capacity and voltage respectively then what are the dimensions of \(\lambda\) where C/V = \(\lambda\) ?

A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?