JEE Main 2021 (Online) 18th March Evening Shift

Let the system of linear equations 4x + \(\lambda\)y + 2z = 02x \(-\) y + z = 0\(\mu\)x + 2y + 3z = 0, \(\lambda\), \(\mu\)\(\in\)R.has a non-trivial solution. Then which of the following is true?

If \(\sum\limits_{r = 1}^{10} {r!({r^3} + 6{r^2} + 2r + 5) = \alpha (11!)}\), then the value of \(\alpha\) is equal to ___________.

Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the probability of getting exactly 3 successes is equal to :

Let S1 be the sum of first 2n terms of an arithmetic progression. Let S2 be the sum of first 4n terms of the same arithmetic progression. If (S2 \(-\) S1) is 1000, then the sum of the first 6n terms of the arithmetic progression is equal to...

Define a relation R over a class of n \(\times\) n real matrices A and B as "ARB iff there exists a non-singular matrix P such that PAP\(-\)1 = B". Then which of the following is true?

Let in a series of 2n observations, half of them are equal to a and remaining half are equal to \(-\)a. Also by adding a constant b in each of these observations, the mean and standard deviation of new set become 5 and 20, respectively. The...

Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral triangle be along the straight line x + y = 3. If R and r be the radius of circumcircle and incircle respectively of \(\Delta\)ABC, th...

If 15sin4\(\alpha\) + 10cos4\(\alpha\) = 6, for some \(\alpha\)\(\in\)R, then the value of 27sec6\(\alpha\) + 8cosec6\(\alpha\) is equal to :

Let \(\overrightarrow a\) and \(\overrightarrow b\) be two non-zero vectors perpendicular to each other and \(|\overrightarrow a | = |\overrightarrow b |\). If \(|\overrightarrow a \times \overrightarrow b | = |\overrightarrow a |\), the...

In a triangle ABC, if \(|\overrightarrow {BC} | = 8,|\overrightarrow {CA} | = 7,|\overrightarrow {AB} | = 10\), then the projection of the vector \(\overrightarrow {AB}\) on \(\overrightarrow {AC}\) is equal to :

In a series LCR circuit, the inductive reactance (XL) is 10\(\Omega\) and the capacitive reactance (XC) is 4\(\Omega\). The resistance (R) in the circuit is 6\(\Omega\). The power factor of the circuit is :

The decay of a proton to neutron is :

An object of mass m1 collides with another object of mass m2, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses m2 : m1 is :

The projectile motion of a particle of mass 5 g is shown in the figure.The initial velocity of the particle is \(5\sqrt 2\) ms-1 and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points...

A particle of mass m moves in a circular orbit under the central potential field, \(U(r) = - {C \over r}\), where C is a positive constant. The correct radius \(-\) velocity graph of the particle's motion is :

A TV transmission tower antenna is at a height of 20 m. Suppose that the receiving antenna is at.(i) ground level(ii) a height of 5 m.The increase in antenna range in case (ii) relative to case (i) is n%.The value of n, to the nearest integ...

Two wires of same length and thickness having specific resistances 6\(\Omega\) cm and 3\(\Omega\) cm respectively are connected in parallel. The effective resistivity is \(\rho\)\(\Omega\) cm. The value of \(\rho\), to the nearest integer, ...

Consider a 72 cm long wire AB as shown in the figure. The galvanometer jockey is placed at P on AB at a distance x cm from A. The galvanometer shows zero deflection.The value of x, to the nearest integer, is ___________.

The speed of electrons in a scanning electron microscope is 1 \(\times\) 107 ms-1. If the protons having the same speed are used instead of electrons, then the resolving power of scanning proton microscope will be changed by a factor of :

The time taken for the magnetic energy to reach 25% of its maximum value, when a solenoid of resistance R, inductance L is connected to a battery, is :

A plane electromagnetic wave propagating along y-direction can have the following pair of electric field \(\left( {\overrightarrow E } \right)\) and magnetic field \(\left( {\overrightarrow B } \right)\) components.

The typical output characteristics curve for a transistor working in the common-emitter configuration is shown in the figure.The estimated current gain from the figure is __________.

The correct relation between \(\alpha\) (ratio of collector current to emitter current) and \(\beta\) (ratio of collector current to base current) of a transistor is :

An infinite number of point charges, each carrying 1 \(\mu\)C charge, are placed along the y-axis at y = 1 m, 2 m, 4 m, 8 m ...............The total force on a 1C point charge, placed at the origin, is x \(\times\) 103 N.The value of x, to ...

Three rays of light, namely red (R), green (G) and blue (B) are incident on the face PQ of a right angled prism PQR as shown in the figure.The refractive indices of the material of the prism for red, green and blue wavelength are 1.27, 1.42...

The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is \({\overrightarrow L }\). The magnitude of the areal velocity of the planet is :

If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately : [Take g = 10 ms\(-\)2, the radius of earth, R = 6400 \(\times\) 103 m, Take \(\pi\) = ...

An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is S1 and that of the other part is S2. Given that S1 > S2. If the piston is removed then the total entropy of the system will be :

For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where \(\gamma\) is the ratio of specific heats) :

Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be :(Molecular weight of oxygen is 32g/mol; R = 8.3 J K\(-\)1 mol\(-\)1)

Which of the following statements are correct?(A) Electric monopoles do not exist whereas magnetic monopoles exist.(B) Magnetic field lines due to a solenoid at its ends and outside cannot be completely straight and confined.(C) Magnetic fi...

A proton and an \(\alpha\)-particle, having kinetic energies Kp and K\(\alpha\) respectively, enter into a magnetic field at right angles.The ratio of the radii of trajectory of proton to that of \(\alpha\)-particle is 2 : 1. The ratio of K...

The velocity \(-\) displacement graph of a particle is shown in the figure.The acceleration \(-\) displacement graph of the same particle is represented by :

Consider a water tank as shown in the figure. It's cross-sectional area is 0.4 m2. The tank has an opening B near the bottom whose cross-section area is 1 cm2. A load of 24 kg is applied on the water at the top when the height of the water ...

Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the center is :

A solid cylinder of mass m is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is :[The coefficient of static ...

The function of time representing a simple harmonic motion with a period of \({\pi \over \omega }\) is :

The radius of a sphere is measured to be (7.50 \(\pm\) 0.85) cm. Suppose the percentage error in its volume is x. The value of x, to the nearest x, is __________.

A galaxy is moving away from the earth at a speed of 286 kms\(-\)1. The shift in the wavelength of a redline at 630 nm is x \(\times\) 10\(-\)10 m. The value of x, to the nearest integer, is ____________. [Take the value of speed of light c...

A ball of mass 4 kg, moving with a velocity of 10 ms\(-\)1, collides with a spring of length 8 m and force constant 100 Nm\(-\)1. The length of the compressed spring is x m. The value of x, to the nearest integer, is ____________.