JEE Main 2021 (Online) 16th March Morning Shift

Let \(P = \left[ {\matrix{ { - 30} & {20} & {56} \cr {90} & {140} & {112} \cr {120} & {60} & {14} \cr } } \right]\) and $$A = \left[ {\matrix{
2 & 7 & {{\omega ^2}} \cr
{ - 1} & { - \omega } & 1 \cr
0 & { - \om...

If the three normals drawn to the parabola, y2 = 2x pass through the point (a, 0) a \(\ne\) 0, then 'a' must be greater than :

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is :

Let ABCD be a square of side of unit length. Let a circle C1 centered at A with unit radius is drawn. Another circle C2 which touches C1 and the lines AD and AB are tangent to it, is also drawn. Let a tangent line from the point C to the ci...

Consider an arithmetic series and a geometric series having four initial terms from the set {11, 8, 21, 16, 26, 32, 4}. If the last terms of these series are the maximum possible four digit numbers, then the number of common terms in these ...

The number of elements in the set {x \(\in\) R : (|x| \(-\) 3) |x + 4| = 6} is equal to :

Consider three observations a, b, and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?

The number of roots of the equation, (81)sin2x + (81)cos2x = 30 in the interval [ 0, \(\pi\) ] is equal to :

If for x \(\in\) \(\left( {0,{\pi \over 2}} \right)\), log10sinx + log10cosx = \(-\)1 and log10(sinx + cosx) = \({1 \over 2}\)(log10 n \(-\) 1), n > 0, then the value of n is equal to :

Let a vector \(\alpha \widehat i + \beta \widehat j\) be obtained by rotating the vector \(\sqrt 3 \widehat i + \widehat j\) by an angle 45\(^\circ\) about the origin in counterclockwise direction in the first quadrant. Then the area of tri...

An RC circuit as shown in the figure is driven by a AC source generating a square wave. The output wave pattern monitored by CRO would look close to :

A sinusoidal voltage of peak value 250 V is applied to a series LCR circuit, in which R = 8\(\Omega\), L = 24 mH and C = 60 \(\mu\)F. The value of power dissipated at resonant condition is 'x' kW. The value of x to the nearest integer is __...

The first three spectral lines of H-atom in the Balmer series are given \(\lambda\)1, \(\lambda\)2, \(\lambda\)3 considering the Bohr atomic model, the wave lengths of first and third spectral lines $$\left( \frac{\lambda_{1} }{\lambda_{3} ...

For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is \({3 \over 4}\)d, wher...

Four equal masses, m each are placed at the comers of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be :

A ball of mass 10 kg moving with a velocity \(10\sqrt 3\) m s\(-\)1 along X-axis, hits another ball of mass 20 kg which is at rest. After collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One o...

A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm. If the block takes 40 s to complete one round, the normal force by the side walls of the groove is :

A 25 m long antenna is mounted on an antenna tower. The height of the antenna tower is 75 m. The wavelength (in meter) of the signal transmitted by this antenna would be :

In the figure given, the electric current flowing through the 5 k\(\Omega\) resistor is 'x' mA.The value of x to the nearest integer is ____________.

A conducting wire of length 'l', area of cross-section A and electric resistivity \(\rho\) is connected between the terminals of a battery. A potential difference V is developed between its ends, causing an electric current.If the length of...

The stopping potential in the context of photoelectric effect depends on the following property of incident electromagnetic radiation :

A conducting bar of length L is free to slide on two parallel conducting rails as shown in the figure Two resistors R1 and R2 are connected across the ends of the rails. There is a uniform magnetic field \(\overrightarrow B\) pointing into...

For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric (Ue) and magnetic (Um) fields is :

A plane electromagnetic wave of frequency 500 MHz is travelling in vacuum along y-direction. At a particular point in space and time, \(\overrightarrow B\) = 8.0 \(\times\) 10\(-\)8 \(\widehat z\)T. The value of electric field at this poin...

The value of power dissipated across the zener diode (Vz = 15V) connected in the circuit as shown in the figure is x \(\times\) 10\(-\)1 watt.The value of x, to the nearest integer, is __________.

In the logic circuit shown in the figure, if input A and B are 0 to 1 respectively, the output at Y would be 'x'.The value of x is ____________.

The angle of deviation through a prism is minimum when(A) Incident ray and emergent ray are symmetric to the prism.(B) The refracted ray inside the prism becomes parallel to its base(C) Angle of incidence is equal to that of the angle of em...

The maximum and minimum distances of a comet from the Sun are 1.6 \(\times\) 1012 m and 8.0 \(\times\) 1010 m respectively. If the speed of the comet at the nearest point is 6 \(\times\) 104 ms\(-\)1, the speed at the farthest point is :

In thermodynamics, heat and work are :

The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T. Consider R as universal gas constant. The pressure of the mixture of gases is :

A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle \(\theta\) as shown in figure. The coefficient of kinetic friction is \(\mu\)k. then, the block's acceleration 'a' is given by :(g is accelerat...

A bar magnet of length 14 cm is placed in the magnetic meridian with its north pole pointing towards the geographic north pole. A neutral point is obtained at a distance of 18 cm from the center of the magnet. If BH = 0.4 G, the magnetic mo...

The velocity-displacement graph describing the motion of bicycle is shown in the figure.The acceleration-displacement graph of the bicycle's motion is best described by :

The pressure acting on a submarine is 3 \(\times\) 105 Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be : (Assume that atmospheric pressure is 1 \(\times\) 105 Pa densi...

Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force F = 20 N through a massless string wrapped around is periphery as shown in the fi...

Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure. A vertical force \(\overrightarrow P\) of magnitude 100 N is applied at point A of the frame.Suppose the force is \(\overrightarrow P\) resolved ...

Time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration g/2, the time period of pendulum will be :

One main scale division of a vernier callipers is 'a' cm and nth division of the vernier scale coincide with (n \(-\) 1)th division of the main scale. The least count of the callipers in mm is :

The resistance R = \({V \over I}\), where V = (50 \(\pm\) 2)V and I = (20 \(\pm\) 0.2)A. The percentage error in R is 'x'%. The value of 'x' to the nearest integer is _________.

A fringe width of 6 mm was produced for two slits separated by 1 mm apart. The screen is placed 10 m away. The wavelength of light used is 'x' nm. The value of 'x' to the nearest integer is ____________.