JEE Main 2021 (Online) 17th March Evening Shift

If 1, log10(4x \(-\) 2) and log10\(\left( {{4^x} + {{18} \over 5}} \right)\) are in arithmetic progression for a real number x, then the value of the determinant $$\left| {\matrix{
{2\left( {x - {1 \over 2}} \right)} & {x - 1} & {{x^2}} ...

Let \(A = \left[ {\matrix{ a & b \cr c & d \cr } } \right]\) and \(B = \left[ {\matrix{ \alpha \cr \beta \cr } } \right] \ne \left[ {\matrix{ 0 \cr 0 \cr } } \right]\) such that AB = B and a + d = 2021,...

Let L be a tangent line to the parabola y2 = 4x \(-\) 20 at (6, 2). If L is also a tangent to the ellipse \({{{x^2}} \over 2} + {{{y^2}} \over b} = 1\), then the value of b is equal to :

If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to :

Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be \({1 \over 2}\) and probability of occurrence of 0 at the odd place be \({1 \over 3}\). Then th...

Consider a set of 3n numbers having variance 4. In this set, the mean of first 2n numbers is 6 and the mean of the remaining n numbers is 3. A new set is constructed by adding 1 into each of first 2n numbers, and subtracting 1 from each of ...

Let tan\(\alpha\), tan\(\beta\) and tan\(\gamma\); \(\alpha\), \(\beta\), \(\gamma\) \(\ne\) \({{(2n - 1)\pi } \over 2}\), n\(\in\)N be the slopes of three line segments OA, OB and OC, respectively, where O is origin. If circumcentre of $$\...

The number of solutions of the equation x + 2tanx = \({\pi \over 2}\) in the interval [0, 2\(\pi\)] is :

Let O be the origin. Let \(\overrightarrow {OP} = x\widehat i + y\widehat j - \widehat k\) and \(\overrightarrow {OQ} = - \widehat i + 2\widehat j + 3x\widehat k\), x, y\(\in\)R, x > 0, be such that $$\left| {\overrightarrow {PQ} } \righ...

Let \(\overrightarrow x\) be a vector in the plane containing vectors \(\overrightarrow a = 2\widehat i - \widehat j + \widehat k\) and \(\overrightarrow b = \widehat i + 2\widehat j - \widehat k\). If the vector \(\overrightarrow x\) i...

Match List - I with List - II



List - I

List - II




(a)
Phase difference between current and voltage in a purely resistive AC circuit
(i)
\({\pi \over 2}\); current leads voltage


(b)
...

What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved?

A particle of mass m moves in a circular orbit in a central potential field U(r) = U0r4. If Bohr's quantization conditions are applied, radii of possible orbitals rn vary with \({n^{{1 \over \alpha }}}\), where \(\alpha\) is ____________.

The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in the visible region?

A 2\(\mu\)F capacitor C1 is first charged to a potential difference of 10V using a battery. Then the battery is removed and the capacitor is connected to an uncharged capacitor C2 of 8 \(\mu\)F. The charge in C2 on equilibrium condition is ...

The disc of mass M with uniform surface mass density \(\sigma\) is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position \({x \over 3}{a \over \pi },{x \over 3}{a \over \pi }\) where x is _________...

Two identical blocks A and B each of mass m resting on the smooth horizontal floor are connected by a light spring of natural length L and spring constant K. A third block C of mass m moving with a speed v along the line joining A and B col...

A carrier signal C(t) = 25 sin(2.512 \(\times\) 1010t) is amplitude modulated by a message signal m(t) = 5 sin(1.57 \(\times\) 108t) and transmitted through an antenna. What will be the bandwidth of the modulated signal?

The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of 15\(\Omega\) resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10V is maintained ...

Two cells of emf 2E and E with internal resistance r1 and r2 respectively are connected in series to an external resistor R (see figure). The value of R, at which the potential difference across the terminals of the first cell becomes zero ...

Two identical photocathodes receive the light of frequencies f1 and f2 respectively. If the velocities of the photo-electrons coming out are v1 and v2 respectively, then

Seawater at a frequency f = 9 \(\times\) 102 Hz, has permittivity \(\varepsilon\) = 80\(\varepsilon\)0 and resistivity \(\rho\) = 0.25 \(\Omega\)m. Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating...

The electric field intensity produced by the radiation coming from a 100 W bulb at a distance of 3 m is E. The electric field intensity produced by the radiation coming from 60W at the same distance is \(\sqrt {{x \over 5}}\)E. Where the v...

Which one of the following will be the output of the given circuit?

The electric field in a region is given by \(\overrightarrow E = {2 \over 5}{E_0}\widehat i + {3 \over 5}{E_0}\widehat j\) with \({E_0} = 4.0 \times {10^3}{N \over C}\). The flux of this field through a rectangular surface area 0.4 m2 para...

The image of an object placed in air formed by a convex refracting surface is at a distance of 10 m behind the surface. The image is real and is at \({{{2^{rd}}} \over 3}\) of the distance of the object from the surface. The wavelength of l...

A geostationary satellite is orbiting around an arbitrary planet 'P' at a height of 11R above the surface of 'P', R being the radius of 'P'. The time period of another satellite in hours at a height of 2R from the surface of 'P' is ________...

If one mole of the polyatomic gas is having two vibrational modes and \(\beta\) is the ratio of molar specific heats for polyatomic gas \(\left( {\beta = {{{C_P}} \over {{C_V}}}} \right)\) then the value of \(\beta\) is :

Which one is the correct option for the two different thermodynamic processes?

A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction \({1 \over {\sqrt 3 }}\). It is desired to make the body move by applying the minimum possible force F N. The value of F will be ____________...

A boy of mass 4 kg is standing on a piece of wood having mass 5 kg. If the coefficient of friction between the wood and the floor is 0.5, the maximum force that the boy can exert on the rope so that the piece of wood does not move from its ...

A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point P which lies on the centre of the semicircle?

A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to \({{81} \over {100}}\) of the height through which it falls. Find the average speed of the ball. (Take g = 10 ms\(-\)2)

The velocity of a particle is v = v0 + gt + Ft2. Its position is x = 0 at t = 0; then its displacement after time (t = 1) is :

An object is located at 2 km beneath the surface of the water. If the fractional compression \({{\Delta V} \over V}\) is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ____________. [Given : density of wa...

Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01 cm3 of oleic acid per cm3 of the solution. Then you make a thin film of this solution (monomolecular thickness) of area 4 cm2 by consid...

A sphere of mass 2 kg and radius 0.5 m is rolling with an initial speed of 1 ms-1 goes up an inclined plane which makes an angle of 30\(^\circ\) with the horizontal plane, without slipping. How long will the sphere take to return to the sta...

Two particles A and B of equal masses are suspended from two massless springs of spring constants K1 and K2 respectively. If the maximum velocities during oscillations are equal, the ratio of the amplitude of A and B is

A block of mass 1 kg attached to a spring is made to oscillate with an initial amplitude of 12 cm. After 2 minutes the amplitude decreases to 6 cm. Determine the value of the damping constant for this motion . (take ln 2 = 0.693)

A sound wave of frequency 245 Hz travels with the speed of 300 ms\(-\)1 along the positive x-axis. Each point of the wave moves to and from through a total distance of 6 cm. What will be the mathematical expression of this travelling wave?