JEE MAIN - Physics (2021 - 17th March Evening Shift)

1
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?
উত্তর
(B)
Y(x, t) = 0.03 [ sin 5.1x $$-$$ (1.5 $$\times$$ 10³)t ]
2
Which one of the following will be the output of the given circuit?

উত্তর
(A)
XOR Gate

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)	Phase difference between current and voltage in a pure inductive AC circuit	(ii)	zero
(c)	Phase difference between current and voltage in a pure capacitive AC circuit	(iii)	$${\pi \over 2}$$; current lags voltage
(d)	Phase difference between current and voltage in an LCR series circuit	(iv)	$${\tan ^{ - 1}}\left( {{{{X_C} - {X_L}} \over R}} \right)$$

Choose the most appropriate answer from the options given below :

উত্তর

(A)

(a)-(ii), (b)-(iii), (c)-(i), (d)-(iv)

4
The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in the visible region?
উত্তর
(B)
Balmer series
5
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?

উত্তর
(C)
$${{{\mu _0}I} \over {4\pi r}}(2 + \pi )$$
6
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
উত্তর
(D)
$$v_1^2 - v_2^2 = {{2h} \over m}[{f_1} - {f_2}]$$
7
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 :
উত্তর
(C)
1.2
8
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 is

উত্তর
(B)
$${{{r_1}} \over 2} - {r_2}$$
9
What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved?
উত্তর
(D)
Inductive reactance will be halved and current will be doubled.
10
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 starting point A?

উত্তর
(D)
0.57 s
11
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
উত্তর
(D)
$$\sqrt {{{{K_2}} \over {{K_1}}}} $$
12
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 :
উত্তর
(B)
v₀ + $${g \over 2}$$ + $${F \over 3}$$
13
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)
উত্তর
(A)
2.50 ms^$$-$$1
14
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 across AC.

উত্তর
(B)
4.87 mA
15
Which one is the correct option for the two different thermodynamic processes?

উত্তর
(B)
(c) and (d)
16
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 collides with A. The maximum compression in the spring is

উত্তর
(D)
$$v\sqrt {{m \over {2K}}} $$
17
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 _________. 'P' has the time period of 24 hours.
উত্তর
(A)
3
18
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 water is 1000 kgm^$$-$$3 and g = 9.8 ms^$$-$$2]
উত্তর
(B)
1.44 $$\times$$ 10⁹ Nm^$$-$$2
19
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 considering 100 spherical drops of radius $${\left( {{3 \over {40\pi }}} \right)^{{1 \over 3}}} \times {10^{ - 3}}$$ cm. Then the thickness of oleic acid layer will be x $$\times$$ 10^$$-$$14 m. Where x is ____________.
উত্তর
25
20
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 _____________. (Round off to the Nearest Integer).

[a is an area as shown in the figure]

উত্তর
4
21
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 light inside the surface is $${2 \over 3}$$ times the wavelength in air. The radius of the curved surface is $${x \over {13}}$$ m. The value of 'x' is ___________.
উত্তর
30
22
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 value of x = ____________.
উত্তর
3
23
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 parallel to the Y-Z plane is __________ Nm²C^$$-$$1.
উত্তর
640
24
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 ____________ $$\mu$$C. (Round off to the Nearest Integer)

উত্তর
16
25
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 place is __________ N. (Round off to the Nearest Integer) [Take g = 10 ms^-2 ]

উত্তর
30
26
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 ____________. (Round off to the Nearest Integer) [Take g = 10 ms^$$-$$2 ]
উত্তর
5
27
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 r_n vary with $${n^{{1 \over \alpha }}}$$, where $$\alpha$$ is ____________.
উত্তর
3
28
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 voltage source V(t) = V₀ sin(2$$\pi$$ft). Then the conduction current density becomes 10^x times the displacement current density after time t = $${1 \over {800}}$$s. The value of x is _____________. (Given : $${1 \over {4\pi {\varepsilon _0}}} = 9 \times {10^9}$$ Nm²C^$$-$$2)
উত্তর
6