JEE MAIN - Physics (2021 - 26th February Morning Shift)

1
Consider the combination of 2 capacitors C₁ and C₂ with C₂ > C₁, when connected in parallel, the equivalent capacitance is $${{15} \over 4}$$ times the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, $${{{C_2}} \over {{C_1}}}$$.
پاسخ دهید
(B)
No Solutions
2
An alternating current is given by the equation i = i₁ sin $$\omega$$t + i₂ cos $$\omega$$t. The rms current will be :
پاسخ دهید
(A)
$${1 \over {\sqrt 2 }}{\left( {i_1^2 + i_2^2} \right)^{{1 \over 2}}}$$
3
Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a square of side 'b'. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :
پاسخ دهید
(D)
$${8 \over 5}m{a^2} + 2m{b^2}$$
4
A large number of water drops, each of radius r, combine to have a drop of radius R. If the surface tension is T and mechanical equivalent of heat is J, the rise in heat energy per unit volume will be :
پاسخ دهید
(B)
$${{3T} \over J}\left( {{1 \over r} - {1 \over R}} \right)$$
5
LED is constructed from Ga-As-P semiconducting material. The energy gap of this LED is 1.9 eV. Calculate the wavelength of light emitted and its colour.

[h = 6.63 $$\times$$ 10^$$-$$34 Js and c = 3 $$\times$$ 10⁸ ms^$$-$$1]
پاسخ دهید
(B)
654 nm and red colour
6
A short straight object of height 100 cm lies before the central axis of a spherical mirror whose focal length has absolute value | f | = 40 cm. The image of object produced by the mirror is of height 25 cm and has the same orientation of the object. One may conclude from the information :
پاسخ دهید
(B)
Image is virtual, opposite side of convex mirror.
7
In a Young's double slit experiment two slits are separated by 2 mm and the screen is placed one meter away. When a light of wavelength 500 nm is used, the fringe separation will be :
پاسخ دهید
(B)
0.25 mm
8
Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (R/2) from the earth's centre, where 'R' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period :
پاسخ دهید
(A)
$$2\pi \sqrt {{R \over g}} $$
9
In a typical combustion engine the workdone by a gas molecule is given by $$W = {\alpha ^2}\beta {e^{{{ - \beta {x^2}} \over {kT}}}}$$, where x is the displacement, k is the Boltzmann constant and T is the temperature. If $$\alpha$$ and $$\beta$$ are constants, dimensions of $$\alpha$$ will be :
پاسخ دهید
(A)
$$[{M^0}L{T^0}]$$
10
If two similar springs each of spring constant K₁ are joined in series, the new spring constant and time period would be changed by a factor :
پاسخ دهید
(C)
$${1 \over 2},\sqrt 2 $$
11
A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R³. Its time period of revolution will be given by :
پاسخ دهید
(D)
$$T \propto {R^2}$$
12
The temperature $$\theta$$ at the junction of two insulating sheets, having thermal resistances R₁ and R₂ as well as top and bottom temperatures $$\theta$$₁ and $$\theta$$₂ (as shown in figure) is given by :

پاسخ دهید
(A)
$${{{\theta _1}{R_2} + {\theta _2}{R_1}} \over {{R_1} + {R_2}}}$$
13
Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is a = $${{\sqrt 3 } \over 2}L$$.

پاسخ دهید
(C)
$${Q \over {2\sqrt 3 \pi {\varepsilon _0}{L^2}}}$$
14
A planet revolving in elliptical orbit has :

A. a constant velocity of revolution.

B. has the least velocity when it is nearest to the sun.

C. its areal velocity is directly proportional to its velocity.

D. areal velocity is inversely proportional to its velocity.

E. to follow a trajectory such that the areal velocity is constant.

Choose the correct answer from the options given below :
پاسخ دهید
(B)
E only
15
Given below are two statements : one is labeled as Assertion A and the other is labelled as Reason R.

Assertion A : An electron microscope can achieve better resolving power than an optical microscope.

Reason R : The de Broglie's wavelength of the electrons emitted from an electron gun is much less than wavelength of visible light.

In the light of the above statements, choose the correct answer from the options given below :
پاسخ دهید
(C)
Both A and R are true and R is the correct explanation of A.
16
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : Body 'P' having mass M moving with speed 'u' has head-on collision elastically with another body 'Q' having mass 'm' initially at rest. If m << M, body 'Q' will have a maximum speed equal to '2u' after collision.

Reason R : During elastic collision, the momentum and kinetic energy are both conserved.

In the light of the above statements, choose the most appropriate answer from the options given below :
پاسخ دهید
(C)
Both A and R are correct and R is the correct explanation of A.
17
The normal density of a material is $$\rho$$ and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be :
پاسخ دهید
(C)
$${{\rho P} \over K}$$
18
If $$\lambda$$₁ and $$\lambda$$₂ are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of $$\lambda$$₁ : $$\lambda$$₂ is :
پاسخ دهید
(A)
7 : 135
19
Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If $$\sqrt 8 $$R is the distance between the centres of a ring (of mass 'm') and a sphere (mass 'M') where both have equal radius 'R'.

پاسخ دهید
(C)
$${{\sqrt 8 } \over {27}}.{{GmM} \over {{R^2}}}$$
20
Five equal resistances are connected in a network as shown in figure. The net resistance between the points A and B is :

پاسخ دهید
(D)
R
21
A person standing on a spring balance inside a stationary lift measures 60 kg. The weight of that person if the lift descends with uniform downward acceleration of 1.8 m/s² will be ______________ N. [g = 10 m/s²]
پاسخ دهید
492
22
The circuit contains two diodes each with a forward resistance of 50$$\Omega$$ and with infinite reverse resistance. If the battery voltage is 6V, the current through the 120$$\Omega$$ resistance is ____________ mA.

پاسخ دهید
20
23
In a series LCR resonant circuit, the quality factor is measured as 100. If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be __________.
پاسخ دهید
283
24
The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form y = $$-$$ 0.21 sin (x + 30t) is produced in it, where x is in meter and t is in second. Then, the expected value of tension in the wire is x $$\times$$ 10^$$-$$2 N. Value of x is _________. (Round off to the nearest integer)
پاسخ دهید
1215
25
In an electrical circuit, a battery is connected to pass 20C of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at 15V. The workdone by the battery is __________J.
پاسخ دهید
300
26
A boy pushes a box of mass 2 kg with a force $$\overrightarrow F = \left( {20\widehat i + 10\widehat j} \right)N$$ on a frictionless surface. If the box was initially at rest, then ___________ m is displacement along the x-axis after 10s.
پاسخ دهید
500
27
A radiation is emitted by 1000W bulb and it generates an electric field and magnetic field at P, placed at a distance of 2m. The efficiency of the bulb is 1.25%. The value of peak electric field at P is x $$\times$$ 10^$$-$$1 V/m. Value of x is ___________. (Rounded off to the nearest integer) [Take $${\varepsilon _0} = 8.85 \times {10^{ - 12}}$$ C²N^$$-$$1 m^$$-$$2, c = $$3 \times {10^8}$$ ms^$$-$$1]
پاسخ دهید
137
28
A container is divided into two chambers by a partition. The volume of first chamber is 4.5 litre and second chamber is 5.5 litre. The first chamber contain 3.0 moles of gas at pressure 2.0 atm and second chamber contain 4.0 moles of gas at pressure 3.0 atm. After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is x $$\times$$ 10^$$-$$1 atm. Value of x is ________.
پاسخ دهید
25
29
As shown in the figure, a block of mass $$\sqrt 3 $$ kg is kept on a horizontal rough surface of coefficient of friction $${1 \over {3\sqrt 3 }}$$. The critical force to be applied on the vertical surface as shown at an angle 60$$^\circ$$ with horizontal such that it does not move, will be 3x. The value of x will be _________.

[g = 10 m/s²; sin60$$^\circ$$ = $${{\sqrt 3 } \over 2}$$; cos60$$^\circ$$ = $${1 \over 2}$$]

پاسخ دهید
3.33