JEE MAIN - Physics (2022 - 25th June Morning Shift)

1
If $$Z = {{{A^2}{B^3}} \over {{C^4}}}$$, then the relative error in Z will be :
Respondre
(C)
$${{2\Delta A} \over A} + {{3\Delta B} \over B} + {{4\Delta C} \over C}$$
2
$$\overrightarrow A $$ is a vector quantity such that $$|\overrightarrow A |$$ = non-zero constant. Which of the following expression is true for $$\overrightarrow A $$ ?
Respondre
(C)
$$\overrightarrow A \times \overrightarrow A = 0$$
3
Which of the following relations is true for two unit vector $$\widehat A$$ and $$\widehat B$$ making an angle $$\theta$$ to each other?
Respondre
(B)
$$|\widehat A - \widehat B| = |\widehat A + \widehat B|\tan {\theta \over 2}$$
4
If force $$\overrightarrow F = 3\widehat i + 4\widehat j - 2\widehat k$$ acts on a particle position vector $$2\widehat i + \widehat j + 2\widehat k$$ then, the torque about the origin will be :
Respondre
(B)
$$ - 10\widehat i + 10\widehat j + 5\widehat k$$
5
The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be : (Given g = acceleration due to gravity at the surface of earth).
Respondre
(D)
g/9
6
The terminal velocity (v_t) of the spherical rain drop depends on the radius (r) of the spherical rain drop as :
Respondre
(C)
r²
7
The relation between root mean square speed (v_rms) and most probable sped (v_p) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :
Respondre
(B)
$${v_{rms}} = \sqrt {{3 \over 2}} {v_p}$$
8
In the figure, a very large plane sheet of positive charge is shown. P₁ and P₂ are two points at distance l and 2l from the charge distribution. If $$\sigma$$ is the surface charge density, then the magnitude of electric fields E₁ and E₂ at P₁ and P₂ respectively are :

Respondre
(C)
$${E_1} = {E_2} = \sigma /2{\varepsilon _0}$$

Match List-I with List-II.

	List - I		List -II
(A)	AC generator	(I)	Detects the presence of current in the circuit
(B)	Galvanometer	(II)	Converts mechanical energy into electrical energy
(C)	Transformer	(III)	Works on the principle of resonance in AC circuit
(D)	Metal detector	(IV)	Changes an alternating voltage for smaller or greater value

Choose the correct answer from the options given below :

Respondre

(A)

(A) - (II), (B) - (I), (C) - (IV), (D) - (III)

10
A long straight wire with a circular cross-section having radius R, is carrying a steady current I. The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance r (r < R) from its centre will be :
Respondre
(B)
B $$\propto$$ r
11
If wattless current flows in the AC circuit, then the circuit is :
Respondre
(B)
Purely Inductive circuit
12
The electric field in an electromagnetic wave is given by E = 56.5 sin $$\omega$$(t $$-$$ x/c) NC^$$-$$1. Find the intensity of the wave if it is propagating along x-axis in the free space.

(Given : $$\varepsilon $$₀ = 8.85 $$\times$$ 10^$$-$$12C²N^$$-$$1m^$$-$$2)
Respondre
(B)
4.24 Wm^$$-$$2
13
The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is $$\pi$$/2 at point P and $$\pi$$ at point Q. Then the difference between the resultant intensities at P and Q will be :
Respondre
(B)
6 I
14
A light wave travelling linearly in a medium of dielectric constant 4, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be :

(Given : relative permeability of medium $$\mu$$_r = 1)
Respondre
(D)
60$$^\circ$$
15
The ratio for the speed of the electron in the 3^rd orbit of He⁺ to the speed of the electron in the 3^rd orbit of hydrogen atom will be :
Respondre
(D)
2 : 1
16
The photodiode is used to detect the optical signals. These diodes are preferably operated in reverse biased mode because :
Respondre
(D)
fractional change in minority carriers produce higher reverse bias current
17
The difference of speed of light in the two media A and B (v_A $$-$$ v_B) is 2.6 $$\times$$ 10⁷ m/s. If the refractive index of medium B is 1.47, then the ratio of refractive index of medium B to medium A is : (Given : speed of light in vacuum c = 3 $$\times$$ 10⁸ ms^$$-$$1)
Respondre
(C)
1.13
18
A teacher in his physics laboratory allotted an experiment to determine the resistance (G) of a galvanometer. Students took the observations for $${1 \over 3}$$ deflection in the galvanometer. Which of the below is true for measuring value of G?
Respondre
(B)
$${1 \over 3}$$ deflection method can be used and in this case the G equals to twice the value of shunt resistances.
19
A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the maximum length of the chain hanging from the table is ___________ m.
Respondre
2
20
A 0.5 kg block moving at a speed of 12 ms^$$-$$1 compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be _______________ Nm^$$-$$1.
Respondre
600
21
The velocity of upper layer of water in a river is 36 kmh^$$-$$1. Shearing stress between horizontal layers of water is 10^$$-$$3 Nm^$$-$$2. Depth of the river is __________ m. (Co-efficient of viscosity of water is 10^$$-$$2 Pa.s)
Respondre
100
22
The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm. The length of the open organ pipe is _____________ cm.
Respondre
80
23
The equivalent capacitance between points A and B in below shown figure will be __________ $$\mu$$F.

Respondre
6
24
A resistor develops 300 J of thermal energy in 15 s, when a current of 2 A is passed through it. If the current increases to 3 A, the energy developed in 10 s is ____________ J.
Respondre
450
25
The total current supplied to the circuit as shown in figure by the 5 V battery is ____________ A.

Respondre
2
26
The current in a coil of self inductance 2.0 H is increasing according to I = 2 sin(t²) A. The amount of energy spent during the period when current changes from 0 to 2 A is ____________ J.
Respondre
4
27
A force on an object of mass 100 g is $$\left( {10\widehat i + 5\widehat j} \right)$$ N. The position of that object at t = 2 s is $$\left( {a\widehat i + b\widehat j} \right)$$ m after starting from rest. The value of $${a \over b}$$ will be ___________.
Respondre
2