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 :
คำตอบ
(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 $$\overrightarrow A $$ ?
คำตอบ
(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?
คำตอบ
(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 :
คำตอบ
(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).
คำตอบ
(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 :
คำตอบ
(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 :
คำตอบ
(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 :

คำตอบ
(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 :

คำตอบ

(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 :
คำตอบ
(B)
B $$\propto$$ r
11
If wattless current flows in the AC circuit, then the circuit is :
คำตอบ
(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)
คำตอบ
(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 :
คำตอบ
(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)
คำตอบ
(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 :
คำตอบ
(D)
2 : 1
16
The photodiode is used to detect the optical signals. These diodes are preferably operated in reverse biased mode because :
คำตอบ
(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)
คำตอบ
(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?
คำตอบ
(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.
คำตอบ
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.
คำตอบ
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)
คำตอบ
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.
คำตอบ
80
23
The equivalent capacitance between points A and B in below shown figure will be __________ $$\mu$$F.

คำตอบ
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.
คำตอบ
450
25
The total current supplied to the circuit as shown in figure by the 5 V battery is ____________ A.

คำตอบ
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.
คำตอบ
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 ___________.
คำตอบ
2