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## JEE Main 2022 Physics Question Paper and Solutions – June 25th Shift 2

**SECTION – A**

**Multiple Choice Questions: **This section contains 20 multiple choice questions. Each question has 4 choices (1), (2), (3) and (4), out of which **ONLY ONE **is correct.

**Choose the correct answer :**

**1. Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.**

**Assertion A:** Two identical balls *A* and *B* thrown with same velocity β*u*β at two different angles with horizontal attained the same range *R*. If *A* and *B* reached the maximum height *h*_{1} and *h*_{2} respectively, then

** Reason R: **Product of said heights.

** Choose the correct answer :**

(A) Both **A** and **R** are true and **R** is the correct explanation of **A**.

(B) Both **A** and **R** are true but **R** is NOT the correct explanation of **A**.

(C) **A** is true but **R** is false.

(D) **A** is false but **R** is true.

**Answer (A)**

**Sol. **

**2. Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by X_{P}(t) = Ξ±t + Ξ²t^{2} and X_{Q}(t) = ft β t^{2}. At what time, both the buses have same velocity?**

**Answer (D)**

**Sol. ***X _{P}* = Ξ±

*t*+ Ξ²

*t*

^{2}

*X _{Q}* =

*ft*β

*t*

^{2}

β΄ *V _{P}* = Ξ± + 2Ξ²

*t*

*V _{Q}* =

*f*β 2

*t*

β΅ *V _{P}* =

*V*

_{Q}β Ξ± + 2Ξ²*t* = *f* β 2*t*

**3. A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity Ο. The coefficient of static friction between the bottom of the beaker and the surface of the disc is ΞΌ. The beaker will revolve with the disc if :**

**Answer (B)**

**Sol. **To move together

Ο^{2}*R* β€ ΞΌ*g*

**4. A solid metallic cube having total surface area 24 m ^{2} is uniformly heated. If its temperature is increased by 10Β°C, calculate the increase in volume of the cube.**

** (Given Ξ± = 5.0 Γ 10 ^{β4} Β°C^{β1}).**

(A) 2.4 Γ 10^{6} cm^{3}

(B) 1.2 Γ 10^{5} cm^{3}

(C) 6.0 Γ 10^{4} cm^{3}

(D) 4.8 Γ 10^{5} cm^{3}

**Answer (B)**

**Sol. **6 Γ *l*^{2} = 24

β *l* = 2 m

β Ξ*V* = 3 Γ (Ξ±Ξ*T*) Γ *V*

= 3 Γ 5 Γ 10^{β4} Γ 10 Γ (8)

= 120 Γ 10^{β3} m^{3}

= 120 Γ 10^{β3} Γ 10^{6} cm^{3}

= 1.2 Γ 10^{5} cm^{3}

**5. A copper block of mass 5.0 kg is heated to a temperature of 500Β°C and is placed on a large ice block. What is the maximum amount of ice that can melt?**

** [Specific heat of copper : 0.39 J g ^{β1} Β°C^{β1} and latent heat of fusion of water : 335 J g^{β1}]**

(A) 1.5 kg

(B) 5.8 kg

(C) 2.9 kg

(D) 3.8 kg

**Answer (C)**

**Sol. ***mL* = Ξ*Q* = *ms*Ξ*T*

= 2.9 kg

**6. The ratio of specific heats **

**\(\begin{array}{l}\left ( \frac{C_p}{C_v} \right )\end{array} \)**

**in terms of degree of freedom (**

*f*) is given by:**Answer (B)**

**Sol. **

**7. For a particle in uniform circular motion, the acceleration a at any point P(R, ΞΈ) on the circular path of radius R is (when ΞΈ is measured from the positive x-axis and v is uniform speed):**

**Answer (C)**

**Sol. **

As the particle in uniform circular motion experiences only centripetal acceleration of magnitude Ο^{2}R or

**8. Two metallic plates form a parallel plate capacitor. The distance between the plates is β dβ. A metal sheet of thickness d/2 and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor?**

(A) 2 : 1

(B) 1 : 2

(C) 1 : 4

(D) 4 : 1

**Answer (A)**

**Sol. **

If

**9. Two cells of same emf but different internal resistances r_{1} and r_{2} are connected in series with a resistance R. The value of resistance R, for which the potential difference across second cell is zero, is:**

(A) *r*_{2} β *r*_{1}

(B) *r*_{1} β *r*_{2}

(C) *r*_{1}

(D) *r _{2}*

**Answer (A)**

**Sol. **

As per the question,

**10. Given below are two statements:**

Statement-I : Susceptibilities of paramagnetic and ferromagnetic substances increase with decrease in temperature.

Statement-II : Diamagnetism is a result of orbital motions of electrons developing magnetic moments opposite to the applied magnetic field.

** Choose the correct answer from the options given below:-**

(A) Both Statement-I and Statement-II are true

(B) Both Statement-I and Statement-II are false

(C) Statement-I is true but Statement-II is false

(D) Statement-I is false but Statement-II is true

**Answer (A)**

**Sol. **Statement-I is true as susceptibility of ferromagnetic and paramagnetic materials is inversely related to temperature.

Statement-II is true as because of orbital motion of electrons the diamagnetic material is able to oppose external magnetic field.

**11. A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to**

(A) *B*

(B) 2*B*

(C) 4*B*

(D) B/2

**Answer (A)**

**Sol. **B = ΞΌ_{0}*ni*

Now *i* β 2*i*

And

**12. A sinusoidal voltage V(t) = 210 sin 3000 t volt is applied to a series LCR circuit in which L = 10 mH, C = 25 ΞΌF and R = 100 Ξ©. The phase difference (Ξ¦) between the applied voltage and resultant current will be:**

(A) tan^{β1}(0.17)

(B) tan^{β1}(9.46)

(C) tan^{β1}(0.30)

(D) tan^{β1}(13.33)

**Answer (A)**

**Sol. ***X _{L}* = 3000 Γ 10 Γ 10

^{β3}= 30Ξ©

So

So

**13. The electromagnetic waves travel in a medium at a speed of 2.0 Γ 10 ^{8} m/s. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be:**

(A) 2.25

(B) 4.25

(C) 6.25

(D) 8.25

**Answer (A)**

**Sol. **

So

**14. The interference pattern is obtained with two coherent light sources of intensity ratio 4 : 1. And the ratio **

**\(\begin{array}{l}\frac{l_{max}+l_{min}}{l_{max}-l_{min}}\end{array} \)**

**is 5/x. Then, the value of**

*x*will be equal to:(A) 3

(B) 4

(C) 2

(D) 1

**Answer (B)**

**Sol.**

So *x* = 4

**15. A light whose electric field vectors are completely removed by using a good polaroid, allowed to incident on the surface of the prism at Brewsterβs angle. Choose the most suitable option for the phenomenon related to the prism.**

(A) Reflected and refracted rays will be perpendicular to each other.

(B) Wave will propagate along the surface of prism.

(C) No refraction, and there will be total reflection of light.

(D) No reflection, and there will be total transmission of light.

**Answer (D)**

**Sol. **When electric field vector is completely removed and incident on Brewsterβs angle then only refraction takes place.

**16. A proton, a neutron, an electron and an Ξ±-particle have same energy. If Ξ»_{p}, Ξ»_{n}, Ξ»_{e} and Ξ»_{Ξ±} are the de Broglieβs wavelengths of proton, neutron, electron and Ξ± particle respectively, then choose the correct relation from the following:**

(A) Ξ»* _{p}* = Ξ»

*> Ξ»*

_{n}*> Ξ»*

_{e}_{Ξ±}

(B) Ξ»_{Ξ±} < Ξ»* _{n}* < Ξ»

*< Ξ»*

_{p}

_{e}(C) Ξ»* _{e}* < Ξ»

*= Ξ»*

_{p}*> Ξ»*

_{n}_{Ξ±}

(D) Ξ»* _{e}* = Ξ»

*= Ξ»*

_{p}*= Ξ»*

_{n}_{Ξ±}

**Answer (B)**

**Sol. **de Broglie wavelength

Where *K*: kinetic energy

β For some *K*,

Since *m*_{Ξ±} > *m _{n}* >

*m*>

_{p}*m*

_{e}β Ξ»_{Ξ±} < Ξ»* _{n}* < Ξ»

*< Ξ»*

_{p}

_{e}**17. Which of the following figure represents the variation of **

**\(\begin{array}{l}In\left ( \frac{R}{R_0} \right )\end{array} \)**

**with ln**

*A*(if*R*= radius of a nucleus and*A*= its mass number)**Answer (B)**

**Sol. **We know that

*R* = *R*_{0}*A*^{1/3}

β _{}

β Straight line

**18. Identify the logic operation performed by the given circuit:**

(A) AND gate

(B) OR gate

(C) NOR gate

(D) NAND gate

**Answer (A)**

**Sol. **According to the circuit,

*Y* = (*A*β² + *B*β²)β²

β *Y* = *AB*

β AND gate

**19. Match List I with List II **

List I |
List II |
||

A. | Facsimile | I. | Static Document Image |

B. | Guided media Channel | II. | Local Broadcast Radio |

C. | Frequency Modulation | III. | Rectangular wave |

D. | Digital Single | IV. | Optical Fiber |

** Choose the correct answer from the following options:**

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

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

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

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

**Answer (B)**

**Sol. **The correct match is:

Facsimile | β | Static Document Image |

Guided Media Channel | β | Optical Fiber |

Frequency Modulation | β | Local Broadcast Radio |

Digital single | β | Rectangular Wave |

**20. If n represents the actual number of deflections in a converted galvanometer of resistance G and shunt resistance S. Then the total current I when its figure of merit is K will be**

**Answer (D)**

**Sol. **According to the information, current through galvanometer = *nK*

**SECTION – B**

**Numerical Value Type Questions:** This section contains 10 questions. In Section B, attempt any five questions out of 10. The answer to each question is a **NUMERICAL VALUE.** For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to the second decimal place; e.g. 06.25, 07.00, β00.33, β00.30, 30.27, β27.30) using the mouse and the on-screen virtual numeric keypad in the place designated to enter the answer.

**1. For **

**\(\begin{array}{l}z=a^2x^3y^{\frac{1}{2}},\end{array} \)**

**where ‘**

*a*‘ is a constant. If percentage error in measurement of ‘*x*‘ and ‘y’ are 4% and 12%, respectively, then the percentage error for ‘*z*‘ will be _______ %.**Answer (18)**

**Sol. **% error in *z* =

= 12 + 6 = 18%

**2. A curved in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be 30 m/s without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be ______ m/s. **

**Answer (24)**

**Sol. **

β *V*_{2} = 24 m/s

**3. A block of mass 200 g is kept stationary on a smooth inclined plane by applying a minimum horizontal force **

**\(\begin{array}{l}F=\sqrt{x}~N\end{array} \)**

**as shown in figure.**

**The value of x = ______.**

**Answer (12)**

**Sol.**

** **

*F* cos60Β° = *mg* sin60Β°

β΄ *x* = 12

**4. Moment of Inertia (M.I.) of four bodies having same mass ‘ M‘ and radius ‘2R‘ are as follows :**

*I*_{1} = M.I. of solid sphere about its diameter

* I*_{2} = M.I. of solid cylinder about its axis

*I*_{3} = M.I. of solid circular disc about its diameter.

* I*_{4} = M.I. of thin circular ring about its diameter

If 2(*I*_{2} + *I*_{3}) + *I*_{4} = xβ
*I*_{1} then the value of *x* will be *_________.*

**Answer (5)**

**Sol. **

β *x* = 5

**5. Two satellites S_{1} and S_{2} are revolving in circular orbits around a planet with radius R_{1} = 3200 km and R_{2} = 800 km respectively. The ratio of speed of satellite S_{1} to the speed of satellite S_{2} in their respective orbits would be 1/x where x = **

**Answer (2)**

**Sol. **

*x* = 2

**6. When a gas filled in a closed vessel is heated by raising the temperature by 1ΒΊC, its pressure increases by 0.4%. The initial temperature of the gas is _____ K.**

**Answer (250)**

**Sol. ***PV* = *nRT*

So,

β *T* = 250 K

**7. 27 identical drops are charged at 22 V each. They combine to form a bigger drop. The potential of the bigger drop will be ______ V .**

**Answer (198)**

**Sol. **Let the charge on one drop is *q* and its radius is *r*.

So for one drop

For 27 drops merged new charge will be *Q* = 27*q*

and new radius is *R* = 3*r*

So new potential is

**8. The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ______%.**

**Answer (300)**

**Sol. **Volume is constant so on length doubled

Area is halfed so

So percentage increase will be

**9. In a series LCR circuit, the inductance, capacitance and resistance are L = 100 mH, C = 100 ΞΌF and
R = 10 Ξ© respectively. They are connected to an AC source of voltage 220 V and frequency of 50 Hz. The approximate value of current in the circuit will be ______ A.**

**Answer (22)**

**Sol. **

β10 Ξ©

β Current

**10. In an experiment of CE configuration of n–p–n transistor, the transfer characteristics are observed as given in figure.**

**If the input resistance is 200 Ξ© and output resistance is 60 Ξ©, the voltage gain in this experiment will be_________.**

**Answer (15)**

**Sol. **Voltage gain

β Voltage gain = 15

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