**JEE Main Session 1 28 ^{th} June 2022 Shift 1**

**PHYSICS**

**Section-A**

**IMPORTANT INSTRUCTIONS:**

(1) The test is of **3 hours** duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of **Physics**, **Chemistry** and **Mathematics** having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) **Section-A:** This section contains 20 multiple choice questions which have only one correct answer. each question carries **4 marks** for correct answer and **−1** mark for wrong answer.

(ii) **Section-B:** This section contains 10 questions. In Section-B, attempt any **five questions out of 10.** The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and **−1 mark** for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

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

**Assertion A :** Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity.

**Reason R :** Coefficient of viscosity

Choose the correct answer from the options given below.

(A) Both A and R true, and R is 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.

2. A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k^{2}rt^{2}, where k is a constant. The power delivered to the particle by the force acting on it is given as

(A) Zero

(B) mk^{2}r^{2}t^{2}

(C) mk^{2}r^{2}t

(D) mk^{2}rt

3. Motion of a particle in x-y plane is described by a set of following equations and y = 4sin(ωt) m. The path of the particle will be

(A) Circular

(B) Helical

(C) Parabolic

(D) Elliptical

4. Match List-I with List-II

Choose the correct answer from the options given below.

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

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

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

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

5. Two planets A and B of equal mass are having their period of revolutions T_{A} and T_{B} such that T_{A}= 2T_{B}. These planets are revolving in the circular orbits of radii r_{A} and r_{B} Which out of the following would be the correct relationship of their orbits?

6. A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be

(A) 2.8 × 10^{–4} J

(B) 1.5 × 10^{–3} J

(C) 1.9 × 10^{–4} J

(D) 9.4 × 10^{–5} J

7. Given below are two statements

**Statement-I:** When μ amount of an ideal gas undergoes adiabatic change from state (P_{1}, V_{1}, T_{1}) to state (P_{2}, V_{2}, T_{2}), then work done is and R = universal gas constant.

**Statement-II:** In the above case, when work is done on the gas, the temperature of the gas would rise.

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

8. Given below are two statements

**Statement-I:** A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive.

**Statement-II:** An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero.

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

9. The three charges q/2, q and q/2 are placed at the corners A, B and C of a square of side ‘a’ as shown in figure. The magnitude of electric field (E) at the corner D of the square is

10. An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface.

Choose the correct representation of magnetic field (B) as a function of radial distance (r) from the axis of cylinder.

11. A radar sends an electromagnetic signal of electric field (E_{0}) = 2.25 V/m and magnetic field (B_{0}) = 1.5 × 10^{–8} T which strikes a target on line of sight at a distance of 3 km in a medium. After that, a part of signal (echo) reflects back towards the radar with same velocity and by same path. If the signal was transmitted at time t = 0 from radar, then after how much time echo will reach to the radar?

(A) 2.0 × 10^{–5} s

(B) 4.0 × 10^{–5} s

(C) 1.0 × 10^{–5} s

(D) 8.0 × 10^{–5} s

12. The refracting angle of a prism is A and refractive index of the material of the prism is cot (A/2). Then the angle of minimum deviation will be :

(A) 180 – 2A

(B) 90 – A

(C) 180 + 2A

(D) 180 – 3A

13. The aperture of the objective is 24.4 cm. The resolving power of this telescope, if a light of wavelength 2440 Å is used to see the object will be:

(A) 8.1 × 10^{6}

(B) 10.0 × 10^{7}

(C) 8.2 × 10^{5}

(D) 1.0 × 10^{–8}

14. The de Broglie wavelengths for an electron and a photon are λ_{e} and λ_{p}, respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two?

15. The Q-value of a nuclear reaction and kinetic energy of the projectile particle, K_{p} are related as :

(A) Q = K_{p}

(B) (K_{p} + Q) < 0

(C) Q <K_{p}

(D) (K_{p} + Q) > 0

16. In the following circuit, the correct relation between output (Y) and inputs A and B will be:

(A) Y = AB

(B) Y = A + B

(C)

(D)

17. For using a multimeter to identify diode from electrical components, choose the correct statement out of the following about the diode:

(A) It is two terminal device which conducts current in both directions.

(B) It is two terminal device which conducts current in one direction only

(C) It does not conduct current gives an initial deflection which decays to zero.

(D) It is three terminal device which conducts current in one direction only between central terminal and either of the remaining two terminals.

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

Assertion A :n-p-n transistor permits more current than a p-n-p transistor.

Reason R: Electrons have greater mobility as a charge carrier.

Choose the correct answer from the options given below:

(A) Both A and Rare true, and R is 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.

19. Match List-I with List-II.

Choose the correct answer from the options given below :

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

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

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

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

20. The velocity of sound in a gas, in which two wavelengths, 4.08 m and 4.16 m produce 40 beats in 12 s, will be:

(A) 282.8 ms^{–1}

(B) 175.5 ms^{–1}

(C) 353.6 ms^{–1}

(D) 707.2 ms^{–1}

**SECTION-B**

21. A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200 g. The bob is pulled aside until the string is at 60° with vertical, as shown in the figure. After releasing the bob, the maximum velocity attained by the bob will be ___ ms^{–1}. (if g = 10 m/s^{2})

22. A meter bridge setup is shown in the figure. It is used to determine an unknown resistance R using a given resistor of 15 Ω. The galvanometer (G) shows null deflection when tapping key is at 43 cm mark from end A. If the end correction for end A is 2 cm, then the determined value of R will be ___ Ω.

23. Current measured by the ammeter in the reported circuit when no current flows through 10 Ω resistance, will be ___ A.

24. An AC source is connected to an inductance of 100 mH, a capacitance of 100 μF and a resistance of 120 Ω as shown in the figure. The time in which the resistance having a thermal capacity 2 J/°C will get heated by 16°C is _______ s.

25. The position vector of 1 kg object is and its velocity The magnitude of its angular momentum is √x Nm where x is _________.

26. A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then.thetrolly car starts moving with velocity 2 ms^{–1}. The velocity of the running man was ___________ms^{–1}. when he jumps into the car.

27. A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement. as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation.tension in the string is x/5 Mg for x = _________. Neglect mass of the string and friction of the block (bigger mass) with ice slab. (Given g = acceleration due to gravity)

28. The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will be J. (Given R = 8.31 J/mol.K)

29. A sing1y ionized magnesium atom (A24) ion is accelerated to kinetic energy 5 keV and is projected perpendicularly into a magnetic field B of the magnitude 0.5 T. The radius of path formed will be _________ cm.

30. A telegraph line of length loo km has a capacity of 0.01 µF/km and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is ________ mH. (if π = √10)

**CHEMISTRY**

**SECTION-A**

1. The incorrect statement about the imperfections in solids is :

(A) Schottky defect decreases the density of the substance.

(B) Interstitial defect increases the density of the substance.

(C) Frenkel defect does not alter the density of the substance.

(D) Vacancy defect increases the density of the substance.

2. The Zeta potential is related to which property of colloids?

(A) Colour

(B) Tyndall effect

(C) Charge on the surface of colloidal particles

(D) Brownian movement

3. Element “E” belongs to the period 4 and group 16 of the periodic table. The valence shell electron configuration of the element, which is just above “E” in the group is

(A) 3s^{2}, 3p^{4}

(B) 3d^{10}, 4s^{2}, 4p^{4}

(C) 4d^{10}, 5s^{2}, 5p^{4}

(D) 2s^{2}, 2p^{4}

4. Given are two statements one is labelled as Assertion A and other is labelled as Reason R.

Assertion A : Magnesium can reduce Al2O3 at a temperature below 1350°C, while above 1350°C aluminium can reduce MgO.

Reason R : The melting and boiling points of magnesium are lower than those of aluminium.

In light of the above statements, choose the most appropriate answer from the options given below :

(A) Both A and R are correct, and R is correct explanation of A.

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

(C) A is correct R is not correct.

(D) A is not correct, R is correct.

5. Dihydrogen reacts with CuO to give

(A) CuH_{2}

(B) Cu

(C) Cu_{2}O

(D) Cu(OH)_{2}

6. Nitrogen gas is obtained by thermal decomposition of

(A) Ba(NO_{3})_{2}

(B) Ba(N_{3})_{2}

(C) NaNO_{2}

(D) NaNO_{3}

7. Given below are two statements :

**Statement I:** The pentavalent oxide of group-15 element, E_{2}O_{5}, is less acidic than trivalent oxide, E_{2}O_{3}, of the same element.

**Statement II:** The acidic character of trivalent oxide of group 15 elements, E_{2}O_{3}, decreases down the group.

In light of the above statements, choose most appropriate 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 true, but Statement II is false

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

8. Which one of the lanthanoids given below is the most stable in divalent form?

(A) Ce (Atomic Number 58)

(B) Sm (Atomic Number 62 )

(C) Eu (Atomic Number 63)

(D) Yb (Atomic Number 70)

9. Given below are two statements:

**Statement I:** [Ni(CN)_{4}]^{2–} is square planar and diamagnetic complex, with dsp^{2} hybridization for Ni but [Ni(CO)_{4}] is tetrahedral, paramagnetic and with sp^{3}-hybridization for Ni.

**Statement II:** [NiCl4]^{2–} and [Ni(CO)_{4}] both have same d-electron configuration, have same geometry and are paramagnetic.

In light of the above statements, 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 correct but Statement II is false

(D) Statement I is incorrect but Statement II is true

10. Which amongst the following is not a pesticide?

(A) DDT

(B) Organophosphates

(C) Dieldrin

(D) Sodium arsenite

11. Which one of the following techniques is not used to spot components of a mixture separated on thin layer chromatographic plate?

(A) I2 (Solid)

(B) U.V. Light

(C) Visualisation agent as a component of mobile phase

(D) Spraying of an appropriate reagent

12. Which of the following structures are aromatic in nature?

(A) A, B, C and D

(B) Only A and B

(C) Only A and C

(D) Only B, C and D

13. The major product (P) in the reaction

14. The correct structure of product ‘A’ formed in the following reaction.

15. Which one of the following compounds is inactive towards S_{N}1 reaction?

16. Identify the major product formed in the following sequence of reactions:

17. A primary aliphatic amine on reaction with nitrous acid in cold (273 K) and there after raising temperature of reaction mixture to room temperature (298 K), gives

(A) nitrile

(B) alcohol

(C) diazonium salt

(D) secondary amine

18. Which one of the following is NOT a copolymer?

(A) Buna-S

(B) Neoprene

(C) PHBV

(D) Butadiene-styrene

19. Stability of α-Helix structure of proteins depends upon

(A) dipolar interaction

(B) H-bonding interaction

(C) van der Walls forces

(D) π-stacking interaction

20. The formula of the purple colour formed in Laissaigne’s test for sulphur using sodium nitroprusside is

(A) NaFe[Fe(CN)_{6}]

(B) Na[Cr(NH3)_{2}(NCS)_{4}]

(C) Na_{2}[Fe(CN)_{5}(NO)]

(D) Na_{4}[Fe(CN)_{5}(NOS)]

**SECTION-B**

21. A 2.0 g sample containing MnO_{2} is treated with HCl liberating Cl_{2}. The Cl_{2} gas is passed into a solution of KI and 60.0 mL of 0.1 M Na_{2}S_{2}O_{3} is required to titrate the liberated iodine. The percentage of MnO_{2} in the sample is ______. (Nearest integer)

[Atomic masses (in u) Mn = 55; Cl = 35.5; O = 16, I = 127, Na = 23, K = 39, S = 32]

22. lf the work function of a metal is 6.63 × 10^{–19} J, the maximum wavelength of the photon required to remove a photoelectron from the metal is ______ nm. (Nearest integer)

[Given : h = 6.63 × 10^{–34} J s, and c = 3 × 10^{8} m s^{–1}]

23. The hybridization of P exhibited in PF_{5} is sp_{x}d_{y}. The value of y is _______

24. 4.0 L of an ideal gas is allowed to expand isothermally into vacuum until the total volume is 20 L. The amount of heat absorbed in this expansion is _______ L atm.

25. The vapour pressures of two volatile liquids A and B at 25°C are 50 Torr and 100 Torr, respectively. If the liquid mixture, contains 0.3 mole fraction of A, then the mole fraction of liquid B in the vapour phase is x/17. The value of x is __________.

26. The solubility product of a sparingly soluble salt A_{2}X_{3} is 1.1 × 10^{–23}. If the specific conductance of the solution is 3 × 10^{–5} S m^{–1}, the limiting molar conductivity of the solution is x × 10^{–3} S m^{2}mol^{–1}. The value of x is _______.

27. The quantity of electricity of Faraday needed to reduce 1 mol of Cr_{2}O_{7}^{2}^{−} to Cr^{3+} is _________.

28. For a first order reaction A → B, the rate constant, k = 5.5 × 10^{–14} s^{–1}. The time required for 67% completion of reaction is x × 10^{–1} times the half life of reaction. The value of x is _____ (Nearest integer)

(Given : log 3 = 0.4771)

29. Number of complexes which will exhibit synergic bonding amongst, [Cr(CO)_{6}], [Mn(CO)_{5}] and [Mn_{2}(CO)_{10}] is ________.

30. In the estimation of bromine, 0.5 g of an organic compound gave 0.40 g of silver bromide. The percentage of bromine in the given compound is _________% (nearest integer)

(Relative atomic masses of Ag and Br are 108u and 80u, respectively).

**MATHEMATICS**

**SECTION-A**

1. If where α ∈ R, then the value of 16α is equal to

(A) 1411

(B) 1320

(C) 1615

(D) 1855

2. Let a function f : ℕ →ℕ be defined by

then, f is

(A) One-one but not onto

(B) Onto but not one-one

(C) Neither one-one nor onto

(D) One-one and onto

3. If the system of linear equations

2x + 3y – z = –2

x + y + z = 4

x – y + |λ|z = 4λ – 4

where λ∈ R, has no solution, then

(A) λ = 7

(B) λ = –7

(C) λ = 8

(D) λ^{2} = 1

4. Let A be a matrix of order 3 × 3 and det (A) = 2. Then det (det (A) adj (5 adj (A^{3}))) is equal to ______.

(A) 512 × 10^{6}

(B) 256 × 10^{6}

(C) 1024 × 10^{6}

(D) 256 × 10^{11}

5. The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is

(A) 36

(B) 48

(C) 60

(D) 72

6. Let A_{1}, A_{2}, A_{3}, … be an increasing geometric progression of positive real numbers. If A_{1}A_{3}A_{5}A_{7} = 1/1296 and A_{2} + A_{4} = 7/36 then, the value of A_{6} + A_{8} + A_{10} is equal to

(A) 33

(B) 37

(C) 43

(D) 47

7. Let [t] denote the greatest integer less than or equal to t. Then, the value of the integral is equal to

8. Let f : ℝ→ℝ be defined as

Where a, b, c ∈ ℝ and [t] denotes greatest integer less than or equal to t. Then, which of the following statements is true?

(A) There exists a, b, c ∈**ℝ** such that f iscontinuous on ∈**ℝ** .

(B) If f is discontinuous at exactly one point, then a + b + c = 1

(C) If f is discontinuous at exactly one point, then a + b + c ≠ 1

(D) f is discontinuous at atleast two points, for any values of a, b and c

9. The area of the region S = {(x, y) : y^{2}≤ 8x, y ≥ √2x, x ≥ 1} is

(A) 13√2/6

(B) 11√2/6

(C) 5√2/6

(D) 19√2/6

10. Let the solution curve y = y(x) of the differential equation pass through the points (1, 0) and (2α, α), α > 0. Then α is equal to

11. Let y = y(x) be the solution of the differential equation x > 1, with y(2) = − Then y (3) is equal to

(A) −18

(B) −12

(C) −6

(D) −3

12. The number of real solutions of x^{7} + 5x^{3} + 3x + 1 = 0 is equal to ______.

(A) 0

(B) 1

(C) 3

(D) 5

13. Let the eccentricity of the hyperbola and length of its latus rectum be 6√2, If y = 2x + c is a tangent to the hyperbola H. then the value of c^{2} is equal to

(A) 18

(B) 20

(C) 24

(D) 32

14. If the tangents drawn at the points O(0, 0) and P(1 + √5, 2) on the circle x^{2} + y^{2} – 2x – 4y = 0 intersect at the point Q, then the area of the triangle OPQ is equal to

15. If two distinct points Q, R lie on the line of intersection of the planes –x + 2y – z = 0 and 3x – 5y + 2z = 0 and PQ = PR = √18 where the point P is (1, –2, 3), then the area of the triangle PQR is equal to

16. The acute angle between the planes P_{1} and P_{2}, when P_{1} and P_{2} are the planes passing through the intersection of the planes 5x + 8y + 13z – 29 = 0 and 8x – 7y + z – 20 = 0 and the points (2, 1, 3) and (0, 1, 2), respectively, is

(A) π/3

(B) π/4

(C) π/6

(D) π/12

17. Let the plane contain the line of intersection of two planes and If the plane P passes through the point (2, 3, 1/2), then the value of is equal to

(A) 90

(B) 93

(C) 95

(D) 97

18. The probability, that in a randomly selected 3-digit number at least two digits are odd, is

(A) 19/36

(B) 15/36

(C) 13/36

(D) 23/36

19. Let AB and PQ be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q, which are feet of these two poles. Let π/8 and θ be the angles of elevation from C to P and A, respectively. If the height of pole PQ is twice the height of pole AB, then tan^{2}θ is equal to

20. Let p, q, r be three logical statements. Consider the compound statements

S_{1} : ((~p) ∨q) ∨ ((~p) ∨r) and

S_{2} :p→ (q∨r)

Then, which of the following is NOT true?

(A) If S_{2} is True, then S_{1} is True

(B) If S_{2}is False, then S_{1} is False

(C) If S_{2} is False, then S_{1} is True

(D) If S_{1} is False, then S_{2} is False

**SECTION-B**

21. Let R_{1} and R_{2} be relations on the set {1, 2, ….., 50} such that R_{1} ={(p, p^{n}) :p is a prime and n ≥ 0 is an integer} and R_{2} = {(p, p^{n}) : p is a prime and n = 0 or 1}. Then, the number of elements in R_{1} – R_{2} is ______.

22. The number of real solutions of the equation e^{4x} + 4e^{3x} – 58e^{2x} + 4e^{x} + 1 = 0 is _____.

23. The mean and standard deviation of 15 observations are found to be 8 and 3, respectively. On rechecking, it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to _______.

24. If and are coplanar vectors and then 122 (c_{1} + c_{2} + c_{3}) is equal to _________.

25. A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2 : 1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be (α, β). Then, the value of 7α + 3β is equal to ___________.

26. Let l be a line which is normal to the curve y = 2x^{2} + x + 2 at a point P on the curve. If the point Q(6, 4) lies on the line l and O is origin, then the area of the triangle OPQ is equal to ___________.

27. Let A = {1, a_{1}, a_{2}…a_{18}, 77} be a set of integers with 1 <a_{1}< a_{2}<….< a_{18}< 77. Let the set A + A = {x + y :x, y ∈ A} contain exactly 39 elements. Then, the value of a_{1} + a_{2} +…+ a_{18} is equal to _____.

28. The number of positive integers k such that the constant term in the binomial expansion of is 2^{8}. ℓ, where ℓ is an odd integer, is ____________.

29. The number of elements in the set {z = a + ib∈ ℂ: a, b ∈ ℤ and 1 < |z – 3 + 2i| < 4} is _________.

30. Let the lines y + 2x = √11 + 7√7 and 2y + x = 2√11 + 6√7 be normal to a circle C: (x – h)^{2} + (y – k)^{2} = r^{2}. If the line is tangent to the circle C, then the value of (5h – 8k)^{2} + 5r^{2} is equal to ________.