**JEE Main Session 2 29 ^{th} June 2022 Shift 2**

**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. A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10 m in t s, the distance travelled by the toy in the next t s will be :

(A) 10 m

(B) 20 m

(C) 30 m

(D) 40 m

2. At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm? Both the diameters have been measured at room temperature (27°C).

(Given: coefficient of linear thermal expansion of gold α_{L} = 1.4 × 10^{–5} K^{–1})

(A) 125.7°C

(B) 91.7°C

(C) 425.7°C

(D) 152.7°C

3. Two point charges Q each are placed at a distance d apart. A third point charge q is placed at a distance x from mid-point on the perpendicular bisector. The value of x at which charge q will experience the maximum Coulombs force is :

(A) x = d

(B) x = d/2

(C) x = d/√2

(D) x = d/2√2

4. The speed of light in media ‘A’ and ‘B’ are 2.0 × 10^{10} cm/s and 1.5 × 10^{10} cm/s respectively. A ray of light enters from the medium B to A at an incident angle ‘θ’. If the ray suffers total internal reflection, then

5. In the following nuclear reaction, Mass number of D is 182 and atomic number is 74. Mass number and atomic number of D_{4}, respectively, will be ________.

(A) 174 and 71

(B) 174 and 69

(C) 172 and 69

(D) 172 and 71

6. The electric field at a point associated with a light wave is given by

E = 200[sin(6 × 10^{15})t + sin(9 × 10^{15})t] Vm^{–1}

Given : h = 4.14 × 10^{–15}eVs

If this light falls on a metal surface having a work function of 2.50 eV, the maximum kinetic energy of the photoelectrons will be

(A) 1.90 eV

(B) 3.27 eV

(C) 3.60 eV

(D) 3.42 eV

7. A capacitor is discharging through a resistor R. Consider in time t_{1}, the energy stored in the capacitor reduces to half of its initial value and in time t_{2}, the charge stored reduces to one eighth of its initial value. The ratio t_{1}/t_{2} will be

(A) 1/2

(B) 1/3

(C) 1/4

(D) 1/6

8. Starting with the same initial conditions, an ideal gas expands from volume V_{1} to V_{2} in three different ways. The work done by the gas is W_{1} if the process is purely isothermal, W_{2}, if the process is purely adiabatic and W_{3} if the process is purely isobaric. Then, choose the correct option.

(A) W_{1}< W_{2}< W_{3}

(B) W_{2}< W_{3}< W_{1}

(C) W_{3}< W_{1}< W_{2}

(D) W_{2}< W_{1}< W_{3}

9. Two long current carrying conductors are placed parallel to each other at a distance of 8 cm between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is 30 μT. The equal current flowing in the two conductors is:

(A) 30 A in the same direction

(B) 30 A in the opposite direction

(C) 60 A in the opposite direction

(D) 300 A in the opposite direction

10. The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be

(A) 40 hours

(B) 36 hours

(C) 30 hours

(D) 25 hours

11. The TV transmission tower at a particular station has a height of 125 m. For doubling the coverage of its range, the height of the tower should be increased by

(A) 125 m

(B) 250 m

(C) 375 m

(D) 500 m

12. The motion of a simple pendulum executing S.H.M. is represented by the following equation. y = A sin(πt + φ), where time is measured in second. The length of pendulum is

(A) 97.23 cm

(B) 25.3 cm

(C) 99.4 cm

(D) 406.1 cm

13. A vessel contains 16 g of hydrogen and 128 g of oxygen at standard temperature and pressure. The volume of the vessel in cm^{3} is:

(A) 72 × 10^{5}

(B) 32 × 10^{5}

(C) 27 × 10^{4}

(D) 54 × 10^{4}

14. Given below are two statements:

**Statement I:** The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle.

**Statement II:** The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field.

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

(A) Both statement I and statement II are correct

(B) Both statement I and statement II are incorrect

(C) Statement I is correct but statement II is incorrect

(D) Statement I is incorrect but statement II is correct

15. A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over frictionless pulley as shown below.

The coefficient of kinetic friction between the surface and block is 0.02. The acceleration of block is (Given g = 10 ms^{–2}.)

(A) 1 ms^{−}^{2}

(B) 1/5ms^{−}^{2}

(C) 4/5ms^{−}^{2}

(D) 8/11ms^{−}^{2}

16. In the given figure, the block of mass m is dropped from the point ‘A’. The expression for kinetic energy of block when it reaches point ‘B’ is

(A)

(B)

(C) mg(y – y_{0})

(D) mgy_{0}

17. A block of mass M placed inside a box descends vertically with acceleration ‘a’. The block exerts a force equal to one-fourth of its weight on the floor of the box.

The value of ‘a’ will be

(A) g/4

(B) g/2

(C) 3g/4

(D) g

18. If the electric potential at any point (x, y, z)m in space is given by V = 3x^{2} The electric field at the point (1, 0, 3)m will be

(A) 3 Vm^{–1}, directed along positive x-axis

(B) 3 Vm^{–1}, directed along negative x-axis

(C) 6 Vm^{–1}, directed along positive x-axis

(D) 6 Vm^{–1}, directed along negative x-axis

19. The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of 2 Ω. The value of internal resistance of each cell is

(A) 2 Ω

(B) 4 Ω

(C) 6 Ω

(D) 8 Ω

20. A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?

(A) 25 m

(B) 50 m

(C) 100 m

(D) 200 m

**SECTION-B**

21. The vernier constant of Vernier callipers is 0.1 mm and it has zero error of (–0.05) cm. While measuring diameter of a sphere, the main scale reading is 1.7 cm and coinciding vernier division is 5. The corrected diameter will be ________× 10^{–2}

22. A small spherical ball of radius 0.1 mm and density 104 kg m–3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of h will be ______ m.

(Given g = 10 ms^{–2}, viscosity of water = 1.0 × 10^{–5} N-sm^{–2}).

23. In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms–1. The third resonance is observed when the air column has a length of ______ cm.

24. Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance 2000 Ω is used to measure the potential difference across 500 Ω resistor, the reading of the voltmeter will be _____ V.

25. A potential barrier of 0.4 V exists across a p-n junction. An electron enters the junction from the n-side with a speed of 6.0 × 10^{5}ms^{–1}. The speed with which electrons enters the p side will be the value of x is ________.

(Give mass of electron = 9 × 10^{–31} kg, charge on electron = 1.6 × 10^{–19} C)

26. The displacement current of 4.425 μA is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of 106 Vs^{–1}. The area of each plate of the capacitor is 40 cm^{2}. The distance between each plate of the capacitor x × 10^{–3} The value of x is,

(Permittivity of free space, E_{0} = 8.85 × 10^{–12} C^{2} N^{–1} m^{–2})

27. The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I_{1}. The same rod is bent into a ring and its moment of inertia about a diameter is I_{2}. If then the value of x will be _________.

28. The half life of a radioactive substance is 5 years. After x years, a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The value of x is ________.

29. In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by 5 × 10^{–2} m towards the slits, the change in fringe width is 3 × 10^{–3} If the distance between the slits is 1 mm, then the wavelength of the light will be _______ nm.

30. An inductor of 0.5 mH, a capacitor of 200 μF and a resistor of 2 Ω are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ______ × 10^{2}

**CHEMISTRY**

**SECTION-A**

1. Using the rules for significant figures, the correct answer for the expression will be

(A) 0.005613

(B) 0.00561

(C) 0.0056

(D) 0.006

2. Which of the following is the correct plot for the probability density ψ^{2}(r) as a function of distance ‘r’ of the electron from the nucleus for 2s orbital?

3. Consider the species CH_{4}, NH_{4}^{+} and BH_{4}^{−}.

Choose the correct option with respect to these species.

(A) They are isoelectronic and only two have tetrahedral structures

(B) They are isoelectronic and all have tetrahedral structures.

(C) Only two are isoelectronic and all have tetrahedral structures.

(D) Only two are isoelectronic and only two have tetrahedral structures.

4. 4.0 moles of argon and 5.0 moles of PCl_{5} are introduced into an evacuated flask of 100 litre capacity at 610 K. The system is allowed to equilibrate. At equilibrium, the total pressure of mixture was found to be 6.0 atm. The K_{p} for the reaction is [Given : R = 0.082 L atm K^{–1}mol^{–1}]

(A) 2.25

(B) 6.24

(C) 12.13

(D) 15.24

5. A 42.12% (w, v) solution of NaCl causes precipitation of a certain sol in 10 hours. The coagulating value of NaCl for the sol is

[Given : Molar mass : Na = 23.0 g mol^{–1}; Cl = 35.5 g mol^{–1}]

(A) 36 mmol L^{–1}

(B) 36 mol L^{–1}

(C) 1440 mol L^{–1}

(D) 1440 mmol L^{–1}

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

**Assertion A:** The first ionization enthalpy for oxygen is lower than that of nitrogen.

**Reason R:** The four electrons in 2p orbitals of oxygen experience more electron-electron repulsion.

In the light of the above statements, choose the correct answer from the options given below.

(A) Both A and R are correct and Rj is the correct explanation of A

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

(C) A is correct but R is not correct

(D) A is not correct but R is correct

7. 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-III, B-IV, C-II, D-I

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

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

8. Given below are two statements.

**Statement-I:** In CuSO_{4}.5H_{2}O, Cu-O bonds are present.

**Statement-II:** In CuSO_{4}.5H_{2}O, ligands coordinating with Cu(II) ion are O-and S-based ligands.

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

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

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

(C) Statement-I is correct but Statement-II is incorrect

(D) Statement-I is incorrect but Statement-II is correct.

9. Amongst baking soda, caustic soda and washing soda, carbonate anion is present in

(A) Washing soda only

(B) Washing soda and caustic soda only

(C) Washing soda and baking soda only

(D) Baking soda, caustic soda and washing soda

10. Number of lone pair(s) of electrons on central atom and the shape of BrF_{3} molecule respectively, are

(A) 0, triangular planar

(B) 1, pyramidal

(C) 2, bent T-shape

(D) 1, bent T-shape

11. Aqueous solution of which of the following boron compounds will be strongly basic in nature?

(A) NaBH_{4}

(B) LiBH_{4}

(C) B_{2}H_{6}

(D) Na_{2}B_{4}O_{7}

12. Sulphur dioxide is one of the components of polluted air. SO_{2} is also a major contributor to acid rain. The correct and complete reaction to represent acid rain caused by SO_{2} is

(A) 2SO_{2} + O_{2} → 2SO_{3}

(B) SO_{2} + O_{3} → SO_{3} + O_{2}

(C) SO_{2} + H_{2}O_{2} → H_{2}SO_{4}

(D) 2SO_{2} + O_{2} + 2H_{2}O → 2H_{2}SO_{4}

13. Which of the following carbocations is most stable?

14.

The stable carbocation formed in the above reaction is

15. Two isomers (A) and (B) with Molar mass 184 g/mol and elemental composition C, 52.2%; H, 4.9 % and Br 42.9% gave benzoic acid and p-bromobenzoic acid, respectively on oxidation with KMnO_{4}. Isomer ‘A’ is optically active and gives a pale yellow precipitate when warmed with alcoholic AgNO_{3}. Isomers ‘A’ and ‘B’ are, respectively.

16. In Friedel-Crafts alkylation of aniline, one gets

(A) Alkylated product with ortho and para substitution.

(B) Secondary amine after acidic treatment.

(C) An amide product.

(D) Positively charged nitrogen at benzene ring.

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

**Assertion A:** Dacron is an example of polyester polymer.

**Reason R:** Dacron is made up of ethylene glycol and terephthalic acid monomers.

In the 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 the correct explanation of A.

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

(C) A is correct but R is not correct.

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

18. The structure of protein that is unaffected by heating is

(A) Secondary Structure

(B) Tertiary Structure

(C) Primary Structure

(D) Quaternary Structure

19. The mixture of chloroxylenol and terpineol is an example of

(A) Antiseptic

(B) Pesticide

(C) Disinfectant

(D) Narcotic analgesic

20. A white precipitate was formed when BaCl_{2} was added to water extract of an inorganic salt. Further, a gas ‘X’ with characteristic odour was released when the formed white precipitate was dissolved in dilute HCl. The anion present in the inorganic salt is

(A) I^{−}

(B) SO_{3}^{2}^{−}

(C) S^{2}^{−}

(D) NO_{2}^{−}

**SECTION-B**

21. A box contains 0.90 g of liquid water in equilibrium with water vapour at 27°C. The equilibrium vapour pressure of water at 27°C is 32.0 Torr. When the volume of the box is increased, some of the liquid water evaporates to maintain the equilibrium pressure. If all the liquid water evaporates, then the volume of the box must be ______ litre. [nearest integer]

(Given : R = 0.082 L atm K^{–1}mol^{–1}]

(Ignore the volume of the liquid water and assume water vapours behave as an ideal gas.)

22. 2.2 g of nitrous oxide (N_{2}O) gas is cooled at a constant pressure of 1 atm from 310 K to 270 K causing the compression of the gas from 217.1 mL to 167.75 mL. The change in internal energy of the process, ΔU is ‘–x’ J. The value of ‘x’ is ____. [nearest integer]

(Given : atomic mass of N = 14 g mol^{–1} and of O = 16 g mol^{–1}

Molar heat capacity of N2O is 100 J K^{–1}mol^{–1})

23. Elevation in boiling point for 1.5 molalsolution of glucose in water is 4 K. The depression in freezing point for 4.5 molalsolution of glucose in water is 4 K. The ratio of molal elevation constant to molal depression constant (K_{b}/K_{f}) is _______.

24. The cell potential for the given cell at 298 K

Pt | H_{2} (g, 1 bar) | H+ (aq) || Cu^{2+} (aq) | Cu(s)

is 0.31 V. The pH of the acidic solution is found to be 3, whereas the concentration of Cu^{2+} is 10^{–x} M. The value of x is _________.

(Given: and

25. The equation k = (6.5 × 10^{12}s^{–1})e^{–26000K/T} is followed for the decomposition of compound A. The activation energy for the reaction is ______ kJ mol^{–1}. [nearest integer]

(Given : R = 8.314 J K^{–1}mol^{–1}]

26. Spin only magnetic moment of [MnBr_{6}]^{4–} is ________ B.M. [round off to the closest integer]

27. For the reaction given below:

CoCl_{3}∙ xNH_{3} + AgNO_{3}(aq) →

If two equivalents of AgCl precipitate out, then the value of x will be_______.

28. The number of chiral alcohol(s) with molecular formula C_{4}H_{10}O is ________.

29. In the given reaction,

the number of sp^{2} hybridised carbon(s) in compound ‘X’ is _____.

30. In the given reaction,

The number of π electrons present in the product ‘P’ is_______.

**MATHEMATICS**

**SECTION-A**

1. Let α be a root of the equation 1 + x^{2} + x^{4} = 0. Then the value of α^{1011} + α^{2022} – α^{3033} is equal to

(A) 1

(B) α

(C) 1 + α

(D) 1 + 2α

2. Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z – 1) – arg(z + 1) = π/4 intersect

(A) exactly at one point

(B) exactly at two points

(C) nowhere

(D) at infinitely many points

3. Let . If B = I – ^{5}C_{1}(adjA) + ^{5}C_{2}(adjA)^{2} – …. – ^{5}C_{5}(adjA)^{5}, then the sum of all elements of the matrix B is

(A) –5

(B) –6

(C) –7

(D) –8

4. The sum of the infinite series is equal to

(A) 425/216

(B) 429/216

(C) 288/125

(D) 280/125

5. The value of is equal to

(A) π^{2}/6

(B) π^{2}/3

(C) π^{2}/2

(D) π^{2}

6. Let f : R → R be a function defined by;

Then, which of the following is NOT true?

(A) For n_{1} = 3, n_{2} = 4, there exists α ∈ (3, 5) where f attains local maxima.

(B) For n_{1} = 4, n_{2} = 3, there exists α ∈ (3, 5) where f attains local minima.

(C) For n1 = 3, n2 = 5, there exists α ∈ (3, 5) where f attains local maxima.

(D) For n_{1} = 4, n_{2} = 6, there exists α ∈ (3, 5) where f attains local maxima.

7. Let f be a real valued continuous function on [0, 1] and . Then, which of the following points (x, y) lies on the curve y = f(x)?

(A) (2, 4)

(B) (1, 2)

(C) (4, 17)

(D) (6, 8)

8. If

9. If y = y (x) is the solution of the differential equation and y(0) = 0, then 6(y'(0) + (y(log_{e}√3))^{2}) is equal to:

(A) 2

(B) −2

(C) −4

(D) −1

10. Let P : y^{2} = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P make an angle of π/4 with the line y = 3x + 5 touch the parabola P at A and B. Then the value of a for which A, B and S are collinear is

(A) 8 only

(B) 2 only

(C) 1/4 only

(D) any a > 0

11. Let a triangle ABC be inscribed in the circle x^{2} – √2(x + y) + y^{2} = 0 such that ∠BAC= π/2. If the length of side AB is √2, then the area of the ΔABC is equal to :

12. Let lie on the plane px – qy + z = 5, for some p, q ∈ℝ. The shortest distance of the plane from the origin is :

13. The distance of the origin from the centroid of the triangle whose two sides have the equations x – 2y + 1 = 0 and 2x – y – 1 = 0 and whose orthocenter is (7/3, 7/3) is :

(A) √2

(B) 2

(C) 2√2

(D) 4

14. Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y + 2z = 16. Let T be a plane passing through the point Q and contains the line Then, which of the following points lies on T?

(A) (2, 1, 0)

(B) (1, 2, 1)

(C) (1, 2, 2)

(D) (1, 3, 2)

15. Let A, B, C be three points whose position vectors respectively are

If α is the smallest positive integer for which are non collinear, then the length of the median, in ΔABC, through A is:

(A) √82/2

(B) √62/2

(C) √69/2

(D) √66/2

16. The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to

(A) 5/16

(B) 9/16

(C) 11/16

(D) 13/16

17. The number of values of a ∈ℕ such that the variance of 3, 7, 12, a, 43 – a is a natural number is :

(A) 0

(B) 2

(C) 5

(D) Infinite

18. From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60°. The pole subtends an angle 30° at the top of the tower. Then the height of the tower is :

(A) 15√3

(B) 20√3

(C) 20 + 10√3

(D) 30

19. Negation of the Boolean statement (p ∨ q) ⇒ ((~ r) ∨ p) is equivalent to

(A) p∧ (~ q) ∧ r

(B) (~ p) ∧ (~ q) ∧ r

(C) (~p) ∧ q ∧ r

(D) p∧ q ∧ (~ r)

20. Let n ≥ 5 be an integer. If 9^{n} – 8n – 1 = 64α and 6^{n} – 5n – 1 = 25β, then α – β is equal to

(A) 1 + ^{n}C_{2}(8 – 5) + ^{n}C_{3}(8^{2} – 5^{2}) + … + ^{n}C_{n}(8^{n}^{−}^{1} – 5^{n}^{−}^{1})

(B) 1 + ^{n}C_{2}(8 – 5) + ^{n}C_{4}(8^{2} – 5^{2}) + … + ^{n}C_{n}(8^{n}^{−}^{2} – 5^{n}^{−}^{2})

(C) ^{n}C_{3}(8 – 5) + ^{n}C_{4}(8^{2} – 5^{2})+ … + ^{n}C_{n}(8^{n}^{−}^{2} – 5^{n}^{−}^{2})

(D) ^{n}C_{4}(8 – 5) + ^{n}C_{5}(8^{2} – 5^{2})+ … + ^{n}C_{n}(8^{n}^{−}^{3} – 5^{n}^{−}^{3})

**SECTION-B**

21. Let be a vector such that Then, the value of is equal to _______.

22. Let y = y(x), x > 1, be the solution of the differential equation with then the value of α + β is equal to ________.

23. Let 3, 6, 9, 12, …upto 78 terms and 5, 9, 13, 17, … upto 59 terms be two series. Then, the sum of terms common to both the series is equal to _________.

24. The number of solutions of the equation sin x = cos^{2} x in the interval (0, 10) is _____.

25. For real number a, b (a > b > 0), let

and

Then the value of (a – b)^{2} is equal to _____.

26. Let f and g be twice differentiable even functions on (–2, 2) such that f(1) = 1 and g(1) = 2 Then, the minimum number of solutions of f(x)g′′(x) + f′(x)g′(x) = 0 in (–2, 2) is equal to_____.

27. Let the coefficients of x^{–1} and x^{–3} in the expansion of be m and n respectively. If r is a positive integer such that mn^{2} = ^{15}C_{r}∙ 2^{r} then the value of r is equal to ________.

28. The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to _______.

29. Let where α is a non-zero real number an If (I – M^{2})N = −2I, then the positive integral value of α is ________.

30. Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x)) = 8x^{2} – 2x and g(f(x)) = 4x^{2} + 6x + 1, then the value of f(2) + g(2) is ____________ .