**JEE Main Session 2 25 ^{th} July 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. In AM modulation, a signal is modulated on a carrier wave such that maximum and minimum amplitudes are found to be 6 V and 2 V, respectively. The modulation index is

(A) 100%

(B) 80%

(C) 60%

(D) 50%

2. The electric current in a circular coil of 2 turns produces a magnetic induction B_{1} at its centre. The coil is unwound and is rewound into a circular coil of 5 turns and the same current produces a magnetic induction B_{2} at its centre. The ratio of B_{2}/B_{1} is

(A) 5/2

(B) 25/4

(C) 5/4

(D) 25/2

3. A drop of liquid of density ρ is floating half immersed in a liquid of density σ and surface tension 7.5 × 10^{–4} N cm^{–1}. The radius of drop in cm will be (g = 10 ms^{–2})

4. Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 ms^{–1 }collide and rebound with the same speed. If the time duration of contact is t = 0.005 s, then what is the force exerted on the ball due to each other?

(A) 100 N

(B) 200 N

(C) 300 N

(D) 400 N

5. For a free body diagram shown in the figure, the four forces are applied in the ‘x’ and ‘y’ directions. What additional force must be applied and at what angle with positive x-axis so that net acceleration of body is zero?

(A) √2 N, 45°

(B) √2 N, 135°

(C)

(D) 2 N, 45°

6. Capacitance of an isolated conducting sphere of radius R_{1} becomes n times when it is enclosed by a concentric conducting sphere of radius R_{2} connected to earth. The ratio of their radii (R_{2}/R_{1}) is:

7. The ratio of wavelengths of proton and deuteron accelerated by potential V_{p} and V_{d} is 1 : √2. Then, the ratio of V_{p} to V_{d} will be:

(A) 1 : 1

(B) √2 : 1

(C) 2 : 1

(D) 4 : 1

8. For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a screen placed at a distance 12 cm form the lens. A glass plate of refractive index 1.5 and thickness 1 cm is introduced between lens and screen such that the glass plate plane faces parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screen?

(A) 0.8 m

(B) 3.2 m

(C) 1.2 m

(D) 5.6 m

9. Light wave traveling in air along x-direction is given by E_{y} = 540 sin π × 10^{4} (x – ct)Vm^{–1}. Then, the peak value of magnetic field of wave will be (Given c = 3 × 10^{8}ms^{–1})

(A) 18 × 10^{–7} T

(B) 54 × 10^{–7} T

(C) 54 × 10^{–8} T

(D) 18 × 10^{–8} T

10. When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on:

(A) Electromagnetic induction

(B) Resonance in ac circuits

(C) Mutual induction in ac circuits

(D) Interference of electromagnetic waves

11. An electron with energy 0.1 keV moves at right angle to the earth’s magnetic field of 1 × 10^{–4}Wbm^{–2}. The frequency of revolution of the electron will be

(Take mass of electron = 9.0 × 10^{–31} kg)

(A) 1.6 × 10^{5} Hz

(B) 5.6 × 10^{5} Hz

(C) 2.8 × 10^{6} Hz

(D) 1.8 × 10^{6} Hz

12. A current of 15 mA flows in the circuit as shown in figure. The value of potential difference between the points A and B will be

(A) 50 V

(B) 75 V

(C) 150 V

(D) 275 V

13. The length of a seconds pendulum at a height h = 2R from earth surface will be

(Given R = Radius of earth and acceleration due to gravity at the surface of earth, g = π^{2}ms^{–2})

(A) 2/9 m

(B) 4/9 m

(C) 8/9 m

(D) 1/9 m

14. Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is √2 times the speed of sound, then the value of n will be

(A) 1

(B) 2

(C) 3

(D) 4

15. Let η_{1} is the efficiency of an engine at T_{1} = 447°C and T_{2} = 147°C while η_{2} is the efficiency at T_{1} = 947°C and T_{2} = 47°C. The ratio η_{1}/ η_{2} will be

(A) 0.41

(B) 0.56

(C) 0.73

(D) 0.70

16. An object is taken to a height above the surface of earth at a distance (5/4)R from the centre of the earth. Where radius of earth, R = 6400 km. The percentage decrease in the weight of the object will be

(A) 36%

(B) 50%

(C) 64%

(D) 25%

17. A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed 10 ms^{–1} gets embedded in it, then loss of kinetic energy will be

(A) 4.9 J

(B) 9.8 J

(C) 14.7 J

(D) 19.6 J

18. A ball is projected from the ground with a speed 15 ms^{–1} at an angle θ with horizontal so that its range and maximum height are equal, then ‘tan θ’ will be equal to

(A) 1/4

(B) 1/2

(C) 2

(D) 4

19. The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 1%, 2% and 3% respectively. The maximum percentage error in the detection of the dissipated heat will be

(A) 2

(B) 4

(C) 6

(D) 8

20. Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength λ. The value of principal quantum number ‘n’ of the excited state will be, (R: Rydberg constant)

**SECTION-B**

21. A particle is moving in a straight line such that its velocity is increasing at 5 ms^{–1} per meter. The acceleration of the particle is _______ms^{–2} at a point where its velocity is 20 ms^{–1}.

22. Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be √x m. The value of x is ________.

23. A block of ice of mass 120 g at temperature 0°C is put in 300 g of water at 25°C. The x g of ice melts as the temperature of the water reaches 0°C. The value of x is _______.

[Use specific heat capacity of water = 4200 Jkg^{–1}K^{–1}, Latent heat of ice = 3.5 ×10^{5}Jkg^{–1}]

24. is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its

(i) Third permitted energy level to the second level and

(ii) The highest permitted energy level to the second permitted level.

The value of x will be ______.

25. In a potentiometer arrangement, a cell of emf 1.20 V gives a balance point at 36 cm length of wire. This cell is now replaced by another cell of emf 1.80 V. The difference in balancing length of potentiometer wire in above conditions will be _______ cm.

26. Two ideal diodes are connected in the network as shown is figure. The equivalent resistance between A and B is ________ Ω.

27. Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the √3 times of amplitude of individual motions. The phase difference between the two motions is _________ (degree).

28. Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18 V. The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric constant 9. The final potential difference across the combination of capacitors will be ________ V.

29. A convex lens of focal length 20 cm is placed in front of a convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm. A point object is placed on principal axis at a distance of 60 cm from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is _________ cm.

30. Magnetic flux (in weber) in a closed circuit of resistance 20 Ω varies with time t(s) as φ = 8t^{2} – 9t + 5. The magnitude of the induced current at t = 0.25 s will be _______ mA.

**CHEMISTRY**

**SECTION-A**

1. Match List I with List II:

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

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

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

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

2. Two solutions A and B are prepared by dissolving 1 g of non-volatile solutes X and Y. respectively in 1 kg of water. The ratio of depression in freezing points for A and B is found to be 1 : 4. The ratio of molar masses of X and Y is :

(A) 1 : 4

(B) 1 : 0.25

(C) 1 : 0.20

(D) 1 : 5

3. are the respective ionization constants for the following reactions (a),(b), and (c).

The relationship between is given as

4. The molar conductivity of a conductivity cell filled with 10 moles of 20 mL NaCl solution is Λ_{m1} and that of 20 moles another identical cell heaving 80 mL NaCl solution is Λ_{m2}, The conductivities exhibited by these two cells are same. The relationship between Λ_{m2} and Λ_{m1} is

(A) Λ_{m2} = 2Λ_{m1}

(B) Λ_{m2} = Λ_{m1}/2

(C) Λ_{m2} = Λ_{m1}

(D) Λ_{m2} = 4Λ_{m1}

5. For micelle formation, which of the following statements are correct?

(A) Micelle formation is an exothermic process.

(B) Micelle formation is an endothermic process.

(C) The entropy change is positive.

(D)The entropy change is negative.

(A) A and D only

(B) A and C only

(C) B and C only

(D) B and D only

6. The first ionization enthalpies of Be, B, N and O follow the order

(A) O < N < B < Be

(B) Be < B < N < O

(C) B < Be < N < O

(D) B < Be < O < N

7. Given below are two statements.

**Statement I:**Pig iron is obtained by heating cast iron with scrap iron.

**Statement II:**Pig iron has a relatively lower carbon content than that of cast iron. 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 not correct.

(C) Statement I is correct but Statement II is not correct

(D) Statement I is not correct but Statement II is correct.

8. High purity (>99.95%) dihydrogen is obtained by

(A) reaction of zinc with aqueous alkali.

(B) electrolysis of acidified water using platinum electrodes.

(C) electrolysis of warm aqueous barium hydroxide solution between nickel electrodes.

(D) reaction of zinc with dilute acid.

9. The correct order of density is

(A) Be > Mg >Ca>Sr

(B) Sr>Ca> Mg > Be

(C) Sr> Be > Mg >Ca

(D) Be >Sr> Mg >Ca

10. The total number of acidic oxides from the : NO, N_{2}O, B_{2}O_{3}, N_{2}O_{5} , CO, SO_{3} , P_{4}O_{10}

(A) 3

(B) 4

(C) 5

(D) 6

11. The correct order of energy of absorption for the following metal complexes is

A: [Ni(en)_{3} ]^{2+}, B: [Ni(NH_{3})_{6} ]^{2+}, C: [Ni(H_{2} O)_{6} ]^{2+}

(A) C < B < A

(B) B < C < A

(C) C < A < B

(D) A < C < B

12. Match List I with List II.

Choose the correct answer from the options given below:

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

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

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

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

13. Major product of the following reaction is

14. What is the major product of the following reaction?

15. Arrange the following in decreasing acidic strength.

(A) A > B > C > D

(B) B > A > C > D

(C) D > C > A > B

(D) D > C > B > A

16.

The correct structure of C is

17. Match List I with List II:

Choose the correct answer from the options given below:

(A) A–III, B-I, C-IV, D-II

(B) A–III, B-IV, C-I, D-II

(C) A–II, B-I, C-IV, D-III

(D) A–II, B-IV, C-I, D-III

18. Glycosidic linkage between C_{1} of a-glucose and C_{2} of b-fructose is found in

(A) maltose

(B) sucrose

(C) lactose

(D) amylose

19. Some drugs bind to a site other than, the active site of an enzyme. This site is known as

(A) non-active site

(B) allosteric site

(C) competitive site

(D) therapeutic site

20. In base vs. Acid titration, at the end point methyl orange is present as

(A) quinonoid form

(B) heterocyclic form

(C) phenolic form

(D) benzenoid form

**SECTION-B**

21. 56.0 L of nitrogen gas is mixed with excess of hydrogen gas and it is found that 20 L of ammonia gas is produced. The volume of unused nitrogen gas is found to be______ L.

22. A sealed flask with a capacity of 2 dm^{3} contains 11 g of propane gas. The flask is so weak that it will burst if the pressure becomes 2 MPa. The minimum temperature at which the flask will burst is _______ °C. [Nearest integer]

(Given: R = 8.3 J K^{–1}mol^{–1}. Atomic masses of C and H are 12u and 1u respectively.) (Assume that propane behaves as an ideal gas.)

23. When the excited electron of a H atom from n = 5 drops to the ground state, the maximum number of emission lines observed are _____

24. While performing a thermodynamics experiment, a student made the following observations,

HCl + NaOH→NaCl + H_{2}O ∆H = –57.3 kJ mol^{–1} CH_{3}COOH + NaOH→ CH_{3}COONa + H_{2}O ∆H = –55.3 kJ mol^{–1}. The enthalpy of ionization of CH3 COOH as calculated by the student is ______ kJ mol^{–1}. (nearest integer)

25. For the decomposition of azomethane. CH_{3}N_{2}CH_{3}(g) → CH_{3}CH_{3}(g) + N_{2}(g) a first order reaction, the variation in partial pressure with time at 600 K is given as

The half life of the reaction is _____ × 10^{–5}s. [Nearest integer]

26. The sum of number of lone pairs of electrons present on the central atoms of XeO_{3}, XeOF_{4} and XeF_{6} is ___________

27. The spin-only magnetic moment value of M^{3+} ion (in gaseous state) from the pairs Cr^{3+}/Cr^{2+}, Mn^{3+}/Mn^{2}, Fe^{3+}/Fe^{2+} and Co^{3+}/Co^{2+} that has negative standard electrode potential, is B.M. [Nearest integer]

28. A sample of 4.5 mg of an unknown monohydric alcohol, R–OH was added to methylmagnesium iodide. A gas is evolved and is collected and its volume measured to be 3.1 mL. The molecular weight of the unknown alcohol is ____ g/mol. [Nearest integer]

29. The separation of two coloured substances was done by paper chromatography. The distances travelled by solvent front, substance A and substance B from the base line are 3.25 cm. 2.08 cm and 1.05 cm. respectively. The ratio of R_{f} values of A to B is ______

30. The total number of monobromo derivatives formed by the alkanes with molecular formula C_{5}H_{12} is (excluding stereo isomers) _____

**MATHEMATICS**

**SECTION-A**

1. z ∈ ℂ if the minimum value of (|z – 3√2| + |z – p√2i|) is 5√2, then a value of p is _________.

(A) 3

(B) 7/2

(C) 4

(D) 9/2

2. The number of real values of λ, such that the system of linear equations

2x – 3y + 5z = 9

x + 3y – z = –18

3x – y + (λ^{2} – | λ |)z = 16

has no solutions, is

(A) 0

(B) 1

(C) 2

(D) 4

3. The number of bijective functions f : {1, 3, 5, 7, …, 99} → {2, 4, 6, 8, ….., 100} such that f(3) ≥ f(9) ≥ f(15) ≥ f(21) ≥ … ≥ f(99) is _________.

(A) ^{50}P_{17}

(B) ^{50}P_{33}

(C) 33! × 17!

(D) 50!/2

4. The remainder when (11)^{1011} + (1011)^{11} is divided by 9 is

(A) 1

(B) 4

(C) 6

(D) 8

5. The sum is equal to

(A) 7/87

(B) 7/29

(C) 14/87

(D) 21/29

6. is equal to

(A) 14

(B) 7

(C) 14√2

(D) 7√2

7. is equal to

(A) 1/2

(B) 1

(C) 2

(D) −2

8. If A and B are two events such that P(A) = 1/3, P(B) = 1/5 and (A ∪ B) = 1/2, then P(A|B’) + P(B|A’|) is equal to

(A) 3/4

(B) 5/8

(C) 5/4

(D) 7/8

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

(A)

(B) 52/e

(C)

(D) 104/e

10. Let the point P(α, β) be at a unit distance from each of the two lines L_{1} : 3x – 4y + 12 = 0 and L_{2} : 8x + 6y + 11 = 0. If P lies below L_{1} and above L_{2}, then 100(α + β) is equal to

(A) −14

(B) 42

(C) −22

(D) 14

11. Let a smooth curve y = f(x) be such that the slope of the tangent at any point (x, y) on it is directly proportional to (-y/x). If the curve passes through the points (1, 2) and (8, 1), then |y(1/8)| is equal to

(A) 2 log_{e}2

(B) 4

(C) 1

(D) 4 log_{e}2

12. If the ellipse meets the line on the x-axis and the line on the y-axis, then the eccentricity of the ellipse is

(A) 5/7

(B) 2√6/7

(C) 3/7

(D) 2√5/7

13. The tangents at the points A(1, 3) and B(1, –1) on the parabola y^{2} – 2x – 2y = 1 meet at the point P. Then the area (in unit2) of the triangle PAB is :

(A) 4

(B) 6

(C) 7

(D) 8

14. Let the foci of the ellipse and the hyperbola coincide. Then the length of the latus rectum of the hyperbola is :

(A) 32/9

(B) 18/5

(C) 27/4

(D) 27/10

15. A plane E is perpendicular to the two planes 2x – 2y + z = 0 and x – y + 2z = 4, and passes through the point P(1, –1, 1). If the distance of the plane E from the point Q(a, a, 2) is 3√2, then (PQ)^{2} is equal to

(A) 9

(B) 12

(C) 21

(D) 33

16. The shortest distance between the lines is

(A) 2√29

(B) 1

(C)

(D) √29/2

17. Let be a vector such that Then the projection of on the vector is :-

18. If the mean deviation about median for the number 3, 5, 7, 2k, 12, 16, 21, 24 arranged in the ascending order, is 6 then the median is

(A) 11.5

(B) 10.5

(C) 12

(D) 11

19. is equal to

(A) 3/16

(B) 1/16

(C) 1/32

(D) 9/32

20. Consider the following statements :

P :Ramu is intelligent.

Q :Ramu is rich.

R :Ramu is not honest.

The negation of the statement “Ramu is intelligent and honest if and only if Ramu is not rich” can be expressed as :

(A) ((P ∧ (~ R)) ∧ Q) ∧ ((~ Q) ∧ ((~ P) ∨ R))

(B) ((P ∧ R) ∧ Q) ∨ ((~ Q) ∧ ((~ P) ∨ (~ R)))

(C) ((P ∧ R) ∧ Q) ∧ ((~ Q) ∧ (( ~ P) ∨ (~ R)))

(D) ((P ∧ (~ R)) ∧ Q) ∨ ((~ Q) ∧ ((~ P) ∧ R))

**SECTION-B**

21. Let A = {1, 2, 3, 4, 5, 6, 7}. Define B = {T ⊆A : either ∉ T or 2 ∈ T} and C = T ⊆ A : T The sum of all the elements of T is prime number}.Then the number of elements in the set B ∪ C is ______.

22. Let f(x) be a quadratic polynomial with leading coefficient 1 such that f(0) = p, p ≠ 0, and f(1) = 1/3 . If the equations f(x) = 0 and fofofo f(x) = 0 have a common real root, then f(–3) is equal to ______.

23. Let If for some n ∈ N, then n + a + b is equal to ________

24. The sum of the maximum and minimum values of the function f(x) = |5x – 7| + [x^{2} + 2x] in the interval [5/4, 2], where [t] is the greatest integer ≤ t, is ______.

25. Let y = y(x) be the solution of the differential equation If for some n ∈ N, y(2) ∈ [n – 1, n), then n is equal to _________.

26. Let f be a twice differentiable function on R. If f’(0) = 4 and then (2a + 1)^{5} a^{2} is equal to _________

27. Let for n ∈ Then the sum of all the elements of the set {n ∈ N : a_{n}∈ (2, 30)} is ______

28. If the circles x^{2} + y^{2} + 6x + 8y + 16 = 0 and x^{2} + y^{2} + 2(3 – √3)x + x + 2(4 – √6)y = k + 6√3 + 8√6, k > 0, touch internally at the point P(α, β), then (α + √3)^{2} + (β + √6)^{2} is equal to _________

29. Let the area enclosed by the x-axis, and the tangent and normal drawn to the curve 4x^{3} – 3xy^{2} + 6x^{2} – 5xy – 8y^{2} + 9x + 14 = 0 at the point (–2, 3) be A. Then 8A is equal to _______.

30. Let x = sin(2tan^{−}^{1}α) and If S = {α∈ R : y^{2} = 1 – x}, then is equal to _______