**JEE Main Session 2 26 ^{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. Two projectiles are thrown with same initial velocity making an angle of 45° and 30° with the horizontal, respectively. The ratio of their respective ranges will be

(A) 1 :√2

(B) √2 : 1

(C) 2 :√3

(D) √3 : 2

2. In aVernierCalipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Verniercalipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and 4th Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to 1 mm. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between 30 and 31 divisions of main scale reading and 6th Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be

(A) 3.02 cm

(B) 3.06cm

(C) 3.10cm

(D) 3.20cm

3. A ball of mass 0.15 kg hits the wall with its initial speed of 12 ms^{–1} and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is 100 N, calculate the time duration of the contact of ball with the wall.

(A) 0.018 s

(B) 0.036s

(C) 0.009s

(D) 0.072s

4. A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be

(A) 1 : 1

(B) 2 : 1

(C) 1 : 4

(D) 4 : 1

5. Two uniformly charged spherical conductors, A and B of radii 5 mm and 10 mm are separated by a distance of 2 cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitude of the electric fields at surface of the spheres A and B will be

(A) 1 : 2

(B) 2 : 1

(C) 1 : 1

(D) 1 : 4

6. The oscillating magnetic field in a plane electromagnetic wave is given by By = 5 × 10^{–6} sin1000π (5x – 4 × 10^{8}t)T. The amplitude of electric field will be:

(A) 15 × 10^{2}Vm^{–1}

(B) 5 × 10^{–6}Vm^{–1}

(C) 16 × 10^{12}Vm^{–1}

(D) 4 × 10^{2}Vm^{–1}

7. Light travels in two media M_{1} and M_{2} with speeds 1.5 × 10^{8}ms–1 and 2.0 × 10^{8}ms^{–1}, respectively. The critical angle between them is:

(A) tan^{−}^{1}(3/√7)

(B) tan^{−}^{1}(2/3)

(C) cos^{−}^{1}(3/4)

(D) sin^{−}^{1}(2/3)

8. A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be:

(Take radius of earth = 6400 km and g = 10 ms^{–2})

(A) 800 km

(B) 1600 km

(C) 2133 km

(D) 4800 km

9. The maximum and minimum voltage of an amplitude modulated signal are 60 V and 20 V, respectively. The percentage modulation index will be:

(A) 0.5%

(B) 50%

(C) 2%

(D) 30%

10. A nucleus of mass M at rest splits into two parts having masses The ratio of de Broglie wavelength of two parts will be:

(A) 1 : 2

(B) 2 : 1

(C) 1 : 1

(D) 2 : 3

11. An ice cube of dimensions 60 cm × 50 cm × 20 cm is placed in an insulation box of wall thickness 1 cm. The box keeping the ice cube at 0°C of temperature is brought to a room of temperature 40°C. The rate of melting of ice is approximately.

(Latent heat of fusion of ice is 3.4 × 105 J kg–1 and thermal conducting of insulation wall is 0.05 Wm^{–1}°C^{–1})

(A) 61 × 10^{−}^{3} kgs^{−}^{1}

(B) 61 × 10^{−}^{5} kgs^{−}^{1}

(C) 208 kgs^{−}^{1}

(D) 30 × 10^{−}^{5} kgs^{−}^{1}

12. A gas has n degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be

13. A transverse wave is represented by y = 2sin(ωt – kx) cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be

(A) 4π

(B) 2π

(C) π

(D) 2

14. A battery of 6 V is connected to the circuit as shown below. The current I drawn from the battery is

(A) 1A

(B) 2A

(C)

(D)

15. A source of potential difference V is connected to the combination of two identical capacitors as shown in the figure. When key ‘K’ is closed, the total energy stored across the combination is E_{1}. Now key ‘K’ is opened and dielectric of dielectric constant 5 is introduced between the plates of the capacitors. The total energy stored across the combination is now E_{2}. The ratio E_{1}/E_{2} will be

(A) 1/10

(B) 2/5

(C) 5/13

(D) 5/26

16. Two concentric circular loops of radii r_{1} = 30 cm and r_{2} = 50 cm are placed in X–Y plane as shown in the figure. A current I = 7 A is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately

17. A velocity selector consists of electric field and magnetic field with B = 12 mT. The value of E required for an electron of energy 728 eV moving along the positive x-axis to pass undeflected is

(Given, mass of electron = 9.1 × 10^{–31} kg)

(A) 192 kVm^{−}^{1}

(B) 192 mVm^{−}^{1}

(C) 9600kVm^{−}^{1}

(D) 16kVm^{−}^{1}

18. Two masses M_{1} and M_{2} are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass M_{2} is twice that of M_{1}, the acceleration of the system is a1. When the mass M_{2} is thrice that of M_{1}, the acceleration of the system is a2. The ratio a_{1}/a_{2} will be

(A) 1/3

(B) 2/3

(C) 3/2

(D) 1/2

19. Mass numbers of two nuclei are in the ratio of 4 : 3. Their nuclear densities will be in the ratio of

(A) 4 : 3

(B) (3/4)^{1/3}

(C) 1 : 1

(D) (4/3)^{1/3}

20. The area of cross section of the rope used to lift a load by a crane is 2.5 × 10^{–4} m^{2}. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, The required area of cross section of the rope should be

(take g = 10 ms^{–2})

(A) 6.25 × 10^{–4} m^{2}

(B) 10 × 10^{–4} m^{2}

(C) 1 × 10^{–4} m^{2}

(D) 1.67 × 10^{–4} m^{2}

**SECTION-B**

21. If The magnitude of component of vector will be _________ m.

22. The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be _________m.

Given the length of the rod is 10√3 m.

23. In the given figure, the face AC of the equilateral prism is immersed in a liquid of refractive index ‘n‘. For incident angle 60° at the side AC the refracted light beam just grazes along face AC. The refractive index of the liquid The value of x is _______.

(Given refractive index of glass = 1.5)

24. Two lighter nuclei combine to from a comparatively heavier nucleus by the relation given below:

The binding energies per nucleon for are 1.1 MeV and 7.6 MeV respectively. The energy released in the process is ______ MeV.

25. A uniform heavy rod of mass 20 kg, cross sectional area 0.4 m^{2} and length 20 m is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is x × 10^{–9} The value of x is ________

(Given Young’s modulus Y = 2 × 10^{11} Nm^{–2} andg = 10 ms^{–2})

26. The typical transfer characteristics of a transistor in CE configuration is shown in figure. A load resistor of 2 kΩ is connected in the collector branch of the circuit used. The input resistance of the transistor is 0.50 kΩ. The voltage gain of the transistor is ________.

27. Three point charges of magnitude 5 μC, 0.16μC and 0.3μC are located at the vertices, B, C of a right angled triangle whose sides are AB = 3 cm, BC = 3√2 cm and CA = 3 cm and point A is the right angle corner. Charge at point A, experiences ______N of electrostatic force due to the other two charges.

28. In a coil of resistance 8Ω, the magnetic flux due to an external magnetic field varies with time as . The value of total heat produced in the coil, till the flux becomes zero, will be ______ J.

29. A potentiometer wire of length 300 cm is connected in series with a resistance 780 Ω and a standard cell of emf 4V. A constant current flows through potentiometer wire. The length of the null point for cell of emf20 mV is found to be 60 cm. The resistance of the potentiometer wire is _____ Ω.

30. As per given figures, two springs of spring constants k and 2k are connected to mass m. If the period of oscillation in figure (a)is 3s, then the period of oscillation in figure (b) will be √x s. The value of x is _______

**CHEMISTRY**

**SECTION-A**

1. Hemoglobin contains 0.34% of iron by mass. The number of Fe atoms in 3.3 g of hemoglobin is : (Given : Atomic mass of Fe is 56 u, NA in 6.022 × 10^{23}mol^{–1})

(A) 1.21 × 10^{5}

(B) 12.0 × 10^{16}

(C) 1.21 × 10^{20}

(D) 3.4 × 10^{22}

2. Arrange the following in increasing order of their covalent character.

(A) CaF_{2} (B) CaCl_{2} (C) CaBr_{2} (D) CaI_{2} Choose the correct answer from the options given below.

(A) B < A < C < D

(B) A < B < C < D

(C) A < B < D < C

(D) A < C < B < D

3. Class XII students were asked to prepare one litre of buffer solution of pH 8.26 by their chemistry teacher. The amount of ammonium chloride to be dissolved by the student in 0.2 M ammonia solution to make one litre of the buffer is (Given pK_{b} (NH_{3}) = 4.74; Molar mass of NH_{3} = 17 g mol^{−}^{1}; Molar mass of NH_{4}Cl = 53.5 g mol^{–1})

(A) 53.5 g

(B) 72.3 g

(C) 107.0 g

(D) 126.0 g

4. At 30°C, the half life for the decomposition of AB_{2} is 200 s and is independent of the initial concentration of AB_{2}. The time required for 80% of the AB2 to decompose is (Given: log 2 = 0.30; log 3 = 0.48)

(A) 200 s

(B) 323 s

(C) 467 s

(D) 532 s

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

**Assertion A :** Finest gold is red in colour, as the size of the particles increases, it appears purple then blue and finally gold.

**Assertion R :** The colour of the colloidal solution depends on the wavelength of light scattered by the dispersed particles.

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

(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

6. The metal that has very low melting point and its periodic position is closer to a metalloid is :

(A) Al

(B) Ga

(C) Se

(D) In

7. The metal that is not extracted from its sulphide ore is :

(A) Aluminium

(B) Iron

(C) Lead

(D) Zinc

8. The products obtained from a reaction of hydrogen peroxide and acidified potassium permanganate are

(A) Mn^{4+}, H_{2}O only

(B) Mn^{2+}, H_{2}O only

(C) Mn^{4+}, H_{2}O, O_{2} only

(D) Mn^{2+}, H_{2}O, O_{2} only

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

**Assertion A :**LiF is sparingly soluble in water.

**Reason R :** The ionic radius of Li^{+} ion is smallest among its group members, hence has least hydration enthalpy.

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

(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

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

**Assertion A :** Boric acid is a weak acid

**Reason R :** Boric acid is not able to release H+ ion on its own. It receives OH^{–} ion from water and releases H^{+} ion.

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

11. The metal complex that is diamagnetic is (Atomic number : Fe, 26; Cu, 29)

(A) K_{3}[Cu(CN)_{4}]

(B) K_{2}[Cu(CN)_{4}]

(C) K_{3}[Fe(CN)_{4}]

(D) K_{4}[FeCl_{6}]

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

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

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

13. The correct decreasing order of priority of functional groups in naming an organic compound as per IUPAC system of nomenclature is :

14. Which of the following is not an example of benzenoidcompound ?

15. Hydrolysis of which compound will give carbolic acid ?

(A) Cumene

(B) Benzenediazonium chloride

(C) Benzal chloride

(D) Ethylene glycol ketal

16.

Consider the above reaction and predict the major product.

17. The correct sequential order of the reagents for the given reaction is :

(A) HNO_{2}, Fe/H^{+}, HNO_{2}, KI, H_{2}O/H^{+}

(B) HNO_{2}, KI, Fe/H^{+}, HNO_{2}, H_{2}O/warm

(C) HNO_{2}, KI, HNO_{2}, Fe/H^{+}, H_{2}O/H^{+}

(D) HNO_{2}, Fe/H^{+}, KI, HNO_{2}, H_{2}O/warm

18. Vulcanization of rubber is carried out by heating a mixture of :

(A) isoprene and styrene

(B) neoprene and sulphur

(C) isoprene and sulphur

(D) neoprene and styrene

19. Animal starch is the other name of :

(A) amylose

(B) maltose

(C) glycogen

(D) amylopectin

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

**Assertion A :**Phenolphthalein is a pH dependent indicator, remains colourless in acidic solution and gives pink colour in basic medium

**Reason R :** Phenolphthalein is a weak acid. It doesn’t dissociate in basic medium.

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

(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

**SECTION-B**

21. A 10 g mixture of hydrogen and helium is contained in a vessel of capacity 0.0125 m^{3} at 6 bar and 27°C. The mass of helium in the mixture is _______ g. (nearest integer) Given : R = 8.3 JK^{–1}mol^{–1} (Atomic masses of H and He are 1u and 4u, respectively)

22. Consider an imaginary ion The nucleus contains ‘a’% more neutrons than the number of electrons in the ion. The value of ‘a’ is ______. [nearest integer]

23. For the reaction

H_{2}F_{2}(g) → H_{2}(g) + F_{2}(g)

∆U = –59.6 kJ mol^{–1} at 27°C.

The enthalpy change for the above reaction is (–) ______ kJ mol^{–1} [nearest integer] Given : R = 8.314 JK^{–1}mol^{–1}.

24. The elevation in boiling point for 1 molal solution of non-volatile solute A is 3K. The depression in freezing point for 2 molalsolution of A in the same solvent is 6 K. The ratio of K_{b} and K_{f}e., K_{b}/K_{f} is 1 : X. The value of X is [nearest integer]

25. 20 mL of 0.02 M hypo solution is used for the titration of 10 mL of copper sulphate solution, in the presence of excess of KI using starch as an indicator. The molarity of Cu^{2+} is found to be _____ × 10^{−}^{2} M [nearest integer]

Given : 2Cu2+ + 4I^{−}→ Cu_{2}I_{2} + I_{2}I2 + 2S_{2}O_{3}^{2−}→ 2I^{−} + S_{4}O_{6}^{2−}

26. The number of non-ionisable protons present in the product B obtained from the following reaction is _____. C_{2}H_{5}OH + PCl_{3}→ C_{2}H_{5}Cl + A

A + PCl_{3}→ B

27. The spin-only magnetic moment value of the compound with strongest oxidizing ability among MnF_{4}, MnF_{3} and MnF_{2} is ______ B.M. [nearest integer]

28. Total number of isomers (including stereoisomers) obtained on monochlorination of methylcyclohexane is ________.

29. A 100 mL solution of CH_{3}CH_{2}MgBr on treatment with methanol produces 2.24 mL of a gas at STP. The weight of gas produced is _______ mg. [nearest integer]

30. How many of the following drugs is/are example(s) of broad spectrum antibiotic ?Ofloxacin, Penicillin G, Terpineol, Salvarsan

**MATHEMATICS**

**SECTION-A**

1. The minimum value of the sum of the squares of the roots of x^{2} + (3 – a)x + 1 = 2a is:

(A) 4

(B) 5

(C) 6

(D) 8

2. If z = x + iy satisfies | z | – 2 = 0 and |z – i| – | z + 5i| = 0, then

(A) x + 2y – 4 = 0

(B) x^{2} + y – 4 = 0

(C) x + 2y + 4 = 0

(D) x^{2} – y + 3 = 0

3. Let then the value of A’BA is

(A) 1224

(B) 1042

(C) 540

(D) 539

4. is equal to

(A) 2^{2n} – ^{2n}C_{n}

(B) 2^{2n – 1 }–^{2n – 1}C_{n – 1 }

(C)

(D) 2^{n – 1 } +^{2n – 1}C_{n}

5. Let P and Q be any points on the curves (x – 1)^{2} + (y + 1)^{2} = 1 and y = x^{2}, respectively. The distance between P and Q is minimum for some value of the abscissa of P in the interval

(A) (0, 1/4)

(B) (1/2, 3/4)

(C) (1/4, 1/2)

(D) (3/4, 1)

6. If the maximum value of a, for which the functionf_{a}(x) = tan^{−}^{1}2x – 3ax + 7 is non-decreasing in is equal to

7. Let for some α ∈ ℝ. Then the value of α + β is :

(A) 14/5

(B) 3/25

(C) 5/2

(D) 7/2

8. The value of is

(A) −2√2

(B) 2√2

(C) −4

(D) 4

9. is equal to :-

(A) 10(π + 4)

(B) 10(π + 2)

(C) 20(π – 2)

(D) 20(π + 2)

10. Let the solution curve y = f(x) of the differential equation pass through the origin. Then

11. The acute angle between the pair of tangents drawn to the ellipse 2x^{2} + 3y^{2} = 5 from the point (1, 3) is

12. The equation of a common tangent to the parabolas y = x^{2} and y = –(x – 2)^{2} is

(A) y = 4(x – 2)

(B) y = 4(x – 1)

(C) y = 4(x + 1)

(D) y = 4(x + 2)

13. Let the abscissae of the two points P and Q on a circle be the roots of x^{2} – 4x – 6 = 0 and the ordinates of P and Q be the roots of y^{2} + 2y – 7 = 0. If PQ is a diameter of the circle x^{2} + y^{2} + 2ax + 2by + c = 0, then the value of (a + b – c) is

(A) 12

(B) 13

(C) 14

(D) 16

14. If the line x – 1 = 0 is a directrix of the hyperbola kx^{2} – y^{2} = 6, then the hyperbola passes through the point

(A) (−2√5, 6)

(B) (−√5, 3)

(C) (√5, −2)

(D) (2√5, 3√6)

15. A vector is parallel to the line of intersection of the plane determined by the vectors and the plane determined by the vectors The obtuse angle between is

(A) 3π/4

(B) 2π/3

(C) 4π/5

(D) 5π/6

16. If then a value of is

17. Negation of the Boolean expression p⇔ (q ⇒ p) is

(A) (~ p) ∧q

(B) p∧ (~ q)

(C) (~ p) ∨ (~ q)

(D) (~ p) ∧ (~ q)

18. Let X be a binomially distributed random variable with mean 4 and variance 4/3. Then, 54 P(X ≤ 2) is equal to

(A) 73/27

(B) 146/27

(C) 146/81

(D) 126/81

19. The integral is equal to

20. The area bounded by the curves y = |x^{2} – 1| and y = 1 is

**SECTION-B**

21. Let A = {1, 2, 3, 4, 5, 6, 7} and B = {3, 6, 7, 9}. Then the number of elements in the set {C ⊆ A : C ∩ B ≠ϕ} is ________

22. The largest value of a, for which the perpendicular distance of the plane containing the lines and from the point (2, 1, 4) is √3, is _________.

23. Numbers are to be formed between 1000 and 3000, which are divisible by 4, using the digits 1, 2, 3, 4, 5 and 6 without repetition of digits. Then the total number of such numbers is ______________.

24. If where m and n are co-prime, them m + n is equal to

25. If the sum of solutions of the system of equations 2sin^{2}θ – cos2θ = 0 and 2cos^{2}θ + 3sinθ = 0 in the interval [0, 2π] is kπ, then k is equal to _______.

26. The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If σ is the standard deviation of the data after omitting the two wrong observations from the data, then 38σ^{2} is equal to ___________.

27. The plane passing through the line L :ℓx – y + 3(1 – ℓ) z = 1, x + 2y – z = 2 and perpendicular to the plane 3x + 2y + z = 6 is 3x – 8y + 7z = 4. If θ is the acute angle between the line L and the y-axis, then 415 cos^{2}θ is equal to ________.

28. Suppose y = y(x) be the solution curve to the differential equation such that is finite. If a and bare respectively the x – and y – intercepts of the tangent to the curve at x = 0, then the value of a – 4b is equal to _______.

29. Different A.P.’s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the common differences of all such A.P.’s having at least 3 terms and at most 33 terms is ________.

30. The number of matrices where a, b, c, d ∈ {−1, 0, 1, 2, 3,………..,10}, such that A = A^{−}^{1}, is _______.