JEE Main Session 2 25th 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. 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 ’u’ at two different angles with horizontal attained the same range R. If A and B reached the maximum height h1 and h2 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.
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 XP(t) = αt + βt2 and XQ(t) = ft – t2. At what time, both the buses have same velocity?
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 ω. The coefficient of static friction between the bottom of the beaker and the surface of the disc is μ. The beaker will revolve with the disc if :
4. A solid metallic cube having total surface area 24 m2 is uniformly heated. If its temperature is increased by 10°C, calculate the increase in volume of the cube.
(Given α = 5.0 × 10–4 °C–1).
(A) 2.4 × 106 cm3
(B) 1.2 × 105 cm3
(C) 6.0 × 104 cm3
(D) 4.8 × 105 cm3
5. A copper block of mass 5.0 kg is heated to a temperature of 500°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–1 °C–1 and latent heat of fusion of water : 335 J g–1]
(A) 1.5 kg
(B) 5.8 kg
(C) 2.9 kg
(D) 3.8 kg
6. The ratio of specific heats (CP/CV) in terms of degree of freedom (f) is given by:
7. For a particle in uniform circular motion, the acceleration a at any point P(R, θ) on the circular path of radius R is (when θ is measured from the positive x-axis and v is uniform speed):
8. Two metallic plates form a parallel plate capacitor. The distance between the plates is ‘d’. 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
9. Two cells of same emf but different internal resistances r1 and r2 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) r2 – r1
(B) r1 – r2
(C) r1
(D) r2
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
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) 2B
(C) 4B
(D) B/2
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 μF and R = 100 Ω. The phase difference (Φ) between the applied voltage and resultant current will be:
(A) tan−1 (0.17)
(B) tan−1 (9.46)
(C) tan−1 (0.30)
(D) tan−1 (13.33)
13. The electromagnetic waves travel in a medium at a speed of 2.0 × 108 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
14. The interference pattern is obtained with two coherent light sources of intensity ratio 4 : 1. And the ratio Then, the value of x will be equal to :
(A) 3
(B) 4
(C) 2
(D) 1
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 Brewster’s 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.
16. A proton, a neutron, an electron and an α-particle have same energy. If λp, λn, λe and λα are the de Broglie’s wavelengths of proton, neutron, electron and α particle respectively, then choose the correct relation from the following:
(A) λp = λn>λe> λα
(B) λα<λn<λp<λe
(C) λe<λp = λn> λα
(D) λe = λp = λn = λα
17. Which of the following figure represents the variation of with ln A (if R = radius of a nucleus and A = its mass number)
18. Identify the logic operation performed by the given circuit:
(A) AND gate
(B) ORgate
(C) NORgate
(D) NANDgate
19. Match List I with List II
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
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
SECTION-B
21. For z = a2x3y1/2, 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 _______ %.
22. 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.
23. A block of mass 200 g is kept stationary on a smooth inclined plane by applying a minimum horizontal force F = √xN as shown in figure. The value of x = _________.
24. Moment of Inertia (M.I.) of four bodies having same mass ‘M‘ and radius ‘2R‘ are as follows :
I1 = M.I. of solid sphere about its diameter
I2 = M.I. of solid cylinder about its axis
I3 = M.I. of solid circular disc about its diameter.
I4 = M.I. of thin circular ring about its diameter
If 2(I2 + I3) + I4 = x⋅ I1 then the value of x will be _________.
25. Two satellites S1 and S2 are revolving in circular orbits around a planet with radius R1 = 3200 km and R2 = 800 km respectively. The ratio of speed of satellite S1 to the speed of satellite S2 in their respective orbits would be 1/x where x =
26. When a gas filled in a closed vessel is heated by raising the temperature by 1ºC, its pressure increases by 0.4%. The initial temperature of the gas is _____ K.
27. 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.
28. 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 ______%.
29. In a series LCR circuit, the inductance, capacitance and resistance are L = 100 mH, C = 100 μF and R = 10 Ω 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.
30. 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 Ω and output resistance is 60 Ω, the voltage gain in this experiment will be_________.
CHEMISTRY
SECTION-A
1. The minimum energy that must be possessed by photons in order to produce the photoelectric effect with platinum metal is
[Given The threshold frequency of platinum is 1.3 × 1015 s–1 and h = 6.6 × 10–34Js.]
(A) 3.21 × 10–14 J
(B) 6.24 × 10–16 J
(C) 8.58 × 10–19 J
(D) 9.76 × 10–20 J
2. At 25°C and 1 atm pressure, the enthalpy of combustion of benzene (I) and acetylene (g) are –3268 kJ mol–1 and –1300 kJ mol–1, respectively. The change in enthalpy for the reaction 3C2H2(g) → C6H6(I), is
(A) +324 kJ mol–1
(B) +632 kJ mol–1
(C) –632 kJ mol–1
(D) –732 kJ mo1–1
3. Solute A associates in water. When 0.7 g of solute A is dissolved in 42.0 gof water, it depresses the freezing point by 0.2°C. The percentage association of solute A in water is :
[Given : Molar mass of A = 93 g mol–1. Molal depression constant of water is 1.86 K kg mol–1.]
(A) 50%
(B) 60%
(C) 70%
(D) 80%
4. The Ksp for bismuth sulphide (Bi2S3) is 1.08 × 10–73. The solubility of Bi2S3 in mol L–1 at 298 K is
(A) 1.0 × 10–15
(B) 2.7 × 10–12
(C) 3.2 × 10–10
(D) 4.2 × 10–8
5. Match List I with List II.
Choose the correct answer from the options given below.
(A) A-II, B-III, C-I, D-IV
(B) A-II, B-III, C-IV, D-I
(C) A-III, B-II, C-IV, D-I
(D) A-III, B-II, C-I, D-IV
6. The correct order of electron gain enthalpies of Cl, F, Te and Po is
(A) F <Cl<Te< Po
(B) Po <Te< F <Cl
(C) Te< Po <Cl< F
(D) Cl< F <Te< Po
7. Given below are two statements.
Statement-I: During electrolytic refining, blister copper deposits precious metals.
Statement-II: In the process of obtaining pure copper by electrolysis method, copper blister is used to make the anode.
In the 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 true but Statement II is false.
(D) Statement-I is false but Statement-II is true
8. Given below are two statements one is labelled as Assertion A and the other is labelled as Reason R:
Assertion A: The amphoteric nature of water is explained by using Lewis acid/base concept
Reason R: Water acts as an acid with NH3 and as a base with H2S.
In the light of the above statements choose the correct 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.
9. The correct order of reduction potentials of the following pairs is
(A) Cl2/Cl−
(B) I2/I−
(C) Na+/Na
(D) Li+/Li
Choose the correct answer from the options given below:
(A) A > C > B > D > E
(B) A > B > C > D > E
(C) A > C > B > E > D
(D) A > B > C > E > D
10. The number of bridged oxygen atoms present in compound B formed from the following reactions is
(A) 0
(B) 1
(C) 2
(D) 3
11. The metal ion (in gaseous state) with lowest spin-only magnetic moment value is
(A) V2+
(B) Ni2+
(C) Cr2+
(D) Fe2+
12. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Polluted water may have a value of BOD of the order of 17 ppm.
Reason R: BOD is a measure of oxygen required to oxidise both the bio-degradable and non-biodegradable organic material in water.
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.
13. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: A mixture contains benzoic acid and naphthalene. The pure benzoic acid can be separated out by the use of benzene.
Reason R: Benzoic acid is soluble in hot water.
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.
14. During halogen test, sodium fusion extract is boiled with concentrated HNO3 to
(A) remove unreacted sodium
(B) decompose cyanide or sulphide of sodium
(C) extract halogen from organic compound
(D) maintain the pH of extract.
15. Amongst the following, the major product of the given chemical reaction is
16. In the given reaction
‘A’ can be
(A) Benzyl bromide
(B) Bromo benzene
(C) Cyclohexyl bromide
(D) Methyl bromide
17. Which of the following conditions or reaction sequence will NOT give acetophenone as the major product?
18. The major product formed in the following reaction, is
19. Which of the following ketone will NOT give enamine on treatment with secondary amines? [where t-Bu is –C(CH3)3]
20. An antiseptic Dettol is a mixture of two compounds ‘A’ and ‘B’ where A has 6π electrons and B has 2π electrons. What is ‘B’?
(A) Bithionol
(B) Terpineol
(C) Chloroxylenol
(D) Chloramphenicol
SECTION-B
21. A protein ‘A’ contains 0.30% of glycine (molecular weight 75). The minimum molar mass of the protein ‘A’ is _______ × 103 g mol–1 [nearest integer]
22. A rigid nitrogen tank stored inside a laboratory has a pressure of 30 atm at 06:00 am when the temperature is 27°C. At 03:00 pm, when the temperature is 45°C, the pressure in the tank will be _______ atm. [nearest integer]
23. Amongst BeF2, BF3, H2O, NH3, CCl4 and HCl, the number of molecules with non-zero net dipole moment is ______.
24. At 345 K, the half life for the decomposition of a sample of a gaseous compound initially at 55.5 kPa was 340 s. When the pressure was 27.8 kPa, the half life was found to be 170 s. The order of the reaction is ________. [integer answer]
25. A solution of Fe2(SO4)3 is electrolyzed for ‘x’ min with a current of 1.5 A to deposit 0.3482 g of Fe. The value of x is _______. [nearest integer]
Given : 1 F = 96500 C mol–1
Atomic mass of Fe = 56 g mol–1
26. Consider the following reactions:
PCl3 + H2O → A + HCl
A + H2O → B + HCl
The number of ionisable protons present in the product B is _________.
27. Amongst FeCl3.3H2O, K3[Fe(CN)6)] and [Co(NH3)6]Cl3, the spin-only magnetic moment value of the inner-orbital complex that absorbs light at shortest wavelength is _______B.M. [nearest integer]
28. The Novolac polymer has mass of 963 g. The number of monomer units present in it are
29. How many of the given compounds will give a positive Biuret test_________? Glycine, Glycylalanine, Tripeptide, Biuret.
30. The neutralization occurs when 10 mL of 0.1M acid ‘A’ is allowed to react with 30 mL of 0.05 M base M(OH)2. The basicity of the acid ‘A’ is_________.
[M is a metal]
MATHEMATICS
SECTION A
1. Let A = {x ∈ R : | x + 1 | < 2} and B = {x ∈ R : | x – 1| ≥ 2}. Then which one of the following statements is NOT true?
(A) A – B = (–1, 1)
(B) B – A = R – (–3, 1)
(C) A ⋂ B = (–3, –1]
(D) A U B = R – [1, 3)
2. Let a, b ∈ R be such that the equation ax2 – 2bx + 15 = 0 has a repeated root α. If α and β are the roots of the equation x2 – 2bx + 21 = 0, then α2 + β2 is equal to
(A) 37
(B) 58
(C) 68
(D) 92
3. Let z1 and z2 be two complex numbers such that
4. The system of equations
–kx + 3y – 14z = 25
–15x + 4y – kz = 3
–4x + y + 3z = 4
is consistent for all k in the set
(A) R
(B) R – {–11, 13}
(C) R – {13}
(D) R – {–11, 11}
5. is equal to
(A) 1/12
(B) −1/18
(C) −1/12
(D) −1/6
6. The area of the region enclosed between the parabolas y2 = 2x – 1 and y2 = 4x – 3 is
(A) 1/3
(B) 1/6
(C) 2/3
(D) 3/4
7. The coefficient of x101 in the expression (5 + x)500 + x(5 + x)499 + x2(5 + x)498 + ……+ x500, x > 0, is
(A) 501C101 (5)399
(B) 501C101 (5)400
(C) 501C100 (5)400
(D) 500C101 (5)399
8. The sum 1 + 2 ⋅ 3 + 3 ⋅ 32 + …. + 10 ⋅ 39 is equal to
9. Let P be the plane passing through the intersection of the planes the point (2, 1, −2). Let the position vectors of the points X and Y be
Then the points
(A) X and X + Y are on the same side of P
(B) Y and Y – X are on the opposite sides of P
(C) X and Y are on the opposite sides of P
(D) X + Y and X – Y are on the same side of P
10. A circle touches both the y-axis and the line x + y = 0. Then the locus of its center is
(A) y = √2x
(B) x = √2y
(C) y2 – x2 = 2xy
(D) x2 – y2 = 2xy
11. Water is being filled at the rate of 1 cm3/sec in a right circular conical vessel (vertex downwards) of height 35 cm and diameter 14 cm. When the height of the water level is 10 cm, the rate (in cm2/sec) at which the wet conical surface area of the vessel increase, is
(A) 5
(B) √21/5
(C) √26/5
(D) √26/10
12. If then
(A) b3 – b2, b4 – b3, b5 – b4 are in an A.P. with a common difference
(B) are in an A.P. with common difference 2
(C) b3 – b2, b4 – b3, b5 – b4 are in a G.P.
(D) are in an A.P. with common difference −2
13. If y = y(x) is the solution of the differential equation such that y(e)=e/3, then y(1) is equal to
(A) 1/3
(B) 2/3
(C) 3/2
(D) 3
14. If the angle made by the tangent at the point (x0, y0) on the curve x = 12(t + sin t cos t), y = 12(1 + sin t)2, 0 < t <π/2, with the positive x-axis is π/3, then y0 is equal to
(A) 6(3 + 2√2)
(B) 3(7 + 4√3)
(C) 27
(D) 48
15. The value of 2 sin(12°) – sin(72°) is :
16. A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is 1/n. If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48, is :
(A) 7/211
(B) 7/212
(C) 3/210
(D) 13/212
17. The negation of the Boolean expression ((~ q) ∧ p) ⇒ ((~ p) ∨ q) is logically equivalent to :
(A) p⇒ q
(B) q⇒ p
(C) ~ (p ⇒ q)
(D) ~ (q ⇒ p)
18. If the line y = 4 + kx, k > 0, is the tangent to the parabola y = x – x2 at the point P and V is the vertex of the parabola, then the slope of the line through P and V is :
(A) 3/2
(B) 26/9
(C) 5/2
(D) 23/6
19. The value of is equal to
(A) −π/4
(B) −π/8
(C) −5π/12
(D) −4π/9
20. The line y = x + 1 meets the ellipse at two points P and Q. If r is the radius of the circle with PQ as diameter then (3r)2 is equal to :
(A) 20
(B) 12
(C) 11
(D) 8
SECTION-B
21. Let Then the number of elements in the set {(n, m) : n, m ∈ { 1, 2……….., 10} and nAn + mBm = I} is ____________.
22. Let f(x) = [2x2 + 1] and where [t] is the greatest integer ≤ t. Then, in the open interval (–1, 1), the number of points where fog is discontinuous is equal to _______.
23. The value of b > 3 for which is equal to_____
24. If the sum of the co-efficients of all the positive even powers of x in the binomial expansion of is 510 – β∙39, then β is equal to ________
25. If the mean deviation about the mean of the numbers 1, 2, 3, ….n, where n is odd, is then n is equal to ___________.
26. Let λ ∈ R. If
is a vector such that
then
is equal to
27. The total number of three-digit numbers, with one digit repeated exactly two times, is ______.
28. Let f(x) = |(x – 1)(x2 – 2x – 3)| + x – 3, x ∈ If m and M are, respectively the number of points of local minimum and local maximum of f in the interval (0, 4), then m + M is equal to
29. Let the eccentricity of the hyperbola If the equation of the normal at the point (8/√5, 12/5) on the hyperbola is 8√5 x + β y = λ, then λ – β is equal to _______.
30. Let l1 be the line in xy-plane with x and y intercepts 1/8 and 1/4√2 respectively and l2 be the line in zx-plane with x and z intercepts −1/8 and −1/6√3 respectively. If d is the shortest distance between the line l1 and l2, then d–2 is equal to __________.