JEE Main Session 2 27th 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. The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be :
(A) [ML–1T–1]
(B) [ML–1T–2]
(C) [ML2T–1]
(D) [M–1L3T0]
2. The distance of the Sun from Earth is 1.5 × 1011 m, and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be :
(A) 2.45 × 1010 m
(B) 1.45 × 1010 m
(C) 1.45 × 109 m
(D) 0.14 × 109 m
3. When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :
(A) 19.6 m
(B) 29.4 m
(C) 39.2 m
(D) 73.5 m
4. One end of a massless spring of spring constant k and natural length l0 is fixed while the other end is connected to a small object of mass m lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity ω about an axis passing through fixed end, then the elongation of the spring will be :
5. A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is The value of x is
(A) 3
(B) 2
(C) 1
(D) 5
6. Four spheres each of mass m form a square of side d (as shown in figure). A fifth sphere of mass M is situated at the centre of square. The total gravitational potential energy of the system is:
7. For a perfect gas, two pressures P1 and P2 are shown in the figure. The graph shows:
(A) P1>P2
(B) P1<P2
(C) P1 = P2
(D) Insufficient data to draw any conclusion
8. According to kinetic theory of gases,
(A) The motion of the gas molecules freezes at 0°C
(B) The mean free path of gas molecules decreases if the density of molecules is increased.
(C) The mean free path of gas molecules increases if temperature is increased keeping pressure constant.
(D) Average kinetic energy per molecule per degree of freedom is (for monoatomic gases).
Choose the most appropriate answer from the options given below:
(A) A and C only
(B) B and C only
(C) A and B only
(D) C and D only
9. A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is:
(Given initial temperature of the bullet = 127°C),
Melting point of the bullet = 327°C,
Latent heat of fusion of lead = 2.5 × 104 J kg–1
Specific heat capacity of lead = 125 J/kg K)
(A) 125 ms–1
(B) 500ms–1
(C) 250ms–1
(D) 600ms–1
10. The equation of a particle executing simple harmonic motion is given by At t = 1 s, the speed of the particle will be
(Given : π = 3.14)
(A) 0 cm s−1
(B) 157cm s−1
(C) 272cm s−1
(D) 314cm s−1
11. If a charge q is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be:
12. Three identical charged balls each of charge 2 C are suspended from a common point P by silk threads of 2 m each (as shown in figure). They form an equilateral triangle of side 1 m. The ratio of net force on a charged ball to the force between any two charged balls will be:
(A) 1 : 1
(B) 1 : 4
(C) √3 : 2
(D) √3 : 1
13. Two long parallel conductors S1 and S2 are separated by a distance 10 cm and carrying currents of 4A and 2A respectively. The conductors are placed along x-axis in X-Y plane. There is a point P located between the conductors (as shown in figure). A charge particle of 3π coulomb is passing through the point P with velocity represents unit vector along x & y axis respectively.
The force acting on the charge particle is The value of x is :
(A) 2
(B) 1
(C) 3
(D) −3
14. If L, C and R are the self-inductance, capacitance and resistance, respectively, which of the following does not have the dimension of time?
(A) RC
(B) L/R
(C) √LC
(D) L/C
15. Given below are two statements:
Statement I : A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates EM waves.
Statement II : In a material medium. The EM wave travels with speed
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 correct but statement II is false
(D) Statement I is incorrect but statement II is true
16. A convex lens has power P. It is cut into two halves along its principal axis. Further one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figures). Choose the incorrect option for the reported pieces.
(A) Power of L1 = P/2
(B) Power of L2 = P/2
(C) Power of L3 = P/2
(D) Power of L1 = P
17. If a wave gets refracted into a denser medium, then which of the following is true?
(A) Wavelength, speed and frequency decreases
(B) Wavelength increases, speed decreases and frequency remains constant
(C) Wavelength and speed decreases but frequency remains constant
(D) Wavelength, speed and frequency increases
18. Given below are two statements:
Statement I: In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit (E1) to higher energy orbit (E2), is given as hf = E1 – E2.
Statement II: The jumping of electron from higher energy orbit (E2) to lower energy orbit (E1) is associated with frequency of radiation given as f = (E2 – E1)/h This condition is Bohr’s frequency condition.
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 correct but statement II is false
(D) Statement I is incorrect but statement II is true
19. For a transistor to act as a switch, it must be operated in
(A) Active region
(B) Saturation state only
(C) Cut-off state only
(D) Saturation and cut-off state
20. We do not transmit low frequency signal to long distance because-
(a) The size of the antenna should be comparable to signal wavelength which is unreal solution for a signal of longer wavelength
(b) Effective power radiated by a long wavelength baseband signal would be high
(c) We want to avoid mixing up signals transmitted by different transmitter simultaneously
(d) Low frequency signal can be sent to long distances by superimposing with a high frequency wave as well
Therefore, the most suitable option will be:
(A) All statements are true
(B) (a), (b) and (c) are true only
(C) (a), (c) and (d) are true only
(D) (b), (c) and (d) are true only
SECTION-B
21. A mass of 10 kg is suspended vertically by a rope of length 5 m from the roof. A force of 30 N is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is θ = tan–1 (x × 10–1). The value of x is _______.
(Given, g = 10 m/s2)
22. A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface.
The velocity of centre of mass of the wheel when it reaches at the bottom Q of the inclined plane PQ will be The value of x is _________.
23. A diatomic gas (γ = 1.4) does 400 J of work when it is expanded isobarically. The heat given to the gas in the process is _______ J.
24. A particle executes simple harmonic motion. Its amplitude is 8 cm and time period is 6s. The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ________ s.
25. A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is The value of x is _________.
26. The current density in a cylindrical wire of radius r = 4.0 mm is 1.0 × 106 A/m2. The current through the outer portion of the wire between radial distances r/2 and r is xπ A; where x is _______ .
27. In the given circuit ‘a’ is an arbitrary constant. The value of m for which the equivalent circuit resistance is minimum, will be The value of x is _______.
28. A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If rd and rp are the radii of their circular paths respectively, then the ratio rd/rp will be √x : 1 where x is _________.
29. A metallic rod of length 20 cm is placed in North South direction and is moved at a constant speed of 20 m/s towards East. The horizontal component of the Earth’s magnetic field at that place is 4 × 10–3 T and the angle of dip is 45°. The emf induced in the rod is _______ mV.
30. The cut-off voltage of the diodes (shown in figure) in forward bias is 0.6 V. The current through the resister of 40 Ω is _______ mA.
CHEMISTRY
SECTION-A
1. Which amongst the given plots is the correct plot for pressure (p) vs density (d) for an ideal gas?
2. Identify the incorrect statement for PCI5 from the following.
(A) In this molecule, orbitals of phosphorous are assumed to undergo sp3d hybridization.
(B) The geometry of PCl5 is trigonal bipyramidal.
(C) PCl5 has two axial bonds stronger than three equatorial bonds.
(D) The three equatorial bonds of PCl5 lie in a plane
3. Statement-I: Leaching of gold with cyanide ion in absence of air/O2 leads to cyano complex of Au(III).
Statement-II: Zinc is oxidized during the displacement reaction carried out for gold extraction.
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
4. The correct order of increasing intermolecular hydrogen bond strength is
(A) HCN < H2O < NH3
(B) HCN < CH4 < NH3
(C) CH4 < HCN < NH3
(D) CH4 < NH3 < HCN
5. The correct order of increasing ionic radii is
(A) Mg2+ < Na+ < F– < O2– < N3–
(B) N3– < O2– < F– < Na+ < Mg2+
(C) F– < Na+ < O2– < Mg2+ < N3–
(D) Na+ < F– < Mg2+ < O2– < N3–
6. The gas produced by treating an aqueous solution of ammonium chloride with sodium nitrite is
(A) NH3
(B) N2
(C) N2O
(D) Cl2
7. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Fluorine forms one oxoacid.
Reason R: Fluorine has smallest size amongst all halogens and is highly electronegative.
In the light of the above statements, choose the most appropriate answer from the option 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.
8. In 3d series, the metal having the highest M2+/M standard electrode potential is
(A) Cr
(B) Fe
(C) Cu
(D) Zn
9. The ‘f’ orbitals are half and completely filled, respectively in lanthanide ions
[Given: Atomic no. Eu, 63; Sm, 62; Tm, 69; Tb, 65; Yb, 70; Dy, 66]
(A) Eu2+ and Tm2+
(B) Sm2+ and Tm3+
(C) Tb4+ and Yb2+
(D) Dy3+ and Yb3+
10. Arrange the following coordination compounds in the increasing order of magnetic moments. (Atomic numbers: Mn = 25; Fe = 26)
(1) [FeF6]3–
(2) [Fe(CN)6]3–
(3) [MnCl6]3– (high spin)
(4) [Mn(CN)6]3–
Choose the correct answer from the options given below:
(A) 1 < 2 < 4 < 3
(B) 2 < 4 < 3 < 1
(C) 1 < 3 < 4 < 2
(D) 2 < 4 < 1 < 3
11. On the surface of polar stratospheric clouds, hydrolysis of chlorine nitrate gives A and B while its reaction with HCl produces B and C. A, B and C are, respectively
(A) HOCl, HNO3, Cl2
(B) Cl2, HNO3, HOCl
(C) HClO2, HNO2, HOCl
(D) HOCl, HNO2, Cl2O
12. Which of the following is most stable?
13. What will be the major product of the following sequence of reactions?
14. Product ‘A’ of the following sequence of reactions is
15. Match List I with List II.
Choose the correct answer from the options given below:
(A) A-IV, B-III, C-II, D-I
(B) A-IV, B-III, C-I, D-II
(C) A-II, B-III, C-I, D-IV
(D) A-IV, B-II, C-III, D-I
16. Decarboxylation of all six possible forms of diaminobenzoic acid C6H3(NH2)2COOH yields three products A, B and C. Three acids give a product ‘A’, two acids give a product ‘B’ and one acid gives a product ‘C’. The melting point of product ‘C’ is
(A) 63ºC
(B) 90ºC
(C) 104ºC
(D) 142ºC
17. Which is true about Buna-N?
(A) It is a linear polymer of 1, 3-butadiene
(B) It is obtained by copolymerization of 1, 3-butadiene and styrene
(C) It is obtained by copolymerization of 1, 3-butadiene and acrylonitrile
(D) The suffix N in Buna-N stands for its natural occurrence.
18. Given below are two statements
Statement I: Maltose has two α-D-glucose units linked at C1 and C4 and is a reducing sugar.
Statement II: Maltose has two monosaccharides:
α-D-glucose and β-D-glucose linked at C1 and C6 and it is a non-reducing sugar.
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
19. Match List I with List II.
Choose the correct answer from the options given below:
(A) A-III, B-I, C-II, D-IV
(B) A-III, B-I, C-IV, D-II
(C) A-I, B-IV, C-II, D-III
(D) A-I, B-III, C-II, D-IV
20. Match List I with List II.
Choose the correct answer from the options given below:
(A) A-III, B-I, C-II, D-IV
(B) A-II, B-I, C-IV, D-III
(C) A-IV, B-I, C-III, D-II
(D) A-IV, B-I, C-II, D-III
SECTION-B
21. 116 g of a substance upon dissociation reaction, yields 7.5 g of hydrogen, 60 g of oxygen and 48.5 g of carbon. Given that the atomic masses of H, O and C are 1, 16 and 12, respectively. The data agrees with how many formulae of the following? _______.
(A) CH3COOH (B) HCHO
(C) CH3OOCH3 (D) CH3CHO
22. Consider the following set of quantum numbers.
The number of correct sets of quantum numbers is _____.
23. BeO reacts with HF in presence of ammonia to give [A] which on thermal decomposition produces [B] and ammonium fluoride. Oxidation state of Be in [A] is _______
24. When 5 moles of He gas expand isothermally and reversibly at 300 K from 10 litre to 20 litre, the magnitude of the maximum work obtained is _____ J. [nearest integer] (Given : R = 8.3 J K–1 mol–1 and log 2 = 0.3010)
25. A solution containing 2.5 × 10–3 kg of a solute dissolved in 75 × 10–3 kg of water boils at 373.535 K. The molar mass of the solute is ________ g mol–1. [nearest integer] (Given : Kb(H2O) = 0.52 K kg mol–1 and boiling point of water = 373.15 K)
26. pH value of 0.001 M NaOH solution is________.
27. For the reaction taking place in the cell:
Pt(s) | H2(g)| H+(aq)|| Ag+(aq)| Ag(s)
E°Cell = +0.5332 V.
The value of ∆fG° is _______ kJ mol−1. (in nearest integer)
28. It has been found that for a chemical reaction with rise in temperature by 9 K the rate constant gets doubled. Assuming a reaction to be occurring at 300 K, the value of activation energy is found to be _________kJ mol–1. [nearest integer]
Given ln10 = 2.3, R = 8.3 J K–1 mol–1, log 2 = 0.30)
29.
If the initial pressure of a gas 0.03 atm, the mass of the gas absorbed per gram of the adsorbent is __________ × 10–2 g.
30. 0.25 g of an organic compound containing chlorine gave 0.40 g of silver chloride in Carius estimation. The percentage of chlorine present in the compound is __________. [in nearest integer]
(Given : Molar mass of Ag is 108 g mol–1 and that of Cl is 35.5 g mol–1)
MATHEMATICS
SECTION-A
1. The number of points of intersection of |z – (4 + 3i)| = 2 and |z| + |z – 4| = 6, z ∈ C, is
(A) 0
(B) 1
(C) 2
(D) 3
2. Let Then the sum of the square of all the values of a, for which 2f′(10) –f′(5) + 100 = 0, is
(A) 117
(B) 106
(C) 125
(D) 136
3. Let for some real numbers α and β, a = α – iβ. If the system of equations 4ix + (1 + i) y = 0 and has more than one solution then α/β is equal to :
(A) –2 + √3
(B) 2 – √3
(C) 2 + √3
(D) –2 – √3
4. Let A and B be two 3 × 3 matrices such that AB = I and |A| = 1/8. Then |adj (B adj(2A))| is equal to
(A) 16
(B) 32
(C) 64
(D) 128
5. Let then 4S is equal to
(A) (7/3)2
(B) 73/32
(C) (7/3)2
(D) 72/33
6. If a1, a2, a3 ….. and b1, b2, b3 ….. are A.P., and a1 = 2, a10 = 3, a1b1 = 1 = a10b10, then a4b4 is equal to
(A) 35/27
(B) 1
(C) 27/28
(D) 28/27
7. If m and n respectively are the number of local maximum and local minimum points of the function then the ordered pair (m, n) is equal to
(A) (3, 2)
(B) (2, 3)
(C) (2, 2)
(D) (3, 4)
8. Let f be a differentiable function in (0, π/2). If is equal to :
9. The integral where [∙] denotes the greatest integer function is equal to
10. If the solution curve of the differential equation (tan−1 y) – x)dy = (1 + y2) dx passes through the point (1, 0), then the abscissa of the point on the curve whose ordinate is tan(1), is
(A) 2e
(B) 2/e
(C) 2
(D) 1/e
11. If the equation of the parabola, whose vertex is at (5, 4) and the directrix is 3x + y – 29 = 0, is x2 + ay2 + bxy + cx + dy + k = 0, then a + b + c + d + k is equal to
(A) 575
(B) −575
(C) 576
(D) −576
12. The set of values of k, for which the circle C : 4x2 + 4y2 – 12x + 8y + k = 0 lies inside the fourth quadrant and the point (1, -1/3) lies on or inside the circle C, is
(A) An empty set
(B) (6, 95/9]
(C) [80/9, 10)
(D) (9, 92/9]
13. Let the foot of the perpendicular from the point (1, 2, 4) on the line be P. Then the distance of P from the plane 3x + 4y + 12z + 23 = 0
(A) 5
(B) 50/13
(C) 4
(D) 63/13
14. The shortest distance between the lines and
is:
(A) 18/√5
(B) 22/3√5
(C) 46/3√5
(D) 6√3
15. Let be the vectors along the diagonal of parallelogram having area 2√ Let the angle between
be acute
If
then an angle between
is:
(A) π/4
(B) −π/4
(C) 5π/6
(D) 3π/4
16. The mean and variance of the data 4, 5, 6, 6, 7, 8, x, y, where x < y, are 6 and 9/4, respectively. Then x4 + y2 is equal to
(A) 162
(B) 320
(C) 674
(D) 420
17. If a point A(x, y) lies in the region bounded by the y-axis, straight lines 2y + x = 6 and 5x – 6y = 30, then the probability that y < 1 is
(A) 1/6
(B) 5/6
(C) 2/3
(D) 6/7
18. The value is
(A) 26/25
(B) 25/26
(C) 50/51
(D) 52/51
19. α = sin 36º is a root of which of the following equation?
(A) 16x4 – 10x2 – 5 = 0
(B) 16x4 + 20x2 – 5 = 0
(C) 16x4 – 20x2 + 5 = 0
(D) 16x4 – 10x2 + 5 = 0
20. Which of the following statement is a tautology?
(A) ((~ q) ∧ p) ∧ q
(B) ((~ q) ∧ p) ∧ (p ∧ (~ p))
(C) ((~ q) ∧ p) ∨ (p ∨ (~p))
(D) (p ∧ q) ∧ (~ (p ∧ q))
SECTION-B
21. Let S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Define f : S → S as
Let g : S → S be a function such that then g(10) (g(1) + g(2) + g(3) + g(4) + g(5)) is equal to __________.
22. Let α, β be the roots of the equation x2 – 4λx + 5 = 0 and α, γ be the roots of the equation x2 – (3√2 + 2√3)x + 7 + 3λ√3 = 0. If β + γ = 3√2, then (α + 2β + γ)2 is equal to:
23. Let A be a matrix of order 2 × 2, whose entries are from the set {0, 1, 3, 4, 5}. If the sum of all the entries of A is a prime number p, 2 < p < 8, then the number of such matrices A is ___________.
24. If the sum of the coefficients of all the positive powers of x, in the Binomial expansion of is 939, then the sum of all the possible integral values of n is:
25. Let [t] denote the greatest integer ≤ t and {t} denote the fractional part of t. The integral value of α for which the left hand limit of the function at x = 0 is equal to
is ________
26. If at x = 1 is equal to:
27. If the area of the region {(x, y) : x2/3 + y2/3 ≤ 1x + y ≥0, y ≥ 0} is A, then is
28. Let v be the solution of the differential equation −1 < x < 1 and y (0) = 0 if
then k−1 is equal to :
29. Let a circle C of radius 5 lie below the x-axis. The line L1 : 4x + 3y + 2 = 0 passes through the centre P of the circle C and intersects the line L2 : 3x – 4y – 11 = 0 at Q. The line L2 touches C at the point Q. Then the distance of P from the line 5x – 12y + 51 = 0 is _____.
30. Let S = {E1, E2, ……………., E8} be a sample space of a random experiment such that for every n = 1, 2 ….8. Then the number of elements in the set
is ________