JEE Main Session 2 28th 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. Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as Here m and n are constants. The relations for distance and time in two systems respectively are :
2. A ball is spun with angular acceleration α = 6t2 – 2t, where t is in second and α is in rads–2. At t = 0, the ball has angular velocity of 10 rads–1 and angular position of 4 rad. The most appropriate expression for the angular position of the ball is :
3. A block of mass 2 kg moving on a horizontal surface with speed of 4 ms–1 enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by F = –kx where k = 12 Nm–1. The speed of the block as it just crosses the rough surface will be :
(A) Zero
(B) 1.5 ms–1
(C) 2.0 ms–1
(D) 2.5 ms–1
4. A √(34) m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If Ff and Fw are the reaction forces of the floor and the wall, then ratio of Fw/Ff will be:
(Use g = 10 m/s2)
(A) 6/√110
(B) 3/√113
(C) 3/√109
(D) 2/√109
5. Water falls from a 40 m high dam at the rate of 9 × 104 kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydro electric energy number of 100 W lamps, that can be lit, is :
(Take g = 10 ms−2)
(A) 25
(B) 50
(C) 100
(D) 18
6. Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be
7. A water drop of radius 1 μm falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is 1.8 × 10–5 Nsm–2 and its density is negligible as compared to that of water (106gm–3). Terminal velocity of the water drop is
(Take acceleration due to gravity = 10 ms–2)
(A) 145.4 × 10–6ms–1
(B) 118.0 × 10–6ms–1
(C) 132.6 × 10–6ms–1
(D) 123.4 × 10–6ms–1
8. A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work of 50 J is done on the gas during the part BC. The internal energy of the gas at A is 1560 J. The work done by the gas during the part CA is:
(A) 20 J
(B) 30 J
(C) −30 J
(D) −60 J
9. What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?
(A) The velocity of atomic oxygen remains same
(B) The velocity of atomic oxygen doubles
(C) The velocity of atomic oxygen becomes half
(D) The velocity of atomic oxygen becomes four times
10. Two point charges A and B of magnitude +8 × 10–6 C and –8 × 10–6 C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6.4 × 104 NC–1. The distance ‘d’ between the point charges A and B is:
(A) 2.0 m
(B) 3.0 m
(C) 1.0 m
(D) 4.0 m
11. Resistance of the wire is measured as 2 Ω and 3 Ω at 10°C and 30°C respectively. Temperature co-efficient of resistance of the material of the wire is:
(A) 0.033°C–1
(B) –0.033°C–1
(C) 0.011°C–1
(D) 0.055°C–1
12. The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to 1.2 × 10–5. What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?
(A) 1.2 × 10–5
(B) 1.2 × 10–3
(C) 1.8 × 10–3
(D) 2.4 × 10–5
13. Two parallel, long wires are kept 0.20 m apart in vacuum, each carrying current of x A in the same direction. If the force of attraction per meter of each wire is 2 × 10–6 N, then the value of x is approximately:
(A) 1
(B) 2.4
(C) 1.4
(D) 2
14. A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be:
(Assume the coil to be short circuited.)
(A) Halved
(B) Quadrupled
(C) The same
(D) Doubled
15. An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y-direction has maximum magnitude of 60 Vm–1. Choose the correct equations for electric and magnetic field if the EM wave is propagating in vacuum:
16. In Young’s double slit experiment performed using a monochromatic light of wavelength λ, when a glass plate (μ = 1.5) of thickness xλ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of x will be:
(A) 3
(B) 2
(C) 1.5
(D) 0.5
17. Let K1 and K2 be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength λ1 and λ2, respectively are incident on a metallic surface. If λ1 = 3λ2 then:
(A) K1> K2/3
(B) K1< K2/3
(C) K1 = K2/3
(D) K2 = K1/3
18. Following statements related to radioactivity are given below:
(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.
(B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time.
(C) Slope of the graph of loge (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time (τ).
(D) Product of decay constant (λ) and half-life time (T1/2) is not constant.
Choose the most appropriate answer from the options given below:
(A) (A) and (B) only
(B) (B) and (D) only
(C) (B) and (C) only
(D) (C) and (D) only
19. In the given circuit the input voltage Vin is shown in figure. The cut-in voltage of p–n junction diode (D1 or D2) is 0.6 V. Which of the following output voltage (V0) waveform across the diode is correct?
20. Amplitude modulated wave is represented by VAM = 10[1 + 0.4 cos(2π × 104t] cos(2π × 107t). The total bandwidth of the amplitude modulated wave is:
(A) 10 kHz
(B) 20 MHz
(C) 20 kHz
(D) 10 MHz
SECTION-B
21. A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 mm, 1.23 mm, 1.19 mm and 1.20 mm. The percentage error is . Then value of x is _______.
22. A zener of breakdown voltage VZ = 8 V and maximum Zener current, IZM = 10 mA is subjected to an input voltage Vi = 10 V with series resistance R = 100 Ω. In the given circuit RL represents the variable load resistance. The ratio of maximum and minimum value of RL is __________.
23. In a Young’s double slit experiment, an angular width of the fringe is 0.35° on a screen placed at 2 m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index 7/5, is 1/α. The value of α is _________.
24. In the given circuit, the magnitude of VL and VC are twice that of VR. Given that f = 50 Hz, the inductance of the coil is 1/(Kπ) mH. The value of K is ________.
25. All resistances in figure are 1 Ω each. The value of current ‘I‘ is (a/5) A. The value of a is _________.
26. A capacitor C1 of capacitance 5 μF is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor C2 of capacitance 10 μF as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor C2 is ____ μC.
27. A tuning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is ____ cm.
(Velocity of sound in air is 340 ms–1)
28. A liquid of density 750 kgm–3 flows smoothly through a horizontal pipe that tapers incross-sectional area from A1 = 1.2 × 10–2 m2 to The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is ________ × 10–3 m3s–1.
29. A uniform disc with mass M = 4 kg and radius R = 10 cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m = 2 kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is ________ N.
(Take g = 10 ms–2)
30. A car covers AB distance with first one-third at velocity v1ms–1, second one-third at v2ms–1 and last one-third at v3ms–1. If v3 = 3v1, v2 = 2v1 and v1 = 11 ms–1 then the average velocity of the car is ____ ms–1.
CHEMISTRY
SECTION-A
1. Compound A contains 8.7% Hydrogen, 74% Carbon and 17.3% Nitrogen. The molecular formula of the compound is,
Given : Atomic masses of C, H and N are 12, 1 and 14 amu, respectively.
The molar mass of the compound A is 162 g mol–1.
(A) C4H6N2
(B) C2H3N
(C) C5H7N
(D) C10H14N2
2. Consider the following statements :
(A) The principal quantum number ‘n’ is a positive integer with values of ‘n’ = 1, 2, 3, ….
(B) The azimuthal quantum number ‘l’ for a given ‘n’ (principal quantum number) can have values as ‘l’ = 0, 1, 2, …n
(C) Magnetic orbital quantum number ‘ml’ for a particular ‘l’ (azimuthal quantum number) has (2l + 1) values.
(D) ±1/2 are the two possible orientations of electron spin.
(E) For l = 5, there will be a total of 9 orbital
Which of the above statements are correct?
(A) (A), (B) and (C)
(B) (A), (C), (D) and (E)
(C) (A), (C) and (D)
(D) (A), (B), (C) and (D)
3. In the structure of SF4, the lone pair of electrons on S is in.
(A) Equatorial position and there are two lone pair – bond pair repulsions at 90º
(B) Equatorial position and there are three lone pair – bond pair repulsions at 90º
(C) Axial position and there are three lone pair – bond pair repulsion at 90º
(D) Axial position and there are two lone pair – bond pair repulsion at 90º
4. A student needs to prepare a buffer solution of propanoic acid and its sodium salt with pH 4. The ratio of required to make buffer is _____.
Given :Ka(CH3CH2COOH) = 1.3 × 10–5
(A) 0.03
(B) 0.13
(C) 0.23
(D) 0.33
5. 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) – (III), (D) – (IV)
(C) (A) – (II), (B) – (III), (C) – (I), (D) – (IV)
(D) (A) – (I), (B) – (III), (C) – (II), (D) – (IV)
6. Match List-I with List-II:
Choose the correct answer from the options given below:
(A) A-IV, B-III, C-I, D-II
(B) A-IV, B-II, C-I, D-III
(C) A-II, B-IV, C-III, D-I
(D) A-I, B-II, C-III, D-IV
7. In the metallurgical extraction of copper, following reaction is used :
FeO + SiO2 → FeSiO3
FeO and FeSiO3 respectively are.
(A) Gangue and flux
(B) Flux and slag
(C) Slag and flux
(D) Gangue and slag
8. Hydrogen has three isotopes: protium (1H), deuterium (2H or D) and tritium (3H or T). They have nearly same chemical properties but different physical properties. They differ in
(A) Number of protons
(B) Atomic number
(C) Electronic configuration
(D) Atomic mass
9. Among the following, basic oxide is:
(A) SO3
(B) SiO2
(C) CaO
(D) Al2O3
10. Among the given oxides of nitrogen; N2O, N2O3, N2O4 and N2O5, the number of compound/(s) having N – N bond is:
(A) 1
(B) 2
(C) 3
(D) 4
11. Which of the following oxoacids of sulphur contains ‘‘S’’ in two different oxidation states?
(A) H2S2O3
(B) H2S2O6
(C) H2S2O7
(D) H2S2O8
12. Correct statement about photo-chemical smog is:
(A) It occurs in humid climate.
(B) It is a mixture of smoke, fog and SO2.
(C) It is reducing smog.
(D) It results from reaction of unsaturated hydrocarbons.
13. The correct IUPAC name of the following compound is:
(A) 4-methyl-2-nitro-5-oxohept-3-enal
(B) 4-methyl-5-oxo-2-nitrohept-3-enal
(C) 4-methyl-6-nitro-3-oxohept-4-enal
(D) 6-formyl-4-methyl-2-nitrohex-3-enal
14. The major product (P) of the given reaction is (where, Me is –CH3)
15. 4-Bromophenyl acetic acid.
In the above reaction ‘A’ is
16. Isobutyraldehyde on reaction with formaldehyde and K2CO3 gives compound ‘A’. Compound ‘A’ reacts with KCN and yields compound ‘B’, which on hydrolysis gives a stable compound ‘C’. The compound ‘C’ is
17. With respect to the following reaction, consider the given statements:
(A) o-Nitroaniline and p-nitroaniline are the predominant products.
(B) p-Nitroaniline and m-nitroaniline are the predominant products.
(C) HNO3 acts as an acid.
(D) H2SO4 acts as an acid.
Choose the correct option.
(A) (A) and (C) are correct statements.
(B) (A) and (D) are correct statements.
(C) (B) and (D) are correct statements.
(D) (B) and (C) are correct statements.
18. Given below are two statements, one is Assertion (A) and other is Reason (R).
Assertion (A): Natural rubber is a linear polymer of isoprene called cis-polyisoprene with elastic properties.
Reason (R): The cis-polyisoprene molecules consist of various chains held together by strong polar interactions with coiled structure.
In the light of the above statements, choose the correct one 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.
19. When sugar ‘X’ is boiled with dilute H2SO4 in alcoholic solution, two isomers ‘A’ and ‘B’ are formed. ‘A’ on oxidation with HNO3 yields saccharic acid whereas ‘B’ is laevorotatory. The compound ‘X’ is :
(A) Maltose
(B) Sucrose
(C) Lactose
(D) Starch
20. The drug tegamet is:
SECTION-B
21. 100 g of an ideal gas is kept in a cylinder of 416 L volume at 27°C under 1.5 bar pressure. The molar mass of the gas is ________ g mol–1. (Nearest integer).
22. For combustion of one mole of magnesium in an open container at 300 K and 1 bar pressure, ΔCHΘ = –601.70 kJ mol–1, the magnitude of change in internal energy for the reaction is ______ kJ. (Nearest integer)
(Given : R = 8.3 J K–1mol–1)
23. 2.5 g of protein containing only glycine (C2H5NO2) is dissolved in water to make 500 mL of solution. The osmotic pressure of this solution at 300 K is found to be 5.03 × 10–3 bar. The total number of glycine units present in the protein is _______.
(Given : R = 0.083 L bar K–1mol–1)
24. For the given reactions
Sn2+ + 2e– → Sn
Sn4+ + 4e– → Sn
The electrode potentials are; and
The magnitude of standard electrode potential for Sn4+/Sn2+ i.e.
is _______ × 10−2 V. (Nearest integer)
25. A radioactive element has a half-life of 200 days. The percentage of original activity remaining after 83 days is ________. (Nearest integer)
(Given : antilog 0.125 = 1.333, antilog 0.693 = 4.93)
26. [Fe(CN)6]4–
[Fe(CN)6]3–
[Ti(CN)6]3–
[Ni(CN)4]2–
[Co(CN)6]3–
Among the given complexes, number of paramagnetic complexes is_______.
27. (a) CoCl3⋅4 NH3, (b) CoCl3⋅5NH3, (c) CoCl3.6NH3 and (d) CoCl(NO3)2⋅5NH3. Number of complex(es) which will exist in cis-trans form is/are______.
28. The complete combustion of 0.492 g of an organic compound containing ‘C’, ‘H’ and ‘O’ gives 0.793 g of CO2 and 0.442 g of H2 The percentage of oxygen composition in the organic compound is_____.[nearest integer]
29. The major product of the following reaction contains______bromine atom(s).
30. 0.01 M KMnO4solution was added to 20.0 mL of 0.05 M Mohr’s salt solution through a burette. The initial reading of 50 mL burette is zero. The volume of KMnO4 solution left in burette after the end point is _____ml. [nearest integer]
MATHEMATICS
SECTION-A
1. Let R1 = {(a, b) ∈ N × N : |a – b| ≤ 13} and R2 = {(a, b) ∈ N × N : |a – b| ≠ 13}. Then on N:
(A) Both R1 and R2 are equivalence relations
(B) Neither R1 nor R2 is an equivalence relation
(C) R1 is an equivalence relation but R2 is not
(D) R2 is an equivalence relation but R1 is not
2. Let f(x) be a quadratic polynomial such that f(–2) + f(3) = 0. If one of the roots of f(x) = 0 is –1, then the sum of the roots of f(x) = 0 is equal to:
(A) 11/3
(B) 7/3
(C) 13/3
(D) 14/3
3. The number of ways to distribute 30 identical candies among four children C1, C2, C3 and C4 so that C2 receives atleast 4 and atmost 7 candies, C3 receives atleast 2 and atmost 6 candies, is equal to:
(A) 205
(B) 615
(C) 510
(D) 430
4. The term independent of x in the expansion of is
(A) 7/40
(B) 33/200
(C) 39/200
(D) 11/50
5. If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 and a + n = 33, then the value of n is:
(A) 21
(B) 22
(C) 23
(D) 24
6. Let f, g : R → R be functions defined by
Where [x] denotes the greatest integer less than or equal to x. Then, the function fog is discontinuous at exactly :
(A) one point
(B) two points
(C) three points
(D) four points
7. Let f : R → R be a differentiable function such that and let
for
is equal to
(A) 2
(B) 3
(C) 4
(D) −3
8. Let f :R → R be a continuous function satisfying f(x) + f(x + k) = n, for all x ∈ R where k > 0 and n is a positive integer. If then
(A) I1 + 2I2 = 4nk
(B) I1 + 2I2 = 2nk
(C) I1 + nI2 = 4n2k
(D) I1 + nI2 = 6n2k
9. The area of the bounded region enclosed by the curve and the x-axis is
(A) 9/4
(B) 45/16
(C) 27/8
(D) 63/16
10. Let x = x(y) be the solution of the differential equation such that x(1) = 0. Then, x(e) is equal to
(A) eloge(2)
(B) −eloge(2)
(C) e2loge(2)
(D) −e2loge(2)
11. Let the slope of the tangent to a curve y = f(x) at (x, y) be given by 2 tanx(cosx – y). If the curve passes through the point (π/4, 0) then the value of is equal to
12. Let a triangle be bounded by the lines L1 : 2x + 5y = 10; L2 : –4x + 3y = 12 and the line L3, which passes through the point P(2, 3), intersects L2 at A and L1 at B. If the point P divides the line-segment AB, internally in the ratio 1 : 3, then the area of the triangle is equal to
(A) 110/13
(B) 132/13
(C) 142/13
(D) 151/13
13. Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola e′ and ℓ′ respectively the eccentricity and length of the latus rectum of its conjugate hyperbola. If
then the value of 77a + 44b is equal to
(A) 100
(B) 110
(C) 120
(D) 130
14. Let α ∈ where α ∈ R. If the area of the parallelogram whose adjacent sides are represented by the vectors
then the value of
is equal to
(A) 10
(B) 7
(C) 9
(D) 14
15. If vertex of a parabola is (2, –1) and the equation of its directrix is 4x – 3y = 21, then the length of its latus rectum is :
(A) 2
(B) 8
(C) 12
(D) 16
16. Let the plane ax + by + cz = d pass through (2, 3, –5) and is perpendicular to the planes 2x + y – 5z = 10 and 3x + 5y – 7z = 12. If a, b, c, d are integers d > 0 and gcd (|a|, |b|, |c|, d) = 1, then the value of a + 7b + c + 20d is equal to :
(A) 18
(B) 20
(C) 24
(D) 22
17. The probability that a randomly chosen one-one function from the set {a, b, c, d} to the set {1, 2, 3, 4, 5} satisfies f(a) + 2f(b) – f(c) = f(d) is :
(A) 1/24
(B) 1/40
(C) 1/30
(D) 1/20
18. The value of is equal to
(A) 1
(B) 2
(C) 3
(D) 6
19. Let be a vector which is perpendicular to the vector
If
the projection of the vector
on the vector
is
(A) 1/3
(B) 1
(C) 5/3
(D) 7/3
20. If cot α =1 and sec β = −5/3, where then the value of tan(α + β) and the quadrant in which α + β lies, respectively are :
(A) –1/7 and IVth quadrant
(B) 7 and Ist quadrant
(C) –7 and IVth quadrant
(D) 1/7 and Ist quadrant
SECTION-B
21. Let the image of the point P(1, 2, 3) in the line be Q. Let R (α, β, γ) be a point that divides internally the line segment PQ in the ratio 1 : 3. Then the value of 22(α + β + γ) is equal to ________.
22. Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their variance is 20. A student fails in the examination if he/she gets less than 50 marks, then in worst case, the number of students can fail is __________.
23. If one of the diameters of the circle x2 + y2 – 2√2x – 6√2y + 14 = 0 is a chord of the circle (x – 2√2)2 + (y – 2√2)2 = r2, then the value of r2 is equal to _______.
24. If then the value of (a – b) is equal to _______.
25. Let for n = 1, 2, …, 50, Sn be the sum of the infinite geometric progression whose first term is n2 and whose common ratio is Then the value of
is equal to
26. If the system of linear equations
2x – 3y = γ + 5,
αx + 5y = β + 1,
where α, β, γ ∈ R has infinitely many solutions, then the value of |9α + 3β + 5γ| is equal to _______.
27. Let Then, the number of elements in the set {n ∈ {1, 2, ……, 100} : An = A} is
28. Sum of squares of modulus of all the complex numbers z satisfying is equal to
29. Let S = {1, 2, 3, 4}. Then the number of elements in the set {f : S × S → S : f is onto and f(a, b) = f(b, a) ≥ a ∀ (a, b) ∈ S × S is ____________.
30. The maximum number of compound propositions, out of p ∨ r ∨ s, p ∨ r ∨ ~s, p ∨ ~q ∨ s, ~p ∨ ~r ∨ s, ~p ∨ ~r ∨ ~s, ~p ∨ q ∨ ~s, q ∨ r ∨ ~s, q ∨ ~r ∨ ~s, ~p ∨ ~q ∨ ~s that can be made simultaneously true by an assignment of the truth values to p, q, r and s, is equal to ____________ .