JEE Main Session 1 29th June 2022 Shift 1
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 balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial velocity u at t = 2 s. After a certain time, both balls meet 100 m above the ground. Find the value of u in ms–1 [use g = 10 ms–2]
(A) 10
(B) 15
(C) 20
(D) 30
2. A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms–1 and 40 ms–1 respectively. The velocity of the third piece will be
(A) 15 ms−1
(B) 25ms−1
(C) 35ms−1
(D) 50ms−1
3. The activity of a radioactive material is 2.56 × 10–3 If the half life of the material is 5 days, after how many days the activity will become 2 × 10–5Ci?
(A) 30 days
(B) 35days
(C) 40days
(D) 25days
4. A spherical shell of 1 kg mass and radius R is rolling with angular speed ω on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is The value of a will be
(A) 2
(B) 3
(C) 4
(D) 5
5. A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0°C will be
(Given gas constant R = 8.3 JK–1-mol–1)
(A) 249 J
(B) 415 J
(C) 498 J
(D) 830 J
6. A wire of length L is hanging from a fixed support. The length changes to L1 and L2 when masses 1 kg and 2 kg are suspended, respectively, from its free end. Then the value of L is equal to
(A)
(B)
(C) 2L1 – L2
(D) 3L1 – 2L2
7. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The photoelectric effect does not takes place, if the energy of the incident radiation is less than the work function of a metal.
Reason R:Kinetic energy of the photoelectrons is zero, if the energy of the incident radiation is equal to the work function of a metal.
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
8. A particle of mass 500 gm is moving in a straight line with velocity v = bx5/2. The work done by the net force during its displacement from x = 0 to x = 4 m is : (Take b = 0.25 m–3/2s–1).
(A) 2 J
(B) 4 J
(C) 8 J
(D) 16 J
9. A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charge particle
(A) 1 : 1
(B) 1 : 2
(C) 2 : 1
(D) 1 : 4
10. For a series LCR circuit, I vs ω curve is shown :
(a) To the left of ωr, the circuit is mainly capacitive.
(b) To the left of ωr, the circuit is mainly inductive.
(c) At ωr, impedance of the circuit is equal to the resistance of the circuit.
(d) At ωr, impedance of the circuit is 0.
Choose the most appropriate answer from the options given below.
(A) (a) and (d) only
(B) (b) and (d) only
(C) (a) and (c) only
(D) (b) and (c) only
11. A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 kgs–1 and at a speed of 10 ms–1. Then, the initial acceleration of the block, in ms–2, will be:
(A) 3
(B) 6
(C) 5
(D) 4
12. In van der Wall equation P is pressure, V is volume, R is universal gas constant and T is temperature The ratio of constants a/b is dimensionally equal to:
(A) P/V
(B) V/P
(C) PV
(D) PV3
13. Two vectors have equal magnitudes. If magnitude of
is equal to two times the magnitude of
, then the angle between
will be:
(A) sin−1(3/5)
(B) sin−1(1/3)
(C) cos−1(3/5)
(D) cos−1(1/3)
14. The escape velocity of a body on a planet ‘A’ is 12 kms–1. The escape velocity of the body on another planet ‘B’, whose density is four times and radius is half of the planet ‘A’, is:
(A) 12 kms−1
(B) 24kms−1
(C) 36kms−1
(D) 6kms−1
15. At a certain place the angle of dip is 30° and the horizontal component of earth’s magnetic field is 0.5 G. The earth’s total magnetic field (in G), at that certain place, is :
(A) 1/√3
(B) 1/2
(C) √3
(D) 1
16. A longitudinal wave is represented by The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to :
(A) 2π
(B) 5π
(C) π
(D) 5π/2
17. A parallel plate capacitor filled with a medium of dielectric constant 10, is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant 15. Then the energy of capacitor will :
(A) increased by 50%
(B) decrease by 15%
(C) increase by 25%
(D) increase by 33%
18. A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength 1 × 105 NC–1. If the charge on the particle is 40 μC and the initial velocity is 200 ms–1, how much distance it will travel before coming to the rest momentarily?
(A) 1 m
(B) 5 m
(C) 10 m
(D) 0.5 m
19. Using Young’s double slit experiment, a monochromatic light of wavelength 5000 Å produces fringes of fringe width 0.5 mm. If another monochromatic light of wavelength 6000 Å is used and the separation between the slits is doubled, then the new fringe width will be :
(A) 0.5 mm
(B) 1.0mm
(C) 0.6mm
(D) 0.3mm
20. Only 2% of the optical source frequency is the available channel bandwidth for an optical communicating system operating at 1000 nm. If an audio signal requires a bandwidth of 8 kHz, how many channels can be accommodated for transmission?
(A) 375 × 107
(B) 75 × 107
(C) 375 × 108
(D) 75 × 109
SECTION-B
21. Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be _______ min.
22. The intensity of the light from a bulb incident on a surface is 0.22 W/m2. The amplitude of the magnetic field in this light-wave is ______ × 10–9
(Given : Permittivity of vacuum ε0 = 8.85 × 10–12C2N–1–m–2, speed of light in vacuum c = 3 × 108 ms–1)
23. As per the given figure, two plates A and B of thermal conductivity K and 2 K are joined together to form a compound plate. The thickness of plates are 4.0 cm and 2.5 cm, respectively and the area of cross-section is 120 cm2 for each plate. The equivalent thermal conductivity of the compound plate is then the value of α will be ________.
24. A body is performing simple harmonic with an amplitude of 10 cm. The velocity of the body was tripled by air Jet when it is at 5 cm from its mean position. The new amplitude of vibration is √x cm. The value of x is _______.
25. The variation of applied potential and current flowing through a given wire is shown in figure. The length of wire is 31.4 cm. The diameter of wire is measured as 2.4 cm. The resistivity of the given wire is measured as x × 10–3Ω cm. The value of x is ________.
[Take π = 3.14]
26. 300 cal. of heat is given to a heat engine and it rejects 225 cal. of heat. If source temperature is 227°C, then the temperature of sink will be _______°C.
27. √d1 and √d2 are the impact parameters corresponding to scattering angles 60° and 90° respectively, when an α particle is approaching a gold nucleus. For d1 = xd2, the value of x will be _________.
28. A transistor is used in an amplifier circuit in common emitter mode. If the base current changes by 100μA, it brings a change of 10mA in collector current. If the load resistance is 2kΩ and input resistance is 1kΩ, the value of power gain is x×104. The value of x is _______.
29. A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30 cm and refractive index 1.5. The distance from the centre of the globe at which the beam of light can converge is ________ mm.
30. For the network shown below, the value of VB– VA is ________V.
CHEMISTRY
SECTION-A
1. Production of iron in blast furnace follows the following equation Fe3O4(s) + 4CO(g) → 3Fe(l) + 4CO2(g) when 4.640 kg of Fe3O4 and 2.520 kg of CO are allowed to react then the amount of iron (in g) produced is :
[Given : Molar Atomic mass (g mol–1): Fe = 56 Molar Atomic mass (g mol–1) : 0 = 16 Molar Atomic mass (g mol–1): = C = 12
(A) 1400
(B) 2200
(C) 3360
(D) 4200
2. Which of the following statements are correct ?
(A) The electronic configuration of Cr is [Ar] 3d5 4s1.
(B) The magnetic quantum number may have a negative value.
(C) In the ground state of an atom, the orbitals are filled in order of their increasing energies. (D) The total number of nodes are given by n – 2.
Choose the most appropriate answer from the options given below :
(A) (A), (C) and (D) only
(B) (A) and (B) only
(C) (A) and (C) only
(D) (A), (B) and (C) only
3. Arrange the following in the decreasing order of their covalent character :
(A) LiCl
(B) NaCl
(C) KCl
(D) CsCl
Choose the most appropriate answer from the options given below :
(A) (A) > (C) > (B) > (D)
(B) (B) > (A) > (C) > (D)
(C) (A) > (B) > (C) > (D)
(D) (A) > (B) > (D) > (C)
4. The solubility of AgCl will be maximum in which of the following?
(A) 0.01 M KCl
(B) 0.01 M HCl
(C) 0.01 M AgNO3
(D) Deionised water
5. Which of the following is a correct statement?
(A) Brownian motion destabilises sols.
(B) Any amount of dispersed phase can be added to emulsion without destabilising it.
(C) Mixing two oppositely charged sols in equal amount neutralises charges and stabilises colloids.
(D) Presence of equal and similar charges on colloidal particles provides stability to the colloidal solution.
6. The electronic configuration of Pt(atomic number 78) is:
(A) [Xe] 4f14 5d9 6s1
(B) [Kr] 4f14 5d10
(C) [Xe] 4f14 5d10
(D) [Xe] 4f14 5d8 6s2
7. In isolation of which one of the following metals from their ores, the use of cyanide salt is not commonly involved?
(A) Zinc
(B) Gold
(C) Silver
(D) Copper
8. Which one of the following reactions indicates the reducing ability of hydrogen peroxide in basic medium?
(A) HOCl + H2O2→ H3O+ + Cl− + O2
(B) PbS + 4H2O2→ PbSO4 + 4H2O
(C) 2MnO4− + 3H2O2→ 2MnO2 + 3O2 + 2H2O + 2OH−
(D) Mn2++ H2O2→ Mn4+ + 2OH−
9. Match the List-I with List- II.
Choose the most appropriate answer from the options given below:
(A) (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
(B) (A)-(III), (B)-(II), (C)-(I), (D)-(IV)
(C) (A)-(III), (B)-(I), (C)-(II), (D)-(IV)
(D) (A)-(IV), (B)-(II), (C)-(I), (D)-(III)
10. Match the List-I with List- II.
Choose the most appropriate answer from the option given below:
(A) (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
(B) (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
(C) (A)-(II), (B)-(III), (C)-(IV), (D)-(I)
(D) (A)-(I), (B)-(IV), (C)-(II), (D)-(III)
11. The oxoacid of phosphorus that is easily obtained from a reaction of alkali and white phosphorus and has two P-H bonds, is:
(A) Phosphonic acid
(B) Phosphinic acid
(C) Pyrophosphorus acid
(D) Hypophosphoric acid
12. The acid that is believed to be mainly responsible for the damage of TajMahal is
(A) sulfuric acid
(B) hydrofluoric acid
(C) phosphoric acid
(D) hydrochloric acid
13. Two isomers ‘A’ and ‘B’ with molecular formula C4H8 give different products on oxidation with KMnO4/H+ results in effervescence of a gas and gives ketone. The compound ‘A’ is
14.
In the given conversion the compound A is:
15. Given below are two statements :
Statement I : The esterification of carboxylic acid with an alcohol is a nucleophilic acyl substitution.
Statement II : Electron withdrawing groups in the carboxylic acid will increase the rate of esterification reaction.
Choose the most appropriate option :
(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.
16.
Consider the above reactions, the product A and product B, respectively are
17. The polymer, which can be stretched and retains its original status on releasing the force is
(A) Bakelite
(B) Nylon 6, 6
(C) Buna-N
(D) Terylene
18. Sugar moiety in DNA and RNA molecules, respectively are
(A) β-D-2-deoxyribose, β-D-deoxyribose
(B) β-D-2-deoxyribose, β-D-ribose
(C) β-D-ribose, β-D-2-deoxyribose
(D) β-D-deoxyribose, β-D-2-deoxyribose
19. Which of the following compound does not contain sulphur atom?
(A) Cimetidine
(B) Ranitidine
(C) Histamine
(D) Saccharin
20. Given below are two statements.
Statement I : Phenols are weakly acidic.
Statement II : Therefore they are freely soluble in NaOH solution and are weaker acids than alcohols and water.
Choose the most appropriate option.
(A) Both Statement I and Statement II are correct.
(B) Both Statement I and Statement II are correct.
(C) Statement I is correct but Statement II is incorrect.
(D) Statement I is incorrect but Statement II is correct.
SECTION-B
21. Geraniol, a volatile organic compound, is a component of rose oil. The density of the vapour is 0.46 gL–1 at 257°C and 100 mm Hg. The molar mass of geraniol is ______ g mol–1. (Nearest Integer) [Given: R = 0.082 L atm K–1mol–1]
22. 17.0 g of NH3 completely vapourises at – 33.42°C and 1 bar pressure and the enthalpy change in the process is 23.4 kJ mol–1. The enthalpy change for the vapourisation of 85 g of NH3 under the same conditions is ________ kJ.
23. 1.2 mL of acetic acid is dissolved in water to make 2.0 L of solution. The depression in freezing point observed for this strength of acid is 0.0198°C. The percentage of dissociation of the acid is ____ . (Nearest integer)
[Given: Density of acetic acid is 1.02 g mL–1
Molar mass of acetic acid is 60 g mol–1
Kf(H2O) = 1.85 K kg mol–1]
24. A dilute solution of sulphuric acid is electrolysed using a current of 0.10 A for 2 hours to produce hydrogen and oxygen gas. The total volume of gases produced at STP is ______ cm3. (Nearest integer)
[Given : Faraday constant F = 96500 C mol–1 at STP, molar volume of an ideal gas is 22.7 L mol–1]
25. The activation energy of one of the reactions in a biochemical process is 532611 J mol–1. When the temperature falls from 310 K to 300 K, the change in rate constant observed is k300 = x × 10–3 k310. The value of x is _________.
[Given: ln10 = 2.3, R = 8.3 JK–1mol–1]
26. The number of terminal oxygen atoms present in the product B obtained from the following reaction is ________.
FeCr2O4 + Na2CO3 + O2 → A + Fe2O3 + CO2
A + H+ → B + H2O + Na+
27. An acidified manganate solution undergoes disproportionation reaction. The spin-only magnetic moment value of the product having manganese in higher oxidation state is _______ B.M. (Nearest integer)
28. Kjeldahl’s method was used for the estimation of nitrogen in an organic compound. The ammonia evolved from 0.55 g of the compound neutralised 12.5 mL of 1 M H2SO4 The percentage of nitrogen in the compound is ________. (Nearest integer)
29. Observe structures of the following compounds
The total number of structures/compounds which possess asymmetric carbon atoms is _______.
30.
The number of carbon atoms present in the product B is __________.
MATHEMATICS
SECTION-A
1. The probability that a randomly chosen 2 × 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to :
(A) 133/104
(B) 18/103
(C) 19/103
(D) 271/104
2. Let the solution curve of the differential equation y(1) = 3 be y = y(x).
Then y(2) is equal to :
(A) 15
(B) 11
(C) 13
(D) 17
3. If the mirror image of the point (2, 4, 7) in the plane 3x – y + 4z = 2 is (a, b, c), then 2a + b + 2c is equal to:
(A) 54
(B) 50
(C) –60
(D) –42
4. Let f : R ⇒ R be a function defined by :
where [t] is the greatest integer less than or equal to t. Let m be the number of points where f is not differentiable and Then the ordered pair (m, I) is equal to :
(A) (3, 27/4)
(B) (3, 23/4)
(C) (4, 27/4)
(D) (4, 23/4)
5. Let and
where α, β∈ R, be three vectors. If the projection of
is 10/3 and
then the value of α + β equal to :
(A) 3
(B) 4
(C) 5
(D) 6
6. The area enclosed by y2 = 8x and y = √2x that lies outside the triangle formed by y = √2x, x = 1, y = 2√2 is equal to:
(A) 16√2/6
(B) 11√2/6
(C) 13√2/6
(D) 5√2/6
7. If the system of linear equations
2x + y – z = 7
x – 3y + 2z = 1
x + 4y + δz = k, where δ, k ∈ R
has infinitely many solutions, then δ + k is equal to:
(A) –3
(B) 3
(C) 6
(D) 9
8. Let α and β be the roots of the equation x2 + (2i – 1) = 0. Then, the value of |α2 + β2| is equal to:
(A) 50
(B) 250
(C) 1250
(D) 1500
9. Let ∆ ∈ {⋀, ⋁, ⇒, ⇔}be such that (p ⋀ q) ∆ ((p ⋁ q) ⇒ q) is a tautology. Then ∆ is equal to :
(A) ⋀
(B) ⋁
(C) ⇒
(D) ⇔
10. Let A = [aij] be a square matrix of order 3 such that aij = 2j–i, for all i, j = 1, 2, 3. Then, the matrix A2 + A3 + … + A10 is equal to :
11. Let a set A = A1⋃ A2⋃ …⋃Ak, where Ai⋂Aj = Φ for i ≠ j, 1 ≤ i, j ≤ k. Define the relation R from A to A by R = {(x, y) : y ∈ Ai if and only if x ∈ Ai, 1 ≤ i ≤ k}. Then, R is :
(A) reflexive, symmetric but not transitive
(B) reflexive, transitive but not symmetric
(C) reflexive but not symmetric and transitive
(D) an equivalence relation
12. Let be a sequence such that a0 = a1 = 0 and an+2 = 2an+1 – an + 1 for all n ≥ Then,
is equal to
(A) 6/343
(B) 7/216
(C) 8/343
(D) 49/216
13. The distance between the two points A and A′ which lie on y = 2 such that both the line segments AB and A′B (where B is the point (2, 3)) subtend angle π/4 at the origin, is equal to
(A) 10
(B) 48/5
(C) 52/5
(D) 3
14. A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is
15. The domain of the function is :
16. If the constant term in the expansion of is 2kl, where l is an odd integer, then the value of k is equal to
(A) 6
(B) 7
(C) 8
(D) 9
17. , where [t] denotes greatest integer less than or equal to t, is equal to
(A) –3
(B) –2
(C) 2
(D) 0
18. Let PQ be a focal chord of the parabola y2 = 4x such that it subtends an angle of π/2 at the point (3, 0). Let the line segment PQ be also a focal chord of the ellipse If e is the eccentricity of the ellipse E, then the value of 1/e2 is equal to
(A) 1 + √2
(B) 3 + 2√2
(C) 1 + 2√3
(D) 4 + 5√3
19. Let the tangent to the circle C1: x2 + y2 = 2 at the point M(–1, 1) intersect the circle C2: (x – 3)2 + (y – 2)2 = 5, at two distinct points A and B. If the tangents to C2 at the points A and B intersect at N, then the area of the triangle ANB is equal to
(A) 1/2
(B) 2/3
(C) 1/6
(D) 5/3
20. Let the mean and the variance of 5 observations x1, x2, x3, x4, x5 be 24/5 and 194/25, respectively. If the mean and variance of the first 4 observations are 7/2 and a, respectively, then (4a + x5) is equal to
(A) 13
(B) 15
(C) 17
(D) 18
SECTION-B
21. Let S = {z ∈C : |z – 2| ≤ 1, z(1 + i) + Let |z – 4i| attains minimum and maximum values, respectively, at z1∈ S and z2 ∈ If 5(|z1|2 + |z2|2) = α + β√5 where α and β are integers, then the value of α + β is equal to _________.
22. Let y = y(x) be the solution of the differential equation
If
then the value of 3α2 is equal to ______.
23. Let d be the distance between the foot of perpendiculars of the point P(1, 2, –1) and Q(2, –1, 3) on the plane –x + y + z = 1. Then d2 is equal to ________.
24. The number of elements in the set S = {θ∈ [−4π, 4π] : 3 cos2 2θ + 6 cos 2θ – 10 cos2θ + 5 = 0} is _________.
25. The number of solutions of the equation 2θ– cos2θ + √2 = 0 in R is equal to ___________.
26. is equal to _________.
27. Let c, k ∈ If f(x) = (c + 1)x2 + (1 – c2)x + 2k and f(x + y) = f(x) + f(y) – xy, for all x, y ∈ R, then the value of |2(f(1) + f(2) + f(3) + … + f(20))| is equal to _________.
28. Let a > 0, b > 0, be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is 4(2√2 + √14). If the eccentricity H is √11/2, then the value of a2 + b2 is equal to ____________.
29. be a plane. Let P2 be another plane which passes through the points (2, –3, 2), (2, –2, –3) and (1, –4, 2). If the direction ratios of the line of intersection of P1 and P2 be 16, α, β, then the value of α + β is equal to _______.
30. Let b1b2b3b4 be a 4-element permutation with bi{1, 2, 3,…..,100} for 1 ≤ i ≤ 4 and bi ≠ bj for i ≠ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1b2b3b4 is equal to _______.