JEE Main 2022 Session 1 June 24 Shift 1
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.
PHYSICS
SECTION-A
1. The bulk modulus of a liquid is 3 × 1010 Nm−2. The pressure required to reduce the volume of liquid by 2% is :
(A) 3 × 108 Nm−2
(B) 9 × 108 Nm−2
(C) 6 × 108 Nm−2
(D) 12 × 108 Nm−2
2. Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle.
Reason (R) : Moving charged particle experiences magnetic force perpendicular to its direction of motion.
(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.
3. Two identical cells each of emf 1.5 V are connected in parallel across a parallel combination of two resistors each of resistance 20Ω. A voltmeter connected in the circuit measures 1.2 V. The internal resistance of each cell is
(A) 2.5Ω
(B) 4Ω
(C) 5Ω
(D) 10Ω
4. Identify the pair of physical quantities which have different dimensions :
(A) Wave number and Rydberg’s constant
(B) Stress and Coefficient of elasticity
(C) Coercivity and Magnetisation
(D) Specific heat capacity and Latent heat
5. A projectile is projected with velocity of 25 m/s at an angle θ with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of θ will be : [use g = 10 m/s2]
6. A block of mass 10 kg starts sliding on a surface with an initial velocity of 9.8 ms−1. The coefficient of friction between the surface and bock is 0.5. The distance covered by the block before coming to rest is : [use g = 9.8 ms−2]
(A) 4.9 m
(B) 9.8 m
(C) 12.5 m
(D) 19.6 m
7. A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N. If the maximum speed with which the stone can revolve is A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N. If the maximum speed with which the stone can revolve is
(A) 400
(B) 300
(C) 600
(D) 800
8. A vertical electric field of magnitude 4.9 × 105 N/C just prevents a water droplet of a mass 0.1 g from falling. The value of charge on the droplet will be : (Given g = 9.8 m/s2)
(A) 1.6 × 10−9 C
(B) 2.0 × 10−9 C
(C) 3.2 × 10−9 C
(D) 0.5 × 10−9 C
9. A particle experiences a variable force in a horizontal x-y plane. Assume distance in meters and force is newton. If the particle moves from point (1, 2) to point (2, 3) in the x-y plane, the Kinetic Energy changes by
(A) 50.0 J
(B) 12.5 J
(C) 25.0 J
(D) 0 J
10. The approximate height from the surface of earth at which the weight of the body becomes 1/3 of its weight on the surface of earth is : [Radius of earth R = 6400 km and √3 = 1.732]
(A) 3840 km
(B) 4685 km
(C) 2133 km
(D) 4267 km
11. A resistance of 40 Ω is connected to a source of alternating current rated 220 V, 50 Hz. Find the time taken by the current to change from its maximum value to rms value :
(A) 2.5 ms
(B) 1.25 ms
(C) 2.5 s
(D) 0.25 s
12. The equations of two waves are given by :
y1 = 5 sin2π(x – vt) cm
y2 = 3sin2π(x – vt + 1.5)cm
These waves are simultaneously passing through a string. The amplitude of the resulting wave is
(A) 2 cm
(B) 4 cm
(C) 5.8 cm
(D) 8 cm
13. A plane electromagnetic wave travels in a medium of relative permeability 1.61 and relative permittivity 6.44. If magnitude of magnetic intensity is 4.5 × 10−2 Am−1 at a point, what will be the approximate magnitude of electric field intensity at that point ?
(Given : permeability of free space μ0 = 4π × 10−7 NA−2, speed of light in vacuum c = 3 × 108 ms−1)
(A) 16.96 Vm−1
(B) 2.25 × 10−2 Vm−1
(C) 8.48 Vm−1
(D) 6.75 × 106 Vm−1
14. Choose the correct option from the following options given below :
(A) In the ground state of Rutherford’s model electrons are in stable equilibrium. While in Thomson’s model electrons always experience a net-force.
(B) In the ground state of Rutherford’s model electrons are in stable equilibrium. While in Thomson’s model electrons always experience a net-force.
(C) A classical atom based on Rutherford’s model is doomed to collapse.
(D) The positively charged part of the atom possesses most of the mass in Rutherford’s model but not in Thomson’s model.
15. Nucleus A is having mass number 220 and its binding energy per nucleon is 5.6 MeV. It splits in two fragments ‘B’ and ‘C’ of mass numbers 105 and 115. The binding energy of nucleons in ‘B’ and ‘C’ is 6.4 MeV per nucleon. The energy Q released per fission will be :
(A) 0.8 MeV
(B) 275 MeV
(C) 220 MeV
(D) 176 MeV
16. A baseband signal of 3.5 MHz frequency is modulated with a carrier signal of 3.5 GHz frequency using amplitude modulation method. What should be the minimum size of antenna required to transmit the modulated signal ?
(A) 42.8 m
(B) 42.8 mm
(C) 21.4 mm
(D) 21.4 m
17. A Carnot engine whose heat sinks at 27°C, has an efficiency of 25%. By how many degrees should the temperature of the source be changed to increase the efficiency by 100% of the original efficiency ?
(A) Increases by 18°C
(B) Increase by 200°C
(C) Increase by 120°C
(D) Increase by 73°
18. A parallel plate capacitor is formed by two plates each of area 30π cm2 separated by 1 mm. A material of dielectric strength 3.6 × 107 Vm−1 is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is 7 × 10−6 C, the value of dielectric constant of the material is :
(A) 1.66
(B) 1.75
(C) 2.25
(D) 2.33
19. The magnetic field at the centre of a circular coil of radius r, due to current I flowing through it, is B. The magnetic field at a point along the axis at a distance r/2 from the centre is :
(A) B/2
(B) 2B
(C)
(D)
20. Two metallic blocks M1 and M2 of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of M2 is K then the thermal conductivity of M1 will be : [Assume steady state heat conduction]
(A) 10 K
(B) 8 K
(C) 12.5 K
(D) 2 K
SECTION-B
21. 056 kg of Nitrogen is enclosed in a vessel at a temperature of 127°C. The amount of heat required to double the speed of its molecules is _____ k cal. (Take R = 2 cal mole−1K−1)
22. Two identical thin biconvex lenses of focal length 15 cm and refractive index 1.5 are in contact with each other. The space between the lenses is filled with a liquid of refractive index 1.25. The focal length of the combination is ______ cm.
23. A transistor is used in common-emitter mode in an amplifier circuit. When a signal of 10 mV is added to the base-emitter voltage, the base current changes by 10 μA and the collector current changes by 1.5 mA. The load resistance is 5 kΩ. The voltage gain of the transistor will be _____ .
24. As shown in the figure an inductor of inductance 200 mH is connected to an AC source of emf 220 V and frequency 50 Hz. The instantaneous voltage of the source is 0 V when the peak value of current is The value of a is ______.
25. Sodium light of wavelengths 650 nm and 655 nm is used to study diffraction at a single slit of aperture 0.5 mm. The distance between the slit and the screen is 2.0 m. The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is ______ × 10−5
26. When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted election is v1. When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes v2. If v2 = x v1, the value of x will be ______.
27. From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertically downward from the same position with the same speed reaches the ground in 1.5 s. A third ball released, from the rest from the same location, will reach the ground in ________ s.
28. A ball of mass 100 g is dropped from a height h = 10 cm on a platform fixed at the top of vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance h/2. The spring constant is _______ Nm−1. (Use g = 10 ms−2)
29. In a potentiometer arrangement, a cell gives a balancing point at 75 cm length of wire. This cell is now replaced by another cell of unknown emf. If the ratio of the emf’s of two cells respectively is 3 : 2, the difference in the balancing length of the potentiometer wire in above two cases will be ______ cm.
30. A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the other at the 10.0 cm mark the scale is found to be balanced at 40.0 cm mark. The mass of the metre scale is found to be x × 10−2 The value of x is _________.
CHEMISTRY
SECTION-A
1. A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the other at the 10.0 cm mark the scale is found to be balanced at 40.0 cm mark. The mass of the metre scale is found to be x × 10−2 The value of x is
(A) 1188 g and 1296 g
(B) 2376 g and 2592 g
(C) 2592 g and 2376 g
(D) 3429 g and 3142 g
2. Consider the following pairs of electrons
The pairs of electron present in degenerate orbitals is/are:
(A) Only A
(B) Only B
(C) Only C
(D) (B) and (C)
3. Match List-I with List-II
(A) (A)→(II), (B) → (IV), (C) → (I), (D) → (III)
(B) (A) → (III), (B) → (IV), (C) → (I), (D) → (II)
(C) (A) → (III), (B) → (I), (C) → (IV), (D) → (II)
(D) (A) → (II), (B) → (I), (C) → (IV), (D) → (III)
4. For a reaction at equilibrium
the relation between dissociation constant (K), degree of dissociation (α) and equilibrium pressure (p) is given by :
5. Given below are two statements :
Statement I : Emulsions of oil in water are unstable and sometimes they separate into two layers on standing.
Statement II :For stabilisation of an emulsion, excess of electrolyte is added. In the light of the above statements, choose the most appropriate 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.
6. Given below are the oxides:
Na2O, As2O3, N2O, NO and Cl2O7
Number of amphoteric oxides is:
(A) 0
(B) 1
(C) 2
(D) 3
7. Match List – I with List – II
Choose the most appropriate answer from the options given below:
(A) (A) – (IV), (B) – (III), (C) – (II), (D) – (I)
(B) (A) – (IV), (B) – (I), (C) – (II), (D) – (III)
(C) (A) – (II), (B) – (III), (C) – (I), (D) – (IV)
(D) (A) – (III), (B) – (IV), (C) – (II), (D) – (I)
8. The highest industrial consumption of molecular hydrogen is to produce compounds of element:
(A) Carbon
(B) Nitrogen
(C) Oxygen
(D) Chlorine
9. Which of the following statements are correct ?
(A) Both LiCl and MgCl2 are soluble in ethanol.
(B) The oxides Li2O and MgO combine with excess of oxygen to give superoxide.
(C) LiF is less soluble in water than other alkali metal fluorides.
(D) Li2O is more soluble in water than other alkali metal oxides.
Choose the most appropriate answer from the options given below:
(A) (A) and (C) only
(B) (A), C) and (D) only
(C) (B) and (C) only
(D) (A) and (C) only
10. Identify the correct statement for B2H6 from those given below.
(A) In B2H6, all B-H bonds are equivalent.
(B) In B2H6 there are four 3-centre-2-electron bonds.
(C) B2H6 is a Lewis acid.
(D) B2H6 can be synthesized form both BF3 and NaBH4.
(E) B2H6 is a planar molecule.
Choose the most appropriate answer from the options given below :
(A) (A) and (E) only
(B) (B), (C) and (E) only
(C) (C) and (D) only
(D) (C) and (E) only
11. The most stable trihalide of nitrogen is:
(A) NF3
(B) NCl3
(C) NBr3
(D) NI3
12. Which one of the following elemental forms is not present in the enamel of the teeth?
(A) Ca2+
(B) P3+
(C) F−
(D) P5+
13. In the given reactions sequence, the major product ‘C’ is :
14. Two statements are given below :
Statement I: The melting point of monocarboxylic acid with even number of carbon atoms is higher than that of with odd number of carbon atoms acid immediately below and above it in the series.
Statement II : The solubility of monocarboxylic acids in water decreases with increase in molar mass.
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.
15. Which of the following is an example of conjugated diketone?
16.
The major product of the above reaction is
17. Which of the following is an example of polyester?
(A) Butadiene-styrene copolymer
(B) Melamine polymer
(C) Neoprene
(D) Poly-β-hydroxybutyrate-co-β-hydroxy valerate
18. A polysaccharide ‘X’ on boiling with dil H2SO4 at 393 K under 2-3 atm pressure yields ‘Y’.
‘Y’ on treatment with bromine water gives gluconic acid. ‘X’ contains β-glycosidic linkages only. Compound ‘X’ is :
(A) starch
(B) cellulose
(C) amylose
(D) amylopectin
19. Which of the following is not a broad spectrum antibiotic?
(A) Vancomycin
(B) Ampicillin
(C) Ofloxacin
(D) Penicillin G
20. During the qualitative analysis of salt with cation y2+ , addition of a reagent (X) to alkaline solution of the salt gives a bright red precipitate. The reagent (X) and the cation (y2+) present respectively are:
(A) Dimethylglyoxime and Ni2+
(B) Dimethylglyoxime and Co2+
(C) Nessler‟s reagent and Hg2+
(D) Nessler‟s reagent and Ni2+
SECTION-B
21. Atoms of element X form hcp lattice and those of element Y occupy 2/3 Atoms of element X form hcp lattice and those of element Y occupy ________ (Nearest Integer)
22. 2O3(g) ⇌ 3O2(g)
At 300 K, ozone is fifty percent dissociated. The standard free energy change at this temperature and 1 atm pressure is (–) _______J mol –1 (Nearest integer) [Given: ln 1.35 = 0.3 and R = 8.3 J K–1 mol–1]
23. The osmotic pressure of blood is 7.47 bar at 300 K. To inject glucose to a patient intravenously, it has to be isotonic with blood. The concentration of glucose solution in gL–1 is _______ (Molar mass of glucose = 180 g mol–1 R = 0.083 L bar K–1 mol–1) (Nearest integer)
24. The cell potential for the following cell
Pt|H2(g)|H+(aq)||Cu2+(0.01M)|Cu(s)
is 0.576 V at 298 K. The pH of the solution is ___. (Nearest integer)
25. The rate constants for decomposition of acetaldehyde have been measured over the temperature range 700 –1000 K. The data has been analysed by plotting In k vs 103/T graph. The value of activation energy for the reaction is___ kJ mol–1. (Nearest integer) (Given : R = 8.31 J K–1 mol–1)
26. The difference in oxidation state of chromium in chromate and dichromate salts is _______
27. In the cobalt-carbonyl complex: [Co2(CO)8], number of Co-Co bonds is “X” and terminal CO ligands is “Y”. X + Y =______
28. A 0.166 g sample of an organic compound was digested with cone. H2SO4 and then distilled with NaOH. The ammonia gas evolved was passed through 50.0 mL of 0.5 N H2SO4. The used acid required 30.0 mL of 0.25 N NaOH for complete neutralization. The mass percentage of nitrogen in the organic compound is____.
29. Number of electrophilic centre in the given compound is _______
30. The major product ‘A’ of the following given reaction has _____ sp2 hybridized carbon atoms. 2,7 – Dimethyl1 – 2, 6 – octadiene
MATHEMATICS
SECTION-A
1. Let A = {z ∈ C : 1 ≤ |z – (1 + i) |≤2 and
B = {z ∈ A : | z – (1 – i) | = 1}. Then, B:
(A) is an empty set
(B) contains exactly two elements
(C) contains exactly three elements
(D) is an infinite set
2. The remainder when 32022 is divided by 5 is
(A) 1
(B) 2
(C) 3
(D) 4
3. The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds,, it becomes 7 units, then its radius after 9 seconds is :
(A) 9
(B) 10
(C) 11
(D) 12
4. Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn from it at random, are found to be 1 red and 1 black. If the probability that both balls come from Bag A is 6/11, then n is equal to _____ .
(A) 13
(B) 6
(C) 4
(D) 3
5. Let x2 + y2 + Ax + By + C = 0 be a circle passing through (0, 6) and touching the parabola y = x2 at (2, 4). Then A + C is equal to______.
(A) 16
(B) 88/5
(C) 72
(D) −8
6. The number of values of α for which the system of equations :
x + y + z = α
x + 2 αy + 3z = −1
x + 3 αy + 5z = 4
is inconsistent, is
(A) 0
(B) 1
(C) 2
(D) 3
7. If the sum of the squares of the reciprocals of the roots α and β of the equation 3x2 + λx – 1 = 0 is 15, then 6(α3 + β3) is equal to :
(A) 18
(B) 24
(C) 36
(D) 96
8. The set of all values of k for which (tan−1 x)3 + (cot−1 x)3 = kπ3, x ∈ R, is the interval:
9. Let S = {√n : 1 ≤ 1 ≤ n ≤ 50 and n is odd}
Let a ∈ S and
If then λ is equal to
(A) 218
(B) 221
(C) 663
(D) 1717
10. f(x) = 4 loge(x – 1) –2x2 + 4x +5, x > 1, which one of the following is NOT correct ?
(A) f is increasing in (1, 2) and decreasing in (2, ∞)
(B) f(x)= –1 has exactly two solutions
(C) f’(e) –f” (2) < 0
(D) f(x) = 0 has a root in the interval (e, e +1)
11. The tangent at the point (x1, y1) on the curve y = x3 +3x2 + 5 passes through the origin, then (x1, y1) does NOT lie on the curve :
12. The sum of absolute maximum and absolute minimum values of the function f(x) = |2x2 + 3x – 2| + sin x cos x in the interval [0, 1] is:
13. If where n is an even integer , is an arithmetic progression with common difference 1, and
then n is equal to:
(A) 48
(B) 96
(C) 92
(D) 104
14. If x = x(y) is the solution of the differential equation x (1) = 0; then x(e) is equal to :
(A) e3(ee – 1)
(B) ee(e3 – 1)
(C) e2(ee – 1)
(D) ee(e2 – 1)
15. Let λx – 2y = μ be a tangent to the hyperbola a2x2 – y2 = b2. Then is equal to :
(A) −2
(B) −4
(C) 2
(D) 4
16. Let be unit vectors. If
be a vector such that the angle between
is π/12, and
is equal to
(A) 6(3 – √3)
(B) 3 + √3
(C) 6(3 + √3)
(D) 6(√3 + 1)
17. If a random variable X follows the Binomial distribution B (33, p) such that 3P(X = 0) = P(X = 1), then the value of is equal to
(A) 1320
(B) 1088
(C) 120/1331
(D) 1088/1089
18. The domain of the function
19. Let If
then T + n(S) is equal
(A) 7 + √3
(B) 9
(C) 8 + √3
(D) 10
20. The number of choices of ∆ ∈ {⋀, ⋁, ⇒, ⟺}, such that (p∆q) ⇒ ((p∆~q) ⋁ ((~p)∆q)) is a tautology, is
(A) 1
(B) 2
(C) 3
(D) 4
SECTION-B
21. The number of one-one function f : {a, b, c, d} → {0, 1, 2, … .,10} such that 2f(a) – f(b) + 3f(c) + f(d) = 0 is _____.
22. In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct There are 3 marks for each correct answer, −2 marks for each wrong answer and 0 mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets 5 marks is________.
23. Let be a fixed point in the xy-plane. The image of A in y-axis be B and the image of B in x-axis be C. If D(3 cos θ, a sin θ) is a point in the fourth quadrant such that the maximum area of ∆ACD is 12 square units, then a is equal to _______.
24. Let a line having direction ratios 1, −4, 2 intersect the lines and
at the point A and B. Then (AB)2 is equal to __________.
25. The number of points where the function
[t] denotes the greatest integer ≤ t, is discontinuous is _________.
26. Let Then the value of
is __________.
27. Let If
then α1 + α2 is equal to __________
28. If two tangents drawn from a point (α, β) lying on the ellipse 25x2 + 4y2 = l to the parabola y2 = 4x are such that the slope of one tangent is four times the other, then the value of (10α + 5)2 + (16β2 + 50)2 equals __________
29. Let S be the region bounded by the curves y = x3 and y2 = x. The curve y = 2|x| divides S into two regions of areas R1 and R2.
If max {R1, R2} = R2, then R2/R1 is equal to __________.
30.If the shortest distance between the line and
then the integral value of a is equal to