JEE Main Session 1 27th 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. A projectile is launched at an angle ‘α’ with the horizontal with a velocity 20 ms–1. After10 s, its inclination with horizontal is ‘β’. The value of tanβ will be (g = 10 ms–2).
(A) tanα + 5secα
(B) tanα– 5secα
(C) 2tanα– 5secα
(D) 2tanα + 5secα
2. A girl standing on road holds her umbrella at 45° with the vertical to keep the rain away. Ifshe starts running without umbrella with a speed of 15√2 kmh–1, the rain drops hit herhead vertically. The speed of rain drops with respect to the moving girl is
(A) 30 kmh−1
(B)
(C)
(D) 25 kmh−1
3. A silver wire has a mass (0.6 ± 0.006) g, radius (0.5 ± 0.005) mm and length (4 ± 0.04) cm.The maximum percentage error in the measurement of its density will be
(A) 4%
(B) 3%
(C) 6%
(D) 7%
4. A system of two blocks of masses m = 2 kg and M = 8 kg is placed on a smooth table as shown in the figure. The coefficient of static friction between two blocks is 0.5. The maximum horizontal force F that can be applied to the block of mass M so that the blocks move together will be
(A) 9.8 N
(B) 39.2 N
(C) 49 N
(D) 78.4 N
5. Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates(0, 0) cm and (x, 0) cm respectively. The block of 10 kg is moved on the same line through a distance of 6 cm towards the other block. The distance through which the block of 30 kg must be moved to keep the position of centre of mass of the system unchanged is
(A) 4 cm towards the 10 kg block
(B) 2 cm away from the 10 kg block
(C) 2 cm towards the 10 kg block
(D) 4 cm away from the 10 kg block
6. A 72 Ω galvanometer is shunted by a resistance of 8 Ω. The percentage of the total current which passes through the galvanometer is
(A) 0.1%
(B) 10%
(C) 25%
(D) 0.25%
7. Given below are two statements.
Statement-I: The law of gravitation holds good for any pair of bodies in the universe.
Statement-II: The weight of any person becomes zero when the person is at the centre of the earth.
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. What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass? (Assume the collision to be head-on elastic collision)
(A) 50.0%
(B) 66.6%
(C) 55.6%
(D) 33.3%
9. The velocity of a small ball of mass ‘m’ and density d1, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is d2, then the viscous force acting on the ball, will be
10. The susceptibility of a paramagnetic material is 99. The permeability of the material in Wb/A-m, is
[Permeability of free space μ0 = 4π × 10–7Wb/A-m]
(A) 4π × 10–7
(B) 4π × 10–4
(C) 4π × 10–5
(D) 4π × 10–6
11. The current flowing through an ac circuit is given by I = 5 sin(120πt)A. How long will the current take to reach the peak value starting from zero?
(A) 1/60 s
(B) 60 s
(C) 1/120 s
(D) 1/240 s
12. Mach List-I with List – II :
Choose the correct answer from the options given below :
(A) (a)-(iii), (b)-(iv), (c)-(ii), (d)-(i)
(B) (a)-(iii), (b)-(i), (c)-(ii), (d)-(iv)
(C) (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
(D) (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
13. An α particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelengths (λα : λC12) is :
(A) 1: √3
(B) √3 : 1
(C) 3 : 1
(D) 2 : √3
14. A force of 10 N acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be
(A) 5 N
(B) 10 N
(C) 20 N
(D) Zero
15. The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is :
(A) 6 s
(B) 8 s
(C) 12 s
(D) 36 s
16. An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be:
(A) 20%
(B) 10%
(C) 5%
(D) 0%
17. Consider a light ray travelling in air is incident into a medium of refractive index √2n. The incident angle is twice that of refracting angle. Then, the angle of incidence will be:
18. A hydrogen atom in its ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of:
(Given, Planck’s constant = 6.6 × 10–34Js).
(A) 2.10 × 10–34Js
(B) 1.05 × 10–34Js
(C) 3.15 × 10–34Js
(D) 4.2 × 10–34Js
19. Identify the correct Logic Gate for the following output (Y) of two inputs A and B.
20. A mixture of hydrogen and oxygen has volume 2000 cm3, temperature 300 K, pressure 100 kPa and mass 0.76 g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be:
[Take gas constant R = 8.3 JK–1mol–1]
(A) 1/3
(B) 3/1
(C) 1/16
(D) 16/1
SECTION-B
21. In a carnot engine, the temperature of reservoir is 527°C and that of sink is 200 K. If the work done by the engine when it transfers heat from reservoir to sink is 12000 kJ, the quantity of heat absorbed by the engine from reservoir is ___ × 106
22. A 220 V, 50 Hz AC source is connected to a 25 V, 5 W lamp and an additional resistance R in series (as shown in figure) to run the lamp at its peak brightness, then the value of R (in ohm) will be ________.
23. In Young’s double slit experiment the two slits are 0.6 mm distance apart. Interference pattern is observed on a screen at a distance 80 cm from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be _____ nm.
24. A beam of monochromatic light is used to excite the electron in Li++ from the first orbit to the third orbit. The wavelength of monochromatic light is found to be x × 10−10 The value of x is ______. [Given hc = 1242 eV nm]
25. A cell, shunted by a 8 Ω resistance, is balanced across a potentiometer wire of length 3 m. The balancing length is 2 m when the cell is shunted by 4 Ω resistance. The value of internal resistance of the cell will be _______ Ω.
26. The current density in a cylindrical wire of radius 4 mm is 4 × 106 Am–2. The current through the outer portion of the wire between radial distances R/2 and R is _________π A.
27. A capacitor of capacitance 50pF is charged by 100 V source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is ________nJ.
28. The height of a transmitting antenna at the top of a tower is 25 m and that of receiving antenna is, 49 m. The maximum distance between them, for satisfactory communication in LOS (Line-Of-Sight) is K√5 × 102 The value of K is ________. [Assume radius of Earth is 64 × 10+5 m] (Calculate upto nearest integer value)
29. The area of cross-section of a large tank is 0.5 m2. It has a narrow opening near the bottom having area of cross-section 1 cm2. A load of 25 kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is 40 cm above the bottom, will be _______ cms–1. [Take g = 10 ms–2]
30. A pendulum of length 2 m consists of a wooden bob of mass 50 g. A bullet of mass 75 g is fired towards the stationary bob with a speed v. The bullet emerges out of the bob with a speed v/3 and the bob just completes the vertical circle. The value of v is ________ ms–1. (if g = 10 m/s2)
CHEMISTRY
SECTION-A
1. Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : At 10°C, the density of a 5 M solution of KCl [atomic masses of K &Cl are 39 & 35.5 g mol–1 respectively], is ‘x’ g ml–1. The solution is cooled to –21°C. The molality of the solution will remain unchanged.
Reason (R) : The molality of a solution does not change with temperature as mass remains unaffected with temperature.
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.
2. Based upon VSEPR theory, match the shape (geometry) of the molecules in List-I with the molecules in List-II and select the most appropriate option.
List-I List-II
(Shape) (Molecules)
(A) T-shaped (I) XeF4
(B) Trigonal planar (II) SF4
(C) Square planar (III) CIF3
(D) See-saw (IV) BF3
(A) (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
(B) (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
(C) (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
(D) (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
3. Match List-I with List-II
List-I
(A) Spontaneous process
(B) Process with ΔP = 0, ΔT = 0
(C) ΔHreaction
(D) Exothermic Process
List-II
(I) ΔH < 0
(II) ΔGT,P< 0
(III) Isothermal and isobaric process
(IV) [Bond energies of molecules in reactants] – [Bond energies of product molecules]
Choose the correct answer from the options given below :
(A) (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
(B) (A)-(II), (B)-(III), (C)-(IV), (D)-(I)
(C) (A)-(II), (B)-(III), (C)-(I), (D)-(IV)
(D) (A)-(II), (B)-(I), (C)-(III), (D)-(IV)
4. Match List-I with List-II
List-I List-II
(A) Lyophilic colloid (I) Liquid-liquid colloid
(B) Emulsion (II) Protective colloid
(C) Positively charged (III)FeCl3+NaOHcolloid
(D) Negatively charged (IV)FeCl3+hotwatercolloid
Choose the correct answer from the options given below :
(A) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
(B) (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
(C) (A)-(II), (B)-(I), (C)-(III), (D)-(IV)
(D) (A)-(III), (B)-(II), (C)-(I), (D)-(IV)
5. Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The ionic radii of O2– and Mg2+ are same.
Reason (R) : Both O2– and Mg2+ are isoelectronic species.
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.
6. Match List-I with List-II.
List-I List-II
(A) Concentration of (I) AnilineGold ore
(B) Leaching of alumina (II) NaOH
(C) Froth stabiliser (III) SO2
(D) Blister copper (IV) NaCN
Choose the correct answer from the options given below.
(A) (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
(B) (A)-(IV), (B)-(II), (C)-(I), (D)-(III)
(C) (A)-(III), (B)-(II), (C)-(I), (D)-(IV)
(D) (A)-(II), (B)-(IV), (C)-(III), (D)-(I)
7. Addition of H2SO4 to BaO2 produces:
(A) BaO, SO2 and H2O
(B) BaHSO4 and O2
(C) BaSO4, H2 and O2
(D) BaSO4 and H2O2
8. BeCI2 reacts with LiAIH4 to give:
(A) Be + Li[AICI4] + H2
(B) Be + AIH3 + LiCI + HCI
(C) BeH2 + LiCI + AICI3
(D) BeH2 + Li[AICI4]
9. Match List-I with List-II
Choose the correct answer from the options given below:
(A) (A)-(III), (B)-(II), (C)-(I), (D)-(IV)
(B) (A)-(IV), (B)-(I), (C)-(II), (D)-(III)
(C) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
(D) (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
10. Heating white phosphorus with conc. NaOH solution gives mainly:
(A) Na3P and H2O
(B) H3PO and NaH
(C) P(OH)3 and NaH2PO4
(D) PH3 and NaH2PO2
11. Which of the following will have maximum stabilization due to crystal field?
(A) [Ti(H2O)6]3+
(B) [Co(H2O)6]2+
(C) [Co(CN)6]–3
(D) [Cu(NH3)4]2+
12. Given below are two Statements:
Statement I: Classical smog occurs in cool humid climate. It is a reducing mixture of smoke, fog and sulphur dioxide.
Statement II: Photochemical smog has components, ozone, nitric oxide, acrolein, formaldehyde, PAN etc.
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
13. Which of the following is structure of a separating funnel?
14. ‘A’ and ‘B’ respectively are:
(A) 1-methylcyclohex-1, 3-diene &cyclopentene
(B) Cyclohex-1, 3-diene &cyclopentene
(C) 1-methylcyclohex-1, 4-diene & 1-methylcyclo-pent-ene
(D) Cyclohex-1, 3-diene & 1-methylcyclopent-1-ene
15. The major product of the following reaction is:
16. Which of the following reactions will yield benzaldehyde as a product?
(A) (B) and (C)
(B) (C) and (D)
(C) (A) and (D)
(D) (A) and (C)
17. Given below are two statements:
Statement-I : In Hofmann degradation reaction, the migration of only an alkyl group takes place from carbonyl carbon of the amide to the nitrogen atom.
Statement-II : The group is migrated in Hofmann degradation reaction to electron deficient atom.
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
18. 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) –(I) (B) – (II), (C) – (III), (D) – (IV)
(C) (A) –(IV) (B) – (III), (C) – (II), (D) – (I)
(D) (A) –(II) (B) – (III), (C) – (I), (D) – (IV)
19. L-isomer of a compound ‘A’ (C4H8O4) gives a positive test with [Ag(NH3)2]+. Treatment of ‘A’ with acetic anhydride yields triacetate derivative. Compound ‘A’ produces an optically active compound (B) and an optically inactive compound (C) on treatment with bromine water and HNO3 Compound (A) is:
20. Match List-I with List-II
List-II
(I) Dishwashing power
(II) Toothpaste
(III) Laundry soap
(IV) Hair conditional
Choose the correct answer from the options given below:
(A) (A) –(III) (B) – (II), (C) – (IV), (D) – (I)
(B) (A) –(IV) (B) – (II), (C) – (III), (D) – (I)
(C) (A) –(IV) (B) – (III), (C) – (II), (D) – (I)
(D) (A) –(III) (B) – (IV), (C) – (I), (D) – (II)
SECTION-B
21. Metal deficiency defect is shown by Fe93O. In the crystal, some Fe2+cations are missing and loss of positive charge is compensated by the presence of Fe3+ ions. The percentage of Fe2+ ions in the Fe0.93O crystals is ______. (Nearest integer)
22. If the uncertainty in velocity and position of a minute particle in space are, 2.4 × 10–26 (m s–1) and 10–7 (m), respectively. The mass of the particle in g is ________. (Nearest integer)
(Given : h = 6.626 × 10–34Js)
23. 2 g of a non-volatile non-electrolyte solute is dissolved in 200 g of two different solvents A and B whose ebullioscopic constants are in the ratio of 1 : 8. The elevation in boiling points of A and B are in the ratio The value of y is ______. (Nearest Integer)
24. 2NOCl(g) ⇌ 2NO(g) + Cl2(g)
In an experiment, 2.0 moles of NOCl was placed in a one-litre flask and the concentration of NO after equilibrium established, was found to be 0.4 mol/ L. The equilibrium constant at 30°C is ________ × 10–4.
25. The limiting molar conductivities of NaI, NaNO3 and AgNO3 are 12.7, 12.0 and 13.3 mS m2mol–1, respectively (all at 25°C). The limiting molar conductivity of Agl at this temperature is ________ mS m2mol–1.
26. The rate constant for a first order reaction is given by the following equation :
The activation energy for the reaction is given by ______ kJ mol–1. (In nearest integer)
(Given : R = 8.3 J K–1mol–1)
27. The number of statement(s) correct from the following for Copper (at. no. 29) is/are ______.
(A) Cu(II) complexes are always paramagnetic
(B) Cu(I) complexes are generally colourless
(C) Cu(I) is easily oxidized
(D) In Fehling solution, the active reagent has Cu(I)
28. Acidified potassium permanganate solution oxidises oxalic acid. The spin-only magnetic moment of the manganese product formed from the above reaction is ______ B.M. (Nearest Integer)
29. Two elements A and B which form 0.15 moles of A2B and AB3 type compounds. If both A2B and AB3 weigh equally, then the atomic weight of A is _____ times of atomic weight of B.
30. Total number of possible stereoisomers of dimethyl cyclopentane is _______.
MATHEMATICS
SECTION-A
1. The area of the polygon, whose vertices are the non-real roots of the equation is :
(A) 3√3/4
(B) 3√3/2
(C) 3/2
(D) 3/4
2. Let the system of linear equations x + 2y + z = 2, αx + 3y – z = α, –αx + y + 2z = –α be inconsistent. Then α is equal to :
(A) 5/2
(B) −5/2
(C) 7/2
(D) −7/2
3. If where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, abc ≠ 0,
(A) x, y, zare in A.P.
(B) x, y, zare in G.P.
(C) 1/x, 1/y, 1/z are in A.P.
(D)
4. Let where a, b, c are constants, represent a circle passing through the point (2, 5). Then the shortest distance of the point (11, 6) from this circle is
(A) 10
(B) 8
(C) 7
(D) 5
5. Let a be an integer such that exists, where [t] is greatest integer ≤ t. Then a is equal to :
(A) −6
(B) −2
(C) 2
(D) 6
6. The number of distinct real roots of x4 – 4x + 1 = 0 is :
(A) 4
(B) 2
(C) 1
(D) 0
7. The lengths of the sides of a triangle are 10 + x2, 10 + x2 and 20 – 2x2. If for x = k, the area of the triangle is maximum, then 3k2 is equal to :
(A) 5
(B) 8
(C) 10
(D) 12
8. If then:
(A) x2y′′ + xy′ – 25y = 0
(B) x2y′′ – xy′ – 25y = 0
(C) x2y′′ – xy′+ 25y = 0
(D) x2y′′ + xy′+ 25y = 0
9. where C is a constant, then
at x = 1 is equal to :
(A) −3/4
(B) 3/4
(C) −3/2
(D) 3/2
10. The value of the integral is equal to:
(A) 5e2
(B) 3e−2
(C) 4
(D) 6
11. If x, y > 0, y(1) = 1, then y(2) is equal to :
(A) 2 + log2 3
(B) 2 + log3 2
(C) 2 – log3 2
(D) 2 – log2 3
12. In an isosceles triangle ABC, the vertex A is (6, 1) and the equation of the base BC is 2x + y = 4. Let the point B lie on the line x + 3y = 7. If (α, β) is the centroid of ΔABC, then 15(α + β) is equal to :
(A) 39
(B) 41
(C) 51
(D) 63
13. Let the eccentricity of an ellipse a > b, be 1/4. If this ellipse passes through the point
then a2 + b2 is equal to :
(A) 29
(B) 31
(C) 32
(D) 34
14. If two straight lines whose direction cosines are given by the relations l + m – n = 0, 3l2 + m2 + cnl = 0 are parallel, then the positive value of c is :
(A) 6
(B) 4
(C) 3
(D) 2
15. Let Then the number of vectors
and
is:
(A) 0
(B) 1
(C) 2
(D) 3
16. Five numbers, x1, x2, x3, x4, x5 are randomly selected from the numbers 1, 2, 3,….., 18 and are arranged in the increasing order (x1 < x2< x3< x4< x5). The probability that x2 = 7 and x4 = 11 is:
(A) 1/136
(B) 1/72
(C) 1/68
(D) 1/34
17. Let X be a random variable having binomial distribution B(7, p). If P(X = 3) = 5P(X = 4), then the sum of the mean and the variance of X is:
(A) 105/16
(B) 7/16
(C) 77/36
(D) 49/16
18. The value of is equal to:
(A) −1
(B) −1/2
(C) −1/3
(D) −1/4
19. is equal to:
(A) 11π/12
(B) 17π/12
(C) 31π/12
(D) −3π/4
20. The boolean expression (~(p ∧q)) ∨q is equivalent to:
(A) q→ (p ∧q)
(B) p→q
(C) p→ (p→q)
(D) p→ (p∨q)
SECTION-B
21. Let f : R → R be a function defined by Then
is equal to _______.
22. If the sum of all the roots of the equation is logep, then p is equal to ________.
23. The positive value of the determinant of the matrix A, whose is _______.
24. The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is _________.
25. If the coefficient of x10 in the binomial expansion of where l, k∈N and l is co-prime to 5, then k is equal to ___________.
26. Let
A1 = {(x, y) : |x| ≤ y2, |x| + 2y ≤ 8} and
A2 = {(x, y) : |x| + |y| ≤ k}. If 27 (Area A1) = 5 (Area A2), then k is equal to :
27. If the sum of the first ten terms of the series where m and n are co-prime numbers, then m + n is equal to __________.
28. A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is
2x – y + 4 = 0, then the area of R is ________.
29. A circle of radius 2 unit passes through the vertex and the focus of the parabola y2 = 2x and touches the parabola where α > 0. Then (4α – 8)2 is equal to ___________.
30. Let the mirror image of the point (a, b, c) with respect to the plane 3x – 4y + 12z + 19 = 0 be (a – 6, β, γ). If a + b + c = 5, then 7β – 9γ is equal to __________.