JEE Main Session 1 28th June 2022 Shift-1 Question Paper and Answer Key

JEE Main Session 1 28th 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. Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity.

Reason R : Coefficient of viscosity 

Choose the correct answer from the options given below.

(A) Both A and R true, and R is 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.

Answer: (C)

2. A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k2rt2, where k is a constant. The power delivered to the particle by the force acting on it is given as

(A) Zero

(B) mk2r2t2

(C) mk2r2t

(D) mk2rt

Answer: (C)

3. Motion of a particle in x-y plane is described by a set of following equations  and y = 4sin(ωt) m. The path of the particle will be

(A) Circular

(B) Helical

(C) Parabolic

(D) Elliptical

Answer: (A)

4. Match List-I with List-II

Choose the correct answer from the options given below.

(A) A-II, B-I, C-IV, D-III

(B) A-I, B-II, C-IV, D-III

(C) A-II, B-I, C-III, D-IV

(D) A-I, B-II, C-III, D-IV

Answer: (A)

5. Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA= 2TB. These planets are revolving in the circular orbits of radii rA and rB Which out of the following would be the correct relationship of their orbits?

Answer: (C)

6. A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be

(A) 2.8 × 10–4 J

(B) 1.5 × 10–3 J

(C) 1.9 × 10–4 J

(D) 9.4 × 10–5 J

Answer: (A)

7. Given below are two statements

Statement-I: When μ amount of an ideal gas undergoes adiabatic change from state (P1, V1, T1) to state (P2, V2, T2), then work done is  and R = universal gas constant.

Statement-II: In the above case, when work is done on the gas, the temperature of the gas would rise.

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

Answer: (A)

8. Given below are two statements

Statement-I: A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive.

Statement-II: An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero.

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

Answer: (A)

9. The three charges q/2, q and q/2 are placed at the corners A, B and C of a square of side ‘a’ as shown in figure. The magnitude of electric field (E) at the corner D of the square is

Answer: (A)

10. An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface.

Choose the correct representation of magnetic field (B) as a function of radial distance (r) from the axis of cylinder.

Answer: (B)

11. A radar sends an electromagnetic signal of electric field (E0) = 2.25 V/m and magnetic field (B0) = 1.5 × 10–8 T which strikes a target on line of sight at a distance of 3 km in a medium. After that, a part of signal (echo) reflects back towards the radar with same velocity and by same path. If the signal was transmitted at time t = 0 from radar, then after how much time echo will reach to the radar?

(A) 2.0 × 10–5 s

(B) 4.0 × 10–5 s

(C) 1.0 × 10–5 s

(D) 8.0 × 10–5 s

Answer: (B)

12. The refracting angle of a prism is A and refractive index of the material of the prism is cot (A/2). Then the angle of minimum deviation will be :

(A) 180 – 2A

(B) 90 – A

(C) 180 + 2A

(D) 180 – 3A

Answer: (A)

13. The aperture of the objective is 24.4 cm. The resolving power of this telescope, if a light of wavelength 2440 Å is used to see the object will be:

(A) 8.1 × 106

(B) 10.0 × 107

(C) 8.2 × 105

(D) 1.0 × 10–8

Answer: (C)

14. The de Broglie wavelengths for an electron and a photon are λe and λp, respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two?

Answer: (A)

15. The Q-value of a nuclear reaction and kinetic energy of the projectile particle, Kp are related as :

(A) Q = Kp

(B) (Kp + Q) < 0

(C) Q <Kp

(D) (Kp + Q) > 0

Answer: (D)

16. In the following circuit, the correct relation between output (Y) and inputs A and B will be:

(A)  Y = AB

(B)  Y = A + B

(C) 

(D) 

Answer: (C)

17. For using a multimeter to identify diode from electrical components, choose the correct statement out of the following about the diode:

(A) It is two terminal device which conducts current in both directions.

(B) It is two terminal device which conducts current in one direction only

(C) It does not conduct current gives an initial deflection which decays to zero.

(D) It is three terminal device which conducts current in one direction only between central terminal and either of the remaining two terminals.

Answer: (B)

18. Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A :n-p-n transistor permits more current than a p-n-p transistor.

Reason R: Electrons have greater mobility as a charge carrier.

Choose the correct answer from the options given below:

(A) Both A and Rare true, and R is 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.

Answer: (A)

19. Match List-I with List-II.

Choose the correct answer from the options given below :

(A) A-I, B-II, C-III, D-IV

(B) A-IV, B-III, C-I, D-II

(C) A-IV, B-III, C-II, D-I

(D) A-I, B-II, C-IV, D-III

Answer: (C)

20. The velocity of sound in a gas, in which two wavelengths, 4.08 m and 4.16 m produce 40 beats in 12 s, will be:

(A) 282.8 ms–1

(B) 175.5 ms–1

(C) 353.6 ms–1

(D) 707.2 ms–1

Answer: (D)

SECTION-B

21. A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200 g. The bob is pulled aside until the string is at 60° with vertical, as shown in the figure. After releasing the bob, the maximum velocity attained by the bob will be ___ ms–1. (if g = 10 m/s2)

Answer: (5)

22. A meter bridge setup is shown in the figure. It is used to determine an unknown resistance R using a given resistor of 15 Ω. The galvanometer (G) shows null deflection when tapping key is at 43 cm mark from end A. If the end correction for end A is 2 cm, then the determined value of R will be ___ Ω.

Answer: (19)

23. Current measured by the ammeter  in the reported circuit when no current flows through 10 Ω resistance, will be ___ A.

Answer: (10)

24. An AC source is connected to an inductance of 100 mH, a capacitance of 100 μF and a resistance of 120 Ω as shown in the figure. The time in which the resistance having a thermal capacity 2 J/°C will get heated by 16°C is _______ s.

Answer: (15)

25. The position vector of 1 kg object is  and its velocity  The magnitude of its angular momentum is √x Nm where x is _________.

Answer: (91)

26. A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then.thetrolly car starts moving with velocity 2 ms–1. The velocity of the running man was ___________ms–1. when he jumps into the car.

Answer: (6)

27. A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement. as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation.tension in the string is x/5 Mg for x = _________. Neglect mass of the string and friction of the block (bigger mass) with ice slab. (Given g = acceleration due to gravity)

Answer: (6)

28. The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will be J. (Given R = 8.31 J/mol.K)

Answer: (7479)

29. A sing1y ionized magnesium atom (A24) ion is accelerated to kinetic energy 5 keV and is projected perpendicularly into a magnetic field B of the magnitude 0.5 T. The radius of path formed will be _________ cm.

Answer: (10)

30. A telegraph line of length loo km has a capacity of 0.01 µF/km and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is ________ mH. (if π = √10)

Answer: (100)

CHEMISTRY

SECTION-A

1. The incorrect statement about the imperfections in solids is :

(A) Schottky defect decreases the density of the substance.

(B) Interstitial defect increases the density of the substance.

(C) Frenkel defect does not alter the density of the substance.

(D) Vacancy defect increases the density of the substance.

Answer: (D)

2. The Zeta potential is related to which property of colloids?

(A) Colour

(B) Tyndall effect

(C) Charge on the surface of colloidal particles

(D) Brownian movement

Answer: (C)

3. Element “E” belongs to the period 4 and group 16 of the periodic table. The valence shell electron configuration of the element, which is just above “E” in the group is

(A) 3s2, 3p4

(B) 3d10, 4s2, 4p4

(C) 4d10, 5s2, 5p4

(D) 2s2, 2p4

Answer: (A)

4. Given are two statements one is labelled as Assertion A and other is labelled as Reason R.

Assertion A : Magnesium can reduce Al2O3 at a temperature below 1350°C, while above 1350°C aluminium can reduce MgO.

Reason R : The melting and boiling points of magnesium are lower than those of aluminium.

In 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 correct explanation of A.

(B) Both A and R are correct, but R is NOT the correct explanation of A.

(C) A is correct R is not correct.

(D) A is not correct, R is correct.

Answer: (B)

5. Dihydrogen reacts with CuO to give

(A) CuH2

(B) Cu

(C) Cu2O

(D) Cu(OH)2

Answer: (B)

6. Nitrogen gas is obtained by thermal decomposition of

(A) Ba(NO3)2

(B) Ba(N3)2

(C) NaNO2

(D) NaNO3

Answer: (B)

7. Given below are two statements :

Statement I: The pentavalent oxide of group-15 element, E2O5, is less acidic than trivalent oxide, E2O3, of the same element.

Statement II: The acidic character of trivalent oxide of group 15 elements, E2O3, decreases down the group.

In light of the above statements, choose most appropriate 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 true, but Statement II is false

(D) Statement I false, but Statement II is true

Answer: (D)

8. Which one of the lanthanoids given below is the most stable in divalent form?

(A) Ce (Atomic Number 58)

(B) Sm (Atomic Number 62 )

(C) Eu (Atomic Number 63)

(D) Yb (Atomic Number 70)

Answer: (C)

9. Given below are two statements:

Statement I: [Ni(CN)4]2– is square planar and diamagnetic complex, with dsp2 hybridization for Ni but [Ni(CO)4] is tetrahedral, paramagnetic and with sp3-hybridization for Ni.

Statement II: [NiCl4]2– and [Ni(CO)4] both have same d-electron configuration, have same geometry and are paramagnetic.

In 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

Answer: (B)

10. Which amongst the following is not a pesticide?

(A) DDT

(B) Organophosphates

(C) Dieldrin

(D) Sodium arsenite

Answer: (D)

11. Which one of the following techniques is not used to spot components of a mixture separated on thin layer chromatographic plate?

(A) I2 (Solid)

(B) U.V. Light

(C) Visualisation agent as a component of mobile phase

(D) Spraying of an appropriate reagent

Answer: (C)

12. Which of the following structures are aromatic in nature?

(A) A, B, C and D

(B) Only A and B

(C) Only A and C

(D) Only B, C and D

Answer: (B)

13. The major product (P) in the reaction

Answer: (C)

14. The correct structure of product ‘A’ formed in the following reaction.

Answer: (A)

15. Which one of the following compounds is inactive towards SN1 reaction?

Answer: (C)

16. Identify the major product formed in the following sequence of reactions:

Answer: (C)

17. A primary aliphatic amine on reaction with nitrous acid in cold (273 K) and there after raising temperature of reaction mixture to room temperature (298 K), gives

(A) nitrile

(B) alcohol

(C) diazonium salt

(D) secondary amine

Answer: (B)

18. Which one of the following is NOT a copolymer?

(A) Buna-S

(B) Neoprene

(C) PHBV

(D) Butadiene-styrene

Answer: (B)

19. Stability of α-Helix structure of proteins depends upon

(A) dipolar interaction

(B) H-bonding interaction

(C) van der Walls forces

(D) π-stacking interaction

Answer: (B)

20. The formula of the purple colour formed in Laissaigne’s test for sulphur using sodium nitroprusside is

(A) NaFe[Fe(CN)6]

(B) Na[Cr(NH3)2(NCS)4]

(C) Na2[Fe(CN)5(NO)]

(D) Na4[Fe(CN)5(NOS)]

Answer: (D)

SECTION-B

21. A 2.0 g sample containing MnO2 is treated with HCl liberating Cl2. The Cl2 gas is passed into a solution of KI and 60.0 mL of 0.1 M Na2S2O3 is required to titrate the liberated iodine. The percentage of MnO2 in the sample is ______. (Nearest integer)

[Atomic masses (in u) Mn = 55; Cl = 35.5; O = 16, I = 127, Na = 23, K = 39, S = 32]

Answer: (13)

22. lf the work function of a metal is 6.63 × 10–19 J, the maximum wavelength of the photon required to remove a photoelectron from the metal is ______ nm. (Nearest integer)

[Given : h = 6.63 × 10–34 J s, and c = 3 × 108 m s–1]

Answer: (300)

23. The hybridization of P exhibited in PF5 is spxdy. The value of y is _______

Answer: (1)

24. 4.0 L of an ideal gas is allowed to expand isothermally into vacuum until the total volume is 20 L. The amount of heat absorbed in this expansion is _______ L atm.

Answer: (0)

25. The vapour pressures of two volatile liquids A and B at 25°C are 50 Torr and 100 Torr, respectively. If the liquid mixture, contains 0.3 mole fraction of A, then the mole fraction of liquid B in the vapour phase is x/17. The value of x is __________.

Answer: (14)

26. The solubility product of a sparingly soluble salt A2X3 is 1.1 × 10–23. If the specific conductance of the solution is 3 × 10–5 S m–1, the limiting molar conductivity of the solution is x × 10–3 S m2mol–1. The value of x is _______.

Answer: (3)

27. The quantity of electricity of Faraday needed to reduce 1 mol of Cr2O72 to Cr3+ is _________.

Answer: (6)

28. For a first order reaction A → B, the rate constant, k = 5.5 × 10–14 s–1. The time required for 67% completion of reaction is x × 10–1 times the half life of reaction. The value of x is _____ (Nearest integer)

(Given : log 3 = 0.4771)

Answer: (16)

29. Number of complexes which will exhibit synergic bonding amongst, [Cr(CO)6], [Mn(CO)5] and [Mn2(CO)10] is ________.

Answer: (3)

30. In the estimation of bromine, 0.5 g of an organic compound gave 0.40 g of silver bromide. The percentage of bromine in the given compound is _________% (nearest integer)

(Relative atomic masses of Ag and Br are 108u and 80u, respectively).

Answer: (34)

MATHEMATICS

SECTION-A

1. If  where α ∈ R, then the value of 16α is equal to

(A)  1411

(B)  1320

(C)  1615

(D)  1855

Answer: (A)

2. Let a function f : ℕ →ℕ be defined by

then, f is

(A) One-one but not onto

(B) Onto but not one-one

(C) Neither one-one nor onto

(D) One-one and onto

Answer: (D)

3. If the system of linear equations

2x + 3y – z = –2

x + y + z = 4

x – y + |λ|z = 4λ – 4

where λ∈ R, has no solution, then

(A) λ = 7

(B) λ = –7

(C) λ = 8

(D) λ2 = 1

Answer: (B)

4. Let A be a matrix of order 3 × 3 and det (A) = 2. Then det (det (A) adj (5 adj (A3))) is equal to ______.

(A) 512 × 106

(B) 256 × 106

(C) 1024 × 106

(D) 256 × 1011

Answer: (A)

5. The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is

(A)  36

(B)  48

(C)  60

(D)  72

Answer: (D)

6. Let A1, A2, A3, … be an increasing geometric progression of positive real numbers. If A1A3A5A7 = 1/1296 and A2 + A4 = 7/36 then, the value of A6 + A8 + A10 is equal to

(A)  33

(B)  37

(C)  43

(D)  47

Answer: (C)

7. Let [t] denote the greatest integer less than or equal to t. Then, the value of the integral  is equal to

Answer: (C)

8. Let f : ℝ→ℝ be defined as

Where a, b, c ∈ ℝ and [t] denotes greatest integer less than or equal to t. Then, which of the following statements is true?

(A) There exists a, b, c ∈  such that  f iscontinuous on ∈ .

(B) If f is discontinuous at exactly one point, then a + b + c = 1

(C) If f is discontinuous at exactly one point, then a + b + c ≠ 1

(D) f is discontinuous at atleast two points, for any values of a, b and c

Answer: (C)

9. The area of the region S = {(x, y) : y2≤ 8x, y ≥ √2x, x ≥ 1} is

(A)  13√2/6

(B)  11√2/6

(C)  5√2/6

(D)  19√2/6

Answer: (B)

10. Let the solution curve y = y(x) of the differential equation  pass through the points (1, 0) and (2α, α), α > 0. Then α is equal to

Answer: (A)

11. Let y = y(x) be the solution of the differential equation  x > 1, with y(2) = − Then y (3) is equal to

(A)  −18

(B)  −12

(C)  −6

(D)  −3

Answer: (A)

12. The number of real solutions of x7 + 5x3 + 3x + 1 = 0 is equal to ______.

(A)  0

(B)  1

(C)  3

(D)  5

Answer: (B)

13. Let the eccentricity of the hyperbola  and length of its latus rectum be 6√2, If y = 2x + c is a tangent to the hyperbola H. then the value of c2 is equal to

(A)  18

(B)  20

(C)  24

(D)  32

Answer: (B)

14. If the tangents drawn at the points O(0, 0) and P(1 + √5, 2) on the circle x2 + y2 – 2x – 4y = 0 intersect at the point Q, then the area of the triangle OPQ is equal to

Answer: (C)

15. If two distinct points Q, R lie on the line of intersection of the planes –x + 2y – z = 0 and 3x – 5y + 2z = 0 and PQ = PR = √18 where the point P is (1, –2, 3), then the area of the triangle PQR is equal to

Answer: (B)

16. The acute angle between the planes P1 and P2, when P1 and P2 are the planes passing through the intersection of the planes 5x + 8y + 13z – 29 = 0 and 8x – 7y + z – 20 = 0 and the points (2, 1, 3) and (0, 1, 2), respectively, is

(A)  π/3

(B)  π/4

(C)  π/6

(D)  π/12

Answer: (A)

17. Let the plane  contain the line of intersection of two planes  and  If the plane P passes through the point (2, 3, 1/2), then the value of  is equal to

(A)  90

(B)  93

(C)  95

(D)  97

Answer: (B)

18. The probability, that in a randomly selected 3-digit number at least two digits are odd, is

(A)  19/36

(B)  15/36

(C)  13/36

(D)  23/36

Answer: (A)

19. Let AB and PQ be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q, which are feet of these two poles. Let π/8 and θ be the angles of elevation from C to P and A, respectively. If the height of pole PQ is twice the height of pole AB, then tan2θ is equal to

Answer: (C)

20. Let p, q, r be three logical statements. Consider the compound statements

S1 : ((~p) ∨q) ∨ ((~p) ∨r) and

S2 :p→ (q∨r)

Then, which of the following is NOT true?

(A) If S2 is True, then S1 is True

(B) If S2is False, then S1 is False

(C) If S2 is False, then S1 is True

(D) If S1 is False, then S2 is False

Answer: (C)

SECTION-B

21. Let R1 and R2 be relations on the set {1, 2, ….., 50} such that R1 ={(p, pn) :p is a prime and n ≥ 0 is an integer} and R2 = {(p, pn) : p is a prime and n = 0 or 1}. Then, the number of elements in R1 – R2 is ______.

Answer: (8)

22. The number of real solutions of the equation e4x + 4e3x – 58e2x + 4ex + 1 = 0 is _____.

Answer: (2)

23. The mean and standard deviation of 15 observations are found to be 8 and 3, respectively. On rechecking, it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to _______.

Answer: (7)

24. If  and  are coplanar vectors and  then 122 (c1 + c2 + c3) is equal to _________.

Answer: (150)

25. A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2 : 1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be (α, β). Then, the value of 7α + 3β is equal to ___________.

Answer: (31)

26. Let l be a line which is normal to the curve y = 2x2 + x + 2 at a point P on the curve. If the point Q(6, 4) lies on the line l and O is origin, then the area of the triangle OPQ is equal to ___________.

Answer: (13)

27. Let A = {1, a1, a2…a18, 77} be a set of integers with 1 <a1< a2<….< a18< 77. Let the set A + A = {x + y :x, y ∈ A} contain exactly 39 elements. Then, the value of a1 + a2 +…+ a18 is equal to _____.

Answer: (702)

28. The number of positive integers k such that the constant term in the binomial expansion of  is 28. ℓ, where ℓ is an odd integer, is ____________.

Answer: (2)

29. The number of elements in the set {z = a + ib∈ ℂ: a, b ∈ ℤ and 1 < |z – 3 + 2i| < 4} is _________.

Answer: (40)

30. Let the lines y + 2x = √11 + 7√7 and 2y + x = 2√11 + 6√7 be normal to a circle C: (x – h)2 + (y – k)2 = r2. If the line  is tangent to the circle C, then the value of (5h – 8k)2 + 5r2 is equal to ________.

Answer: (816)

JEE Main Session 1 27th June 2022 Shift-1 Question Paper and Answer Key

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

Answer: (B)

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 kmh1

(B) 

(C) 

(D)  25 kmh1

Answer: (C)

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%

Answer: (A)

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

Answer: (C)

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

Answer: (C)

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%

Answer: (B)

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

Answer: (A)

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%

Answer: (C)

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

Answer: (B)

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

Answer: (C)

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

Answer: (D)

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)

Answer: (A)

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

Answer: (B)

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

Answer: (A)

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

Answer: (D)

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%

Answer: (A)

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:

Answer: (D)

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

Answer: (B)

19. Identify the correct Logic Gate for the following output (Y) of two inputs A and B.

Answer: (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

Answer: (B)

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

Answer: (16)

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 ________.

Answer: (975)

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.

Answer: (450)

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 × 1010 The value of x is ______. [Given hc = 1242 eV nm]

Answer: (114)

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.

Answer: (8)

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.

Answer: (48)

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.

Answer: (125)

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)

Answer: (192)

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]

Answer: (300)

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)

Answer: (10)

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.

Answer: (A)

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)

Answer: (B)

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)

Answer: (B)

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)

Answer: (A)

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.

Answer: (D)

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)

Answer: (B)

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

Answer: (D)

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]

Answer: (C)

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)

Answer: (D)

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

Answer: (D)

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+

Answer: (C)

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

Answer: (A)

13. Which of the following is structure of a separating funnel?

Answer: (A)

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

Answer: (D)

15. The major product of the following reaction is:

Answer: (A)

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)

Answer: (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

Answer: (D)

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)

Answer: (A)

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:

Answer: (A)

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)

Answer: (B)

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)

Answer: (85)

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)

Answer: (22)

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)

Answer: (8)

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.

Answer: (125)

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.

Answer: (14)

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)

Answer: (166)

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)

Answer: (3)

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)

Answer: (6)

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.

Answer: (2)

30. Total number of possible stereoisomers of dimethyl cyclopentane is _______.

Answer: (6)

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

Answer: (A)

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

Answer: (D)

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) 

Answer: (C)

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

Answer: (B)

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

Answer: (A)

6. The number of distinct real roots of x4 – 4x + 1 = 0 is :

(A)  4

(B)  2

(C)  1

(D)  0

Answer: (B)

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

Answer: (C)

8. If  then:

(A) x2y′′ + xy′ – 25y = 0

(B) x2y′′ – xy′ – 25y = 0

(C) x2y′′ – xy′+ 25y = 0

(D) x2y′′ + xy′+ 25y = 0

Answer: (D)

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

Answer: (B)

10. The value of the integral is equal to:

(A)  5e2

(B)  3e2

(C)  4

(D)  6

Answer: (D)

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

Answer: (D)

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

Answer: (C)

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

Answer: (B)

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

Answer: (A)

15. Let  Then the number of vectors  and  is:

(A)  0

(B)  1

(C)  2

(D)  3

Answer: (A)

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

Answer: (C)

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

Answer: (C)

18. The value of  is equal to:

(A)  −1

(B)  −1/2

(C)  −1/3

(D)  −1/4

Answer: (B)

19.  is equal to:

(A)  11π/12

(B)  17π/12

(C)  31π/12

(D)  −3π/4

Answer: (A)

20. The boolean expression (~(p ∧q)) ∨q is equivalent to:

(A) q (p ∧q)

(B) pq

(C) p (pq)

(D) p (p∨q)

Answer: (D)

SECTION-B

21. Let f : R R be a function defined by Then  is equal to _______.

Answer: (99)

22. If the sum of all the roots of the equation  is logep, then p is equal to ________.

Answer: (45)

23. The positive value of the determinant of the matrix A, whose  is _______.

Answer: (14)

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 _________.

Answer: (56)

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 ___________.

Answer: (5)

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 :

Answer: (6)

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 __________.

Answer: (276)

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 ________.

Answer: (16)

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 ___________.

Answer: (63)

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 __________.

Answer: (137)

JEE Main Session 1 26th June 2022 Shift-1 Question Paper and Answer Key

JEE Main Session 1 26th June 2022 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. An expression for a dimensionless quantity P is given by  where α and β are constants, x is distance; k is Boltzmann constant and t is the temperature. Then the dimensions of α will be

(A) [M0L–1T0]

(B) [ML0T–2]

(C) [MLT–2]

(D) [ML2T–2]

Answer: (C)

2. A person is standing in an elevator. In which situation, he experiences weight loss?

(A) When the elevator moves upward with constant acceleration

(B) When the elevator moves downward with constant acceleration

(C) When the elevator moves upward with uniform velocity

(D) When the elevator moves downward with uniform velocity

Answer: (B)

3. An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?

(A) Momentum

(B) Potential Energy

(C) Acceleration

(D) Force

Answer: (A)

4. A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is α with respect to point P. Which of the following graphs represent the correct relation between A and α when ball goes from Q to R?

Answer: (C)

5. A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rad s–1 in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass m be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in rad s–1).

Answer: (C)

6. The variation of acceleration due to gravity (g) with distance (r) from the center of the earth is correctly represented by

(Given R = radius of earth)

Answer: (A)

7. The efficiency of a Carnot’s engine, working between steam point and ice point, will be

(A)  26.81%

(B)  37.81%

(C)  47.81%

(D)  57.81%

Answer: (A)

8. Time period of a simple pendulum in a stationary lift is ‘T’. If the lift accelerates with g/6 vertically upwards then the time period will be

(Where g = acceleration due to gravity)

Answer: (C)

9. A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed ν and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by

(R = universal gas constant)

Answer: (B)

10. Two capacitors having capacitance C1 and C2 respectively are connected as shown in figure. Initially, capacitor C1 is charged to a potential difference V volt by a battery. The battery is then removed and the charged capacitor C1 is now connected to uncharged capacitor C2 by closing the switch S. The amount of charge on the capacitor C2, after equilibrium, is

Answer: (A)

11. Given below two statements: One is labelled as Assertion (A) and other is labelled as Reason (R).

Assertion (A) : Non-polar materials do not have any permanent dipole moment.

Reason (R) : When a non-polar material is placed in an electric field, the centre of the positive charge distribution of it’s individual atom or molecule coincides with the centre of the negative charge distribution.

In the light of 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 and (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.

Answer: (C)

12. The magnetic flux through a coil perpendicular to its plane is varying according to the relation φ = (5t3 + 4t2 + 2t – 5) Weber. If the resistance of the coil is 5 ohm, then the induced current through the coil at t = 2 s will be,

(A) 15.6 A

(B) 16.6 A

(C) 17.6 A

(D) 18.6 A

Answer: (A)

13. An aluminium wire is stretched to make its length, 0.4% larger. The percentage change in resistance is :

(A)  0.4%

(B)  0.2%

(C)  0.8%

(D)  0.6%

Answer: (C)

14. A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is :

(A)  1:4

(B)  4:1

(C)  2:1

(D)  1:2

Answer: (C)

15. If electric field intensity of a uniform plane electro-magnetic wave is given as  Then, magnetic intensity ‘H’ of this wave in Am–1 will be :

[Given : Speed of light in vacuum c = 3 × 108ms–1, Permeability of vacuum μ0 = 4π × 10–7 NA–2]

Answer: (C)

16. In free space, an electromagnetic wave of 3 GHz frequency strikes over the edge of an object of size λ/100, where λ is the wavelength of the wave in free space. The phenomenon, which happens there will be:

(A) Reflection

(B) Refraction

(C) Diffraction

(D) Scattering

Answer: (D)

17. An electron with speed υ and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are Ee and pe and that of photon are Eph and pph respectively. Which of the following is correct?

Answer: (B)

18. How many alpha and beta particles are emitted when Uranium 92U238 decays to lead 82Pb206?

(A) 3 alpha particles and 5 beta particles

(B) 6 alpha particles and 4 beta particles

(C) 4 alpha particles and 5 beta particles

(D) 8 alpha particles and 6 beta particles

Answer: (D)

19. The I-V characteristics of a p-n junction diode in forward bias is shown in the figure. The ratio of dynamic resistance, corresponding to forward bias voltage of 2 V and 4 V respectively, is :

(A)  1 : 2

(B)  5 : 1

(C)  1 : 40

(D)  20 : 1

Answer: (B)

20. Choose the correct statement for amplitude modulation :

(A) Amplitude of modulating signal is varied in accordance with the information signal.

(B) Amplitude of modulated signal is varied in accordance with the information signal.

(C) Amplitude of carrier signal is varied in accordance with the information signal.

(D) Amplitude of modulated signal is varied in accordance with the modulating signal.

Answer: (C)

SECTION-B

21. A fighter jet is flying horizontally at a certain altitude with a speed of 200 ms–1. When it passes directly overhead an anti-aircraft gun, a bullet is fired from the gun, at an angle θ with the horizontal, to hit the jet. If the bullet speed is 400 m/s, the value of θ will be _______°.

Answer: (60)

22. A ball of mass 0.5 kg is dropped from the height of 10 m. The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is ___ m.

[Use g = 10 m/s2]

Answer: (5)

23. The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of 5 × 10–4 is ____ kJ/m3. Assume that material is elastic upto the linear strain of 5 × 10–4.

Answer: (25)

24. The elongation of a wire on the surface of the earth is 10–4 The same wire of same dimensions is elongated by 6 × 10–5 m on another planet. The acceleration due to gravity on the planet will be _________ ms–2. (Take acceleration due to gravity on the surface of earth = 10 ms–2)

Answer: (6)

25. A 10 Ω, 20 mH coil carrying constant current is connected to a battery of 20 V through a switch. Now after switch is opened current becomes zero in 100 μs. The average e.m.f. induced in the coil is __________V.

Answer: (400)

26. A light ray is incident, at an incident angle θ1, on the system of two plane mirrors M1 and M2 having an inclination angle 75° between them (as shown in figure). After reflecting from mirror M1 it gets reflected back by the mirror M2 with an angle of reflection 30°. The total deviation of the ray will be ________ degree.

Answer: (210)

27. In a vernier callipers, each cm on the main scale is divided into 20 equal parts. If tenth vernier scale division coincides with nineth main scale division. Then the value of vernier constant will be __________ ×10–2

Answer: (5)

28. As per the given circuit, the value of current through the battery will be ______ A.

Answer: (1)

29. A 110 V,50 Hz, AC source is connected in the circuit (as shown in figure). The current through the resistance 55Ω, at resonance in the circuit, will be _______ A.

Answer: (0)

30. An ideal fluid of density 800 kgm–3, flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from a to a/2. The pressure difference between the wide and narrow sections of pipe is 4100 Pa. At wider section, the velocity of fluid is  for x = ___________ (Given g = 10 m−2)

Answer: (363)

CHEMISTRY

SECTION-A

1. A commercially sold conc. HCl is 35% HCl by mass. If the density of this commercial acid is 1.46 g/mL, the molarity of this solution is :

(Atomic mass : Cl = 35.5 amu, H = 1 amu)

(A) 10.2 M

(B) 12.5 M

(C) 14.0 M

(D) 18.2 M

Answer: (C)

2. An evacuated glass vessel weighs 40.0 g when empty, 135.0 g when filled with a liquid of density 0.95 g mL–1 and 40.5 g when filled with an ideal gas at 0.82 atm at 250 K. The molar mass of the gas in g mol–1 is:

(Given : R = 0.082 L atm K–1 mol–1)

(A)  35

(B)  50

(C)  75

(D)  125

Answer: (D)

3. If the radius of the 3rd Bohr’s orbit of hydrogen atom is r3 and the radius of 4th Bohr’s orbit is r4. Then :

Answer: (B)

4. Consider the ions/molecules

For  increasing bond order the correction  option is:

Answer: (A)

5. The (∂E/∂T)P of different types of half cells are as follows:

(Where E is the electromotive force)

Which of the above half cells would be preferred to be used as reference electrode?

(A)  A

(B)  B

(C)  C

(D)  D

Answer: (C)

6. Choose the correct stability order of group 13 elements in their +1 oxidation state.

(A) Al < Ga < In < Tl

(B) Tl < In < Ga < Al

(C) Al < Ga < Tl < In

(D) Al < Tl < Ga < In

Answer: (A)

7. Given below are two statements:

Statement I: According to the Ellingham diagram, any metal oxide with higher ΔG° is more stable than the one with lower ΔG°.

Statement II: The metal involved in the formation of oxide placed lower in the Ellingham diagram can reduce the oxide of a metal placed higher in the diagram.

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.

Answer: (D)

8. Consider the following reaction:

The dihedral angle in product A in its solid phase at 110 K is :

(A) 104°

(B) 111.5°

(C) 90.2°

(D) 111.0°

Answer: (C)

9. The correct order of melting point is :

(A) Be > Mg > Ca > Sr

(B) Sr > Ca > Mg > Be

(C) Be > Ca > Mg > Sr

(D) Be > Ca > Sr > Mg

Answer: (D)

10. The correct order of melting points of hydrides of group 16 elements is:

(A) H2S < H2Se < H2Te < H2O

(B) H2O < H2S < H2Se < H2Te

(C) H2S < H2Te < H2Se < H2O

(D) H2Se < H2S < H2Te < H2O

Answer: (A)

11. Consider the following reaction:

A + alkali → B (Major Product)

If B is an oxoacid of phosphorus with no P-H bond, then A is:

(A) White P4

(B) Red P4

(C) P2O3

(D) H3PO3

Answer: (B)

12. Polar stratospheric clouds facilitate the formation of:

(A) ClONO2

(B) HOCl

(C) ClO

(D) CH4

Answer: (B)

13. Given below are two statements:

Statement I: In ‘Lassaigne’s Test’, when both nitrogen and sulphur are present in an organic compound, sodium thiocyanate is formed.

Statement II: If both nitrogen and sulphur are present in an organic compound, then the excess of sodium used in sodium fusion will decompose the sodium thiocyanate formed to give NaCN and Na2S.

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.

Answer: (A)

14. 

Consider the above reaction and identify the intermediate ‘X’

Answer: (D)

15. 

Consider the above reaction sequence and identify the product B.

Answer: (A)

16. Which will have the highest enol content?

Answer: (C)

17. Among the following structures, which will show the most stable enamine formation?

(Where Me is –CH3)

Answer: (C)

18. Which of the following sets are correct regarding polymer?

(A) Copolymer : Buna-S

(B) Condensation polymer : Nylon-6,6

(C) Fibres : Nylon-6,6

(D) Thermosetting polymer : Terylene

(E) Homopolymer : Buna-N

Choose the correct answer from given options below:

(A) (A), (B) and (C) are correct

(B) (B), (C) and (D) are correct

(C) (A), (C) and (E) are correct

(D) (A), (B) and (D) are correct

Answer: (A)

19. A chemical which stimulates the secretion of pepsin is:

(A) Anti-histamine

(B) Cimetidine

(C) Histamine

(D) Zantac

Answer: (C)

20. Which statement is not true with respect to nitrate ion test?

(A) A dark brown ring is formed at the junction of two solutions.

(B) Ring is formed due to nitroferrous sulphate complex.

(C) The brown complex is [Fe(H2O)5 (NO)]SO4.

(D) Heating the nitrate salt with conc. H2SO4, light brown fumes are evolved.

Answer: (B)

SECTION-B

21. For complete combustion of methanol

the amount of heat produced as measured by bomb calorimeter is 726 kJ mol–1 at 27°C. The enthalpy of combustion for the reaction is –x kJ mol–1, where x is _________. (Nearest integer)

(Given : R= 8.3 JK–1 mol–1)

Answer: (727)

22. A 0.5 per cent solution of potassium chloride was found to freeze at –0.24°C. The percentage dissociation of potassium chloride is ______. (Nearest integer)

(Molal depression constant for water is 1.80 K kg mol–1 and molar mass of KCl is74.6 g mol–1)

Answer: (98)

23. 50 mL of 0.1 M CH3COOH is being titrated against 0.1 M NaOH. When 25 mL of NaOH has been added, the pH of the solution will be ____ × 10–2. (Nearest integer)

(Given : pKa (CH3COOH) = 4.76)

log 2 = 0.30

log 3 = 0.48

log 5 = 0.69

log 7 = 0.84

log 11 = 1.04

Answer: (476)

24. A flask is filled with equal moles of A and B. The half lives of A and B are 100 s and 50 s respectively and are independent of the initial concentration. The time required for the concentration of A to be four times that of B is ________s.

(Given : In 2 = 0.693)

Answer: (200)

25. 2.0 g of H2 gas is adsorbed on 2.5 g of platinum powder at 300 K and 1 bar pressure. The volume of the gas adsorbed per gram of the adsorbent is _____ mL.

Answer: (9960)

26. The spin-only magnetic moment value of the most basic oxide of vanadium among V2O3, V2O4 and V2O5 is ______ B.M. (Nearest integer)

Answer: (3)

27. The spin-only magnetic moment value of an octahedral complex among CoCl3⋅4NH3, NiCl2⋅6H2O and PtCl4⋅2HCl, which upon reaction with excess of AgNO3 gives 2 moles of AgCl is _______ B.M. (Nearest Integer)

Answer: (3)

28. On complete combustion 0.30 g of an organic compound gave 0.20 g of carbon dioxide and 0.10 g of water. The percentage of carbon in the given organic compound is ______. (Nearest Integer)

Answer: (18)

29. Compound ‘P’ on nitration with dil. HNO3 yields two isomers (A) and (B) show the intramolecular and intermolecular hydrogen bonding respectively. Compound (P) on reaction with conc. HNO3 yields a yellow compound ‘C’, a strong acid. The number of oxygen atoms is present in compound ‘C’ _______

Answer: (7)

30. The number of oxygens present in a nucleotide formed from a base, that is present only in RNA is ________.

Answer: (9)

MATHEMATICS

SECTION-A

1. Let  x ∈ R – {0, −1, 1). If fn+1(x) = f(fn(x)) for all n ∈ N, then f6(6) + f7(7) is equal to:

(A)  7/6

(B)  −3/2

(C)  7/12

(D)  −11/12

Answer: (B)

2. Let 

and

Then A ∩ B is :

(A)  A portion of a circle centred at (0, −1/√3 that lies in the second and third quadrants only

(B)  a portion of a circle centred at (0, −1/√3) that lies in the second quadrant only

(C)  an empty set

(D)  a portion of a circle of radius 2/√3 that lies in the third quadrant only

Answer: (B)

3. Let A be a 3 × 3 invertible matrix. If |adj (24A)| = |adj (3 adj (2A))|, then |A|2 is equal to :

(A)  66

(B)  212

(C)  26

(D)  1

Answer: (C)

4. The ordered pair (a, b), for which the system of linear equations

3x – 2y + z = b 

5x – 8y + 9z = 3 

2x + y + az = –1 

has no solution, is :

(A)  (3, 1/3)

(B)  (−3, 1/3)

(C)  (−3, −1/3)

(D)  (3, −1/3)

Answer: (C)

5. The remainder when (2021)2023 is divided by 7 is :

(A)  1

(B)  2

(C)  5

(D)  6

Answer: (C)

6. is equal to:

(A)  √2

(B)  −√2

(C)  1/√2

(D)  −1/√2

Answer: (D)

7. g : R → R be two real valued functions defined as  where k1 and k2 are real constants. If (goƒ) is differentiable at x = 0, then (goƒ) (–4) + (goƒ) (4) is equal to :

(A)  4(e4 + 1)

(B)  2(2e4 + 1)

(C)  4e4

(D)  2(2e4 – 1)

Answer: (D)

8. The sum of the absolute minimum and the absolute maximum values of the function ƒ(x) = |3x – x2 + 2| – x in the interval [–1, 2] is :

Answer: (A)

9. Let S be the set of all the natural numbers, for which the line  is a tangent to the curve  at the point (a, b), ab ≠ 0. Then :

(A) S = ɸ

(B) n(S) = 1

(C) S = {2k : k ∈ N }

(D) S = N

Answer: (D)

10. The area bounded by the curve y = |x2 – 9| and the line y = 3 is

(A)  4(2√3 + √6 – 4)

(B)  4(4√3 + √6 – 4)

(C)  8(4√3 + 3√6 – 9)

(D)  8(4√3 + √6 – 9)

Answer: (*)

11. Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle, Then the area of ΔPQR is :

(A)  25/4√3

(B)  25√3/2

(C)  25/√3

(D)  25/2√3

Answer: (D)

12. Let C be a circle passing through the points A(2, –1) and B (3, 4). The line segment AB is not a diameter of C. If r is the radius of C and its centre lies on the circle (x – 5)2 + (y – 1)2 = 13/2, then r2 is equal to :

(A)  32

(B)  65/2

(C)  61/2

(D)  30

Answer: (B)

13. Let the normal at the point P on the parabola y2 = 6x pass through the point (5, –8). If the tangent at P to the parabola intersects its directrix at the point Q, then the ordinate of the point Q is :

(A)  −3

(B)  −9/4

(C)  −5/2

(D)  −2

Answer: (B)

14. If the two lines  z = 2 and  perpendicular, then an angle between the lines l­2 and  is :

(A)  cos1(29/4)

(B)  sec1(29/4)

(C)  cos1(2/29)

(D)  cos1(2/√29)

Answer: (B)

15. Let the plane 2x + 3y + z + 20 = 0 be rotated through a right angle about its line of intersection with the plane x – 3y + 5z = 8. If the mirror image of the point (2, −1/2, 2) in the rotated plane is B( a, b, c), then :

Answer: (A)

16. If  then the value of  is :

Answer: (A)

17. Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is:

(A)  275/65

(B)  36/54

(C)  181/55

(D)  46/64

Answer: (D)

18. The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M is equal to:

(A)  60

(B)  55

(C)  50

(D)  45

Answer: (A)

19. Let f(x) = 2cos−1 x + 4 cot−1 x – 3x2 – 2x + 10, x ∈ [−1, 1]. If [a, b] is the range of the function then 4a – b is equal to :

(A)  11

(B)  11 – π

(C)  11 + π

(D)  15 – π

Answer: (B)

20. Let, ∆, ∇ ∈ {⋀, ⋁} be such that p ∇ q ⇒ ((p ∆ q) ∇ r) is a tautology. Then (p ∇ q) ∆ r) is logically equivalent to :

(A)  (p ∆ q) ⋁ q

(B)  (p ∆ r) ⋀ q

(C)  (p ⋀ r) ∆ q

(D)  (p ∇ r) ⋀ q)

Answer: (A)

SECTION-B

21. The sum of the cubes of all the roots of the equation x4 – 3x3 –2x2 + 3x +1 = 0 is _______.

Answer: (36)

22. There are ten boys B1, B2, …, B10 and five girls G1, G2,…, G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group, is ________.

Answer: (1120)

23. Let the common tangents to the curves 4(x2 + y2) = 9 and y2 = 4x intersect at the point Q. Let an ellipse, centered at the origin O, has lengths of semi-minor and semi-major axes equal to OQ and 6, respectively. If e and I respectively denote the eccentricity and the length of the latus rectum of this ellipse, then l/e2 is equal to ________.

Answer: (4)

24. Let f(x) = max{|x + 1|, |x + 2|, …, |x + 5|}. Then  is equal to __________.

Answer: (21)

25. Let the solution curve y = y(x) of the differential equation (4 + x2)dy – 2x(x2 + 3y + 4)dx = 0 pass through the origin. Then y(2) is equal to________.

Answer: (12)

26. If sin2(10°)sin(20°)sin(40°)sin(50°)sin(70°) =  then 16 + α1 is equal to _______.

Answer: (80)

27. Let A = {n ∈ N : H.C.F. (n, 45) = 1} and Let B = {2k : k ∈ {1, 2, …, 100}}. Then the sum of all the elements of A ∩ B is __________.

 

Answer: (5264)

28. The value of the integral  is equal to ________.

Answer: (6)

29. Let  and  Then A + B is equal to ________.

Answer: (1100)

30. Let Let y = y(x), x ∈ S, be the solution curve of the differential equation  If the sum of abscissas of all the points of intersection of the curve y = y(x) with the curve  then k is equal to ___________.

Answer: (42)

JEE Main Session 1 25th June 2022 Shift-1 Question Paper and Answer Key

JEE Main 2022 Session 1 25th June 2022 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. If  then the relative error in Z will be :

Answer: (C)

2.  is a vector quantity such that  Which of the following expressions is true for

Answer: (C)

3. Which of the following relations is true for two unit vector  making an angle θ to each other?

Answer: (B)

4. If force  acts on a particle having position vector  then, the torque about the origin will be :-

Answer: (B)

5. The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be (Given g = acceleration due to gravity at the surface of earth).

(A)  g/2

(B)  g/4

(C)  g/3

(D)  g/9

Answer: (D)

6. The terminal velocity (vt) of the spherical rain drop depends on the radius (r) of the spherical rain drop as

(A)  r1/2

(B)  r

(C)  r2

(D)  r3

Answer: (C)

7. The relation between root mean square speed (vrms) and most probable speed (vp) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be

Answer: (B)

8. In the figure, a very large plane sheet of positive charge is shown. P1 and P2 are two points at distance l and 2l from the charge distribution. If σ is the surface charge density, then the magnitude of electric fields E1 and E2 and P1 and P2 respectively are

(A)  E1 = σ/ε0, E2 = σ/2ε0

(B)  E1 = 2σ/ε0, E2 = σ/ε0

(C)  E1 = E2 = σ/2ε0

(D)  E1 = E2 = σ/ε0

Answer: (C)

9. Match List-I with List-II

Choose the correct answer from the options given below:-

(A) (A) – (II), (B) – (I), (C) – (IV), (D) – (III)

(B) (A) – (II), (B) – (I), (C) – (III), (D) – (IV)

(C) (A) – (III), (B) – (IV), (C) – (II), (D) – (I)

(D) (A) – (III), (B) – (I), (C) – (II), (D) – (IV)

Answer: (A)

10. A long straight wire with a circular cross-section having radius R, is carrying a steady current I. The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance r (r < R) from its centre will be

(A)  B ∝ r2

(B)  B ∝ r

(C)  B ∝ 1/r2

(D)  B ∝ 1/r

Answer: (B)

11. If wattless current flows in the AC circuit, then the circuit is :

(A) Purely Resistive circuit

(B) Purely Inductive circuit

(C) LCR series circuit

(D) RC series circuit only

Answer: (B)

12. The electric field in an electromagnetic wave is given by E = 56.5 sinω(t – x/c) NC–1. Find the intensity of the wave if it is propagating along x-axis in the free space.

(Given ∈0 = 8.85 × 10–12C2N–1m–2)

(A)  5.65 Wm–2

(B)  4.24 Wm–2

(C)  1.9 × 10–7 Wm–2

(D)  56.5 Wm–2

Answer: (B)

13. The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is π/2 at point P and π at point Q. Then the difference between the resultant intensities at P and Q will be:

(A)  2 I

(B)  6 I

(C)  5 I

(D)  7 I

Answer: (B)

14. A light wave travelling linearly in a medium of dielectric constant 4, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be :

(Given : relative permeability of medium μr= 1)

(A)  10°

(B)  20°

(C)  30°

(D)  60°

Answer: (D)

15. Given below are two statements :

Statement I: Davisson-Germer experiment establishes the wave nature of electrons.

Statement II: If electrons have wave nature, they can interfere and show diffraction.

In the light of the above statements choose the correct answer from the option 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.

Answer: (A)

16. The ratio for the speed of the electron in the 3rd orbit of He+ to the speed of the electron in the 3rd orbit of hydrogen atom will be :

(A)  1 : 1

(B)  1 : 2  

(C)  4 : 1

(D)  2 : 1

Answer: (D)

17. The photodiode is used to detect the optical signals. These diodes are preferably operated in reverse biased mode because :

(A) fractional change in majority carriers produce higher forward bias current

(B) fractional change in majority carriers produce higher reverse bias current

(C) fractional change in minority carriers produce higher forward bias current

(D) fractional change in minority carriers produce higher reverse bias current

Answer: (D)

18. A signal of 100 THz frequency can be transmitted with maximum efficiency by :

(A) Coaxial cable

(B) Optical fibre

(C) Twisted pair of copper wires

(D) Water

Answer: (B)

19. The difference of speed of light in the two media A and B(vA – vB) is 2.6 × 107 m/s. If the refractive index of medium B is 1.47, then the ratio of refractive index of medium B to medium A is: (Given: speed of light in vacuum C = 3 × 108ms–1)

(A)  1.303

(B)  1.318

(C)  1.13

(D)  0.12

Answer: (C)

20. A teacher in his physics laboratory allotted an experiment to determine the resistance (G) of a galvanometer. Students took the observations for 1/3 deflection in the galvanometer. Which of the below is true for measuring value of G?

(A)  1/3 deflection method cannot be used for determining the resistance of the galvanometer.

(B)  1/3 deflection method can be used and in this case the G equals to twice the value of shunt resistance(s)

(C)  1/3 deflection method can be used and in this case, the G equals to three times the value of shunt resistance(s)

(D)  1/3 deflection method can be used and in this case the G value equals to the shunt resistance(s)

Answer: (B)

SECTION-B

21. A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the maximum length of the chain hanging from the table is __________m.

Answer: (2)

22. A 0.5 kg block moving at a speed of 12 ms–1 compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be ___ Nm–1.

Answer: (600)

23. The velocity of upper layer of water in a river is 36 kmh–1. Shearing stress between horizontal layers of water is 10–3 Nm–2. Depth of the river is _____________ m. (Co-efficient of viscosity of water is 10–2s)

Answer: (100)

24. A steam engine intakes 50 g of steam at 100°C per minute and cools it down to 20°C. If latent heat of vaporization of steam is 540 cal g–1, then the heat rejected by the steam engine per minute is ___________ × 103

(Given : specific heat capacity of water : 1 cal g–1 °C–1)

Answer: (31)

25. The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm. The length of the open organ pipe is __________ cm.

Answer: (80)

26. The equivalent capacitance between points A and B in below shown figure will be _______μF.

Answer: (6)

27. A resistor develops 300 J of thermal energy in 15 s, when a current of 2 A is passed through it. If the current increases to 3 A, the energy developed in 10 s is _______ J.

Answer: (450)

28. The total current supplied to the circuit as shown in figure by the 5 V battery is _________A.

Answer: (2)

29. The current in a coil of self-inductance 2.0 H is increasing according to I = 2sin(t2)A. The amount of energy spent during the period when current changes from 0 to 2A is _______ J.

Answer: (4)

30. A force on an object of mass 100 g is  The position of that object at t = 2s is  after starting from rest. The value of a/b will be _________

Answer: (2)

CHEMISTRY

SECTION-A

1. Bonding in which of the following diatomic molecule(s) become(s) stronger, on the basis of MO Theory, by removal of an electron?

(A) NO

(B) N2

(C) O2

(D) C2

(E) B2

Choose the most appropriate answer from the options given below :

(A) (A), (B), (C) only

(B) (B), (C), (E) only

(C) (A), (C) only

(D) (D) only

Answer: (C)

2. Incorrect statement for Tyndall effect is :

(A) The refractive indices of the dispersed phase and the dispersion medium differ greatly in magnitude.

(B) The diameter of the dispersed particles is much smaller than the wavelength of the light used.

(C) During projection of movies in the cinemas hall, Tyndall effect is noticed.

(D) It is used to distinguish a true solution from a colloidal solution.

Answer: (B)

3. The pair, in which ions are isoelectronic with Al3+ is:

(A) Br and Be2+

(B) Cl and Li+

(C) S2– and K+

(D) O2– and Mg2+

Answer: (D)

4. Leaching of gold with dilute aqueous solution of NaCN in presence of oxygen gives complex [A], which on reaction with zinc forms the elemental gold and another complex [B]. [A] and [B], respectively are :

(A) [Au(CN)4] and [Zn(CN)2 (OH)2]2−

(B) [Au(CN)2] and [Zn (OH)4]2−

(C) [Au(CN)2] and [Zn (CN)4]2−

(D) [Au(CN)4]2− and [Zn (CN)6]4−

Answer: (C)

5. Number of electron deficient molecules among the following PH3, B2H6, CCl4, NH3, LiH and BCl3 is

(A)  0

(B)  1

(C)  2

(D)  3

Answer: (C)

6. Which one of the following alkaline earth metal ions has the highest ionic mobility in its aqueous solution?

(A)  Be2+

(B)  Mg2+

(C)  Ca2+

(D)  Sr2+

Answer: (D)

7. White precipitate of AgCI dissolves in aqueous ammonia solution due to formation of:

(A)  [Ag(NH3)4]CI2

(B)  [Ag(CI)2(NH3)2]

(C)  [Ag(NH3)2]CI

(D)  [Ag(NH3)CI]CI

Answer: (C)

8. Cerium (IV) has a noble gas configuration. Which of the following is correct statement about it?

(A) It will not prefer to undergo redox reactions.

(B) It will prefer to gain electron and act as an oxidizing agent

(C) It will prefer to give away an electron and behave as reducing agent

(D) It acts as both, oxidizing and reducing agent.

Answer: (B)

9. Among the following which is the strongest oxidizing agent?

(A)  Mn3+

(B)  Fe3+

(C)  Ti3+

(D)  Cr3+

Answer: (A)

10. The eutrophication of water body results in:

(A) loss of Biodiversity.

(B) breakdown of organic matter.

(C) increase in biodiversity.

(D) decrease in BOD.

Answer: (A)

11. Phenol on reaction with dilute nitric acid, gives two products. Which method will be most efficient for large scale separation?

(A) Chromatographic separation

(B) Fractional crystallisation

(C) Steam distillation

(D) Sublimation

Answer: (C)

12. In the following structures, which one is having staggered conformation with maximum dihedral angle?

Answer: (C)

13. The products formed in the following reaction.

Answer: (B)

14. The IUPAC name of ethylidene chloride is:

(A) 1-Chloroethene

(B) 1-Chloroethyne

(C) 1, 2-Dichloroethane

(D) 1, 1-Dichloroethane

Answer: (D)

15. The major product in the reaction

(A) t-Butyl ethyl ether

(B) 2, 2-Dimethyl butane

(C) 2-Methyl pent-1-ene

(D) 2-Methyl prop-1-ene

Answer: (D)

16. The intermediate X, in the reaction :

Answer: (C)

17. In the following reaction:

The compound A and B respectively are:

Answer: (C)

18. The reaction of with bromine and KOH gives RNH2 as the end product. Which one of the following is the intermediate product formed in this reaction?

Answer: (C)

19. Using very little soap while washing clothes, does not serve the purpose of cleaning of clothes, because:

(A) soap particles remain floating in water as ions.

(B) the hydrophobic part of soap is not able to take away grease.

(C) the micelles are not formed due to concentration of soap, below its CMC value.

(D) colloidal structure of soap in water is completely distributed.

Answer: (C)

20. Which one of the following is an example of artificial sweetner?

(A)  Bithional

(B)  Alitame

(C)  Salvarsan

(D)  Lactose

Answer: (B)

SECTION-B

21. The number of N atoms in 681 g of C7H5N3O6 is x × 1021. The value of x is ______. (NA = 6.02 × 1023 mol–1) (Nearest Integer)

Answer: (5418)

22. The distance between Na+ and Cl ions in solid NaCl of density 43.1 g cm–3 is ____ × 10–10 (Nearest Integer)

(Given : NA = 6.02 × 1023 mol–1)

Answer: (1)

23. The longest wavelength of light that can be used for the ionisation of lithium atom (Li) in its ground state is x × 10–8 The value of x is ______. (Nearest Integer)

(Given : Energy of the electron in the first shell of the hydrogen atom is –2.2 x 10–18 J;

h = 6.63 × 10–34 Js and c = 3 × 108 ms–1)

Answer: (4)

24. The standard entropy change for the reaction 4Fe(s) + 3O2(g) 2Fe2O3(s) is –550 J K–1 at 298 K.

[Given: The standard enthalpy change for the reaction is –165 kJ mol–1]. The temperature in K at which the reaction attains equilibrium is ________. (Nearest Integer)

Answer: (300)

25. 1 L aqueous solution of H2SO4 contains 0.02 m mol H2SO4. 50% of this solution is diluted with deionized water to give 1 L solution (A). In solution (A), 0.01 m mol of H2SO4 are added. Total m mols of H2SO4 in the final solution is ______ × 103 m mols.

Answer: (0)

26. The standard free energy change (ΔG°) for 50% dissociation of N2O4 into NO2 at 27°C and 1 atm pressure is –x J mol–1. The value of x is _____. (Nearest Integer)

[Given : R = 8.31 J K–1 mol–1, log 1.33 = 0.1239 ln 10 = 2.3]

Answer: (710)

27. In a cell, the following reactions take place

The standard electrode potential for the spontaneous reaction in the cell is x × 10–2 V at 208 K. The value of x is _______. (Nearest Integer)

Answer: (23)

28. For a given chemical reaction

γ1A + γ2B → γ3C + γ4D

Concentration of C changes from 10 mmol dm–3 to 20 mmol dm–3 in 10 seconds. Rate of appearance of D is 1.5 times the rate of disappearance of B which is twice the rate of disappearance A. The rate of appearance of D has been experimentally determined to be 9 mmol dm–3 s–1. Therefore, the rate of reaction is _____ mmol dm–3 s–1.

Answer: (1)

29. If [Cu(H2O)4]2+ absorbs a light of wavelength 600 nm for d-d transition, then the value of octahedral crystal field splitting energy for [Cu(H2O)6]2+ will be _______ ×10–21 [Nearest integer]

(Given : h = 6.63 × 10–34 Js and c = 3.08 × 108 ms–1)

Answer: (765)

30. Number of grams of bromine that will completely react with 5.0 g of pent-1-ene is ______ × 10–2 (Atomic mass of Br = 80 g/mol) [Nearest integer]

Answer: (1143)

MATHEMATICS

SECTION-A

1. Let a circle C touch the lines L1 : 4x – 3y +K1 = 0 and L2 : 4x – 3y + K2 = 0, K1, K2 ∈ If a line passing through the centre of the circle C intersects L1 at (–1, 2) and L2 at (3, –6), then the equation of the circle C is :

(A) (x – 1)2 + (y – 2)2 = 4

(B) (x + 1)2 + (y – 2)2 = 4

(C) (x – 1)2 + (y + 2)2 = 16

(D) (x – 1)2 + (y – 2)2 = 16

Answer: (C)

2. The value of  is equal to

(A)  π2/4

(B)  π2/2

(C)  π/4

(D)  π/2

Answer: (C)

3. Let a, b and c be the length of sides of a triangle ABC such that  If r and R are the radius of incircle and radius of circumcircle of the triangle ABC, respectively, then the value of R/r is equal to

(A)  5/2

(B)  2

(C)  3/2

(D)  1

Answer: (A)

4. Let f : N→R be a function such that f(x + y) = 2f(x) f(y) for natural numbers x and y. If f(1) = 2, then the value of α for which  holds, is

(A)  2

(B)  3

(C)  4

(D)  6

Answer: (C)

5. Let A be a 3 × 3 real matrix such that  and  If X = (x1, x2, x3)T and I is an identity matrix of order 3, then the system  has

(A) No solution

(B) Infinitely many solutions

(C) Unique solution

(D) Exactly two solutions

Answer: (B)

6. Let f : R→R be defined as f(x) = x3 + x – 5 If g(x) is a function such that f(g(x)) = x, ∀ x ∈ R, then g′ (63) is equal to _______.

(A)  1/49

(B)  3/49

(C)  43/49

(D)  91/49

Answer: (A)

7. Consider the following two propositions :

P1 : ~ (p → ~ q)

P2: (p ∧ ~q) ∧ ((-~p) ∨ q)

If the proposition p → ((~p) ∨ q) is evaluated as FALSE, then :

(A) P1 is TRUE and P2 is FALSE

(B) P1 is FALSE and P2 is TRUE

(C) Both P1 and P2 are FALSE

(D) Both P1 and P2 are TRUE

Answer: (C)

8. If  then the remainder when K is divided by 6 is

(A)  1

(B)  2

(C)  3

(D)  5

Answer: (D)

9. Let f(x) be a polynomial function such that f(x) + f′(x) + f′′(x) = x5 + 64. Then, the value of 

(A)  −15

(B)  −60

(C)  60

(D)  15

Answer: (A)

10. Let E1 and E2 be two events such that the conditional probabilities P(E1|E2) = 1/2, P(E2|E1) = 3/4 and P(E1∩E2) = 1/8. Then:

(A)  P(E1 ∩ E2) = P(E1) ∙ P(E2)

(B)  P(E’1 ∩ E’2) = P(E’1) ∙ P(E2)

(C)  P(E1 ∩ E’2) = P(E1) ∙ P(E2)

(D)  P(E’1 ∩ E2) = P(E1) ∙ P(E2)

Answer: (C)

11. Let  If M and N are two matrices given by  then MN2 is

(A) a non-identity symmetric matrix

(B) a skew-symmetric matrix

(C) neither symmetric nor skew-symmetric matrix

(D) an identity matrix

Answer: (A)

12. Let g : (0, ∞) → R be a differentiable function such that  for all x > 0, where c is an arbitrary constant. Then.

(A)  g is decreasing in (0, π/4)

(B)  g’ is increasing in (0, π/4)

(C)  g + g’ is increasing in (0, π/2)

(D)  g – g’ is increasing in (0, π/2)

Answer: (D)

13. Let f :R→R and g : R → R be two functions defined by f(x) = loge(x2 + 1) – e–x + 1 and  Then, for which of the following range of α, the inequality  holds?

(A) (2, 3)

(B) (–2, –1)

(C) (1, 2)

(D) (–1, 1)

Answer: (A)

14. Let  ai > 0, i = 1, 2, 3 be a vector which makes equal angles with the coordinate axes OX, OY and OZ. Also, let the projection of  on the vector  be 7. Let  be a vector obtained by rotating with 90°. If  and x-axis are coplanar, then projection of a vector  is equal to

(A)  √7

(B)  √2

(C)  2

(D)  7

Answer: (B)

15. Let y = y(x) be the solution of the differential equation (x + 1)y′ – y = e3x(x + 1)2, with y(0) = 1/3. Then, the point x = −4/3 for the curve y = y(x) is:

(A) not a critical point

(B) a point of local minima

(C) a point of local maxima

(D) a point of inflection

Answer: (B)

16. If y = m1x + c1 and y = m2x + c2, m1 ≠ m2 are two common tangents of circle x2 + y2 = 2 and parabola y2 = x, then the value of 8|m1m2| is equal to :

(A)  3 + 4√2

(B)  −5 + 6√2

(C)  −4 + 3√2

(D)  7 + 6√2

Answer: (C)

17. Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S: x + y + z = 5. If a line L passing through (1, –1, –1), parallel to the line PQ meets the plane S at R, then QR2 is equal to :

(A)  2

(B)  5

(C)  7

(D)  11

Answer: (B)

18. If the solution curve y = y(x) of the differential equation y2dx + (x2 – xy + y2)dy = 0, which passes through the point (1,1) and intersects the line y = √3 x at the point (α, √3α), then value of loge(√3α) is equal to

(A)  π/3

(B)  π/2

(C)  π/12

(D)  π/6

Answer: (C)

19. Let x = 2t, y = t2/3 be a conic. Let S be a conic. Let S be the focus and B be the point on the axis of the conic such that SA⊥BA, where A is any point on the conic. If k is the ordinate of the centroid of the ΔSAB, then  equal to

(A)  17/18

(B)  19/18

(C)  11/18

(D)  13/18

Answer: (D)

20. Let a circle C in complex plane pass through the points z1 = 3 + 4i, z2 = 4 + 3i and z3 = 5i. If z(≠ z1) is a point on C such that the line through z and z1 is perpendicular to the line through z2 and z3, then arg(z) is equal to:

Answer: (B)

SECTION-B

21. Let Cr denote the binomial coefficient of xr in the expansion of (1 + x)10. If for α, β ∈ R, C1 + 3⋅2 C2 + 5⋅3 C3 + … upto 10 terms  then the value of α + β is equal to _____

Answer: (286*)

22. The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is ________.

Answer: (63)

23. Let θ be the angle between the vectors  where  Then  is equal to _________

Answer: (576)

24. Let the abscissae of the two points P and Q be the roots of 2x2 – rx + p = 0 and the ordinates of P and Q be the roots of x2 – sx – q = 0. If the equation of the circle described on PQ as diameter is 2(x2 + y2) – 11x – 14y – 22 = 0, then 2r + s – 2q + p is equal to _________.

Answer: (7)

25. The number of values of x in the interval  for which 14cosec2x – 2 sin2x = 21 – 4 cos2x holds, is ___________.

Answer: (4)

26. For a natural number n, let an = 19n – 12n. Then, the value of  is

Answer: (4)

27. Let f : R → R be a function defined by  If the function g(x) = f (f (f (x))) + f (f (x)), then the greatest integer less than or equal to g(1) is ___________.

Answer: (2)

28. Let the lines

intersect at the point S. If a plane ax + by – z + d = 0 passes through S and is parallel to both the lines L1 and L2, then the value of a + b + d is equal to _______.

Answer: (5)

29. Let A be a 3 × 3 matrix having entries from the set {–1, 0, 1}. The number of all such matrices A having sum of all the entries equal to 5, is ____________.

Answer: (414)

30. The greatest integer less than or equal to the sum of first 100 terms of the sequence 1/3, 5/9, 19/27, 65/81, … is equal to ________.

Answer: (98)

JEE Main Session 1 24th June 2022 Shift 1 Question Paper and Answer Key

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 Nm2. The pressure required to reduce the volume of liquid by 2% is :

(A)  3 × 108 Nm2

(B)  9 × 108 Nm2

(C)  6 × 108 Nm2

(D)  12 × 108 Nm2

Answer: (C)

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.

Answer: (A)

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

Answer: (C)

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 

Answer: (D)

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]

Answer: (D)

6. A block of mass 10 kg starts sliding on a surface with an initial velocity of 9.8 ms1. 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 ms2]

(A)  4.9 m

(B)  9.8 m

(C)  12.5 m

(D)  19.6 m

Answer: (B)

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

Answer: (C)

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 × 109 C

(B)  2.0 × 109 C

(C)  3.2 × 109 C

(D)  0.5 × 109 C

Answer: (B)

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

Answer: (C)

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

Answer: (B)

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

Answer: (A)

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

Answer: (A)

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

Answer: (C)

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.

Answer: (C)

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

Answer: (D)

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

Answer: (C)

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°

Answer: (B)

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

Answer: (D)

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) 

Answer: (C)

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

Answer: (B)

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)

Answer: (12)

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.

Answer: (10)

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 _____ .

Answer: (750)

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 ______.

Answer: (242)

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

Answer: (3)

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 ______.

Answer: (2)

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.

Answer: (3)

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 _______ Nm1. (Use g = 10 ms2)

Answer: (120)

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.

Answer: (25)

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 × 102 The value of x is _________.

Answer: (6)

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 × 102 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

Answer: (C)

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)

Answer: (B)

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)

Answer: (B)

4. For a reaction at equilibrium

the relation between dissociation constant (K), degree of dissociation (α) and equilibrium pressure (p) is given by :

Answer: (B)

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.

Answer: (C)

6. Given below are the oxides:

Na2O, AsO3, N2O, NO and Cl­2O7

Number of amphoteric oxides is:

(A)  0

(B)  1

(C)  2

(D)  3

Answer: (B)

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)

Answer: (A)

8. The highest industrial consumption of molecular hydrogen is to produce compounds of element:

(A)  Carbon

(B)  Nitrogen

(C)  Oxygen

(D)  Chlorine

Answer: (B)

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

Answer: (A)

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

Answer: (C)

11. The most stable trihalide of nitrogen is:

(A)  NF3

(B)  NCl3

(C)  NBr3

(D)  NI3

Answer: (A)

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+

Answer: (B)

13. In the given reactions sequence, the major product ‘C’ is :

Answer: (B)

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.

Answer: (A)

15. Which of the following is an example of conjugated diketone?

Answer: (C)

16. 

The major product of the above reaction is

Answer: (D)

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

Answer: (D)

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

Answer: (B)

19. Which of the following is not a broad spectrum antibiotic?

(A)  Vancomycin

(B)  Ampicillin

(C)  Ofloxacin

(D)  Penicillin G

Answer: (D)

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+

Answer: (A)

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)

Answer: (43)

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]

Answer: (747)

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)

Answer: (54)

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)

Answer: (5)

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)

Answer: (154)

26. The difference in oxidation state of chromium in chromate and dichromate salts is _______

Answer: (0)

27. In the cobalt-carbonyl complex: [Co2(CO)8], number of Co-Co bonds is “X” and terminal CO ligands is “Y”. X + Y =______

Answer: (7)

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____.

Answer: (63)

29. Number of electrophilic centre in the given compound is _______

Answer: (3)

30. The major product ‘A’ of the following given reaction has _____ sp2 hybridized carbon atoms. 2,7 – Dimethyl1 – 2, 6 – octadiene 

Answer: (2)

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

Answer: (D)

2. The remainder when 32022 is divided by 5 is

(A)  1

(B)  2

(C)  3

(D)  4

Answer: (D)

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

Answer: (A)

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

Answer: (C)

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

Answer: (A)

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

Answer: (B)

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

Answer: (B)

8. The set of all values of k for which (tan1 x)3 + (cot1 x)3 = kπ3, x ∈ R, is the interval:

Answer: (A)

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

Answer: (B)

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)

Answer: (C)

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 :

Answer: (D)

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:

Answer: (B)

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

Answer: (B)

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)

Answer: (A)

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

Answer: (D)

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)

Answer: (C)

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

Answer: (A)

18. The domain of the function

Answer: (*)

19. Let  If  then T + n(S) is equal

(A)  7 + √3

(B)  9

(C)  8 + √3

(D)  10

Answer: (B)

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

Answer: (B)

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 _____.

Answer: (31)

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________.

Answer: (*)

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 _______.

Answer: (8)

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 __________.

Answer: (84)

25. The number of points where the function

[t] denotes the greatest integer ≤ t, is discontinuous is _________.

Answer: (7)

26. Let  Then the value of is __________.

Answer: (1)

27. Let  If  then α1 + α2 is equal to __________

Answer: (34)

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 __________

Answer: (2929)

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 __________.

Answer: (19)

30.If the shortest distance between the line  and  then the integral value of a is equal to

Answer: (2)

JEE Main Online Computer Based Test (CBT) Examination Held on 16-04-2018 Morning Question Paper With Answer Key

JEE Main Online Computer Based Test (CBT) Examination Morning Held on 16-04-2018

Timing : 9 : 30 AM – 12 : 30 PM

PHYSICS 

1. The percentage errors in quantities P, Q, R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity The maximum percentage error in the value of A will be :

(1)   6.0%

(2)   7.5%

(3)   8.5%

(4)   6.5%

Answer: (4)

2. Let  The magnitude of a coplanar vector  such that  is given by :

(1) 

(2) 

(3) 

(4) 

Answer: (2)

3. A body of mass m starts moving from rest along x-axis so that its velocity varies as  where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first t seconds after the start of the motion is :

(1) 

(2)   8 m a4t2

(3)   4 m a4t2

(4) 

Answer: (1)

4. Two particles of the same mass m are moving in circular orbits because of force, given by

The first particle is at a distance r=1, and the second, at r=4. The best estimate for the ratio of kinetic energies of the first and the second particle is closest to :

(1)   6 × 102

(2)   3 × 103

(3)   10−1

(4)   6 × 102

Answer: (1)

5. An oscillator of mass M is at rest in its equilibrium position in a potential  A particle of mass m comes from right with speed u and collides completely inelastically with M and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after 13 collisions is : (M = 10, m = 5, u = 1, k = 1)

(1) 

(2)   1/2

(3)   2/3

(4) 

Answer: (1)

6. Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence :

(1)   Weight of the object, everywhere on the earth, will increase.

(2)   Weight of the object, everywhere on the earth, will decrease.

(3)   There will be no change in weight anywhere on the earth.

(4)   Except at poles, weight of the object on the earth will decrease.

Answer: (4)

7. A thin circular disk is in the xy plane as shown in the figure. The ratio of its moment of inertia about z and zʹ axes will be :

(1)   1 : 3

(2)   1 : 4

(3)   1 : 5

(4)   1 : 2

Answer: (1)

8. The relative uncertainty in the period of a satellite orbiting around the earth is 10−2. If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is :

(1)   10−2

(2)   2 × 10−2

(3)   3 × 10−2

(4)   6 × 10−2

Answer: (2)

9. A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let P2 be the pressure inside the inner bubble and P0, the pressure outside the outer bubble. Radius of another bubble with pressure difference P2 − P0 between its inside and outside would be :

(1)   12 cm

(2)   2.4 cm

(3)   6 cm

(4)   4.8 cm

Answer: (2)

10. One mole of an ideal monoatomic gas is taken along the path ABCA as shown in the PV diagram. The maximum temperature attained by the gas along the path BC is given by :

(1)  

(2) 

(3) 

(4)    

Answer: (2)

11. Two moles of helium are mixed with n moles of hydrogen. If  for the mixture, then the value of n is :

(1)   1

(2)   3

(3)   2

(4)   3/2

Answer: (3)

12. A particle executes simple harmonic motion and is located at x=a, b and c at times to, 2to and 3to The frequency of the oscillation is :

(1)    

(2) 

(3)    

(4)     

Answer: (1)

13. Two sitar strings, A and B, playing the note ‘Dha’ are slightly out of tune and produce beats of frequency 5 Hz. The tension of the string B is slightly increased and the beat frequency is found to decrease by 3 Hz. If the frequency of A is 425 Hz, the original frequency of B is :

(1)   430 Hz

(2)   420 Hz

(3)   428 Hz

(4)   422 Hz

Answer: (2)

14. Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameters, and the force between them is F. A third identical conducting sphere, C, is uncharged. Sphere C is first touched to A, then to B, and then removed. As a result, the force between A and B would be equal to :

(1)   F

(2)   3F/4

(3)   3F/8

(4)   F/2

Answer: (3)

15. A heating element has a resistance of 100 Ω at room temperature. When it is connected to a supply of 220 V, a steady current of 2 A passes in it and temperature is 500°C more than room temperature. What is the temperature coefficient of resistance of the heating element ?

(1)   0.5 × 104 °C1

(2)   5 × 104 °C1

(3)   1 × 104 °C1

(4)   2 × 104 °C1

Answer: (4)

16. A galvanometer with its coil resistance 25 Ω requires a current of 1 mA for its full deflection. In order to construct an ammeter to read up to a current of 2 A, the approximate value of the shunt resistance should be :

(1)   2.5 × 103 Ω

(2)   1.25 × 102 Ω

(3)   1.25 × 103 Ω

(4)   2.5 × 102 Ω

Answer: (2)

17. In the following circuit, the switch S is closed at t=0. The charge on the capacitor C1 as a function of time will be given by 

(1)   C1E [1 − exp(−tR/C1)]

(2)   C2E [1 − exp(−t/RC2)]

(3)   CeqE [1 − exp(−t/RCeq)]

(4)   CeqE exp (−t/RCeq)

Answer: (3)

18. A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B. When it is rotated with an angular velocity ω, the maximum e.m.f. induced in the coil will be :

(1)   3 nBAω

(2)  

(3)   nBAω

(4)    

Answer: (3)

19. A charge q is spread uniformly over an insulated loop of radius r. If it is rotated with an angular velocity ω with respect to normal axis then the magnetic moment of the loop is :

(1)   q ωr2

(2)    

(3)    

(4)    

Answer: (4)

20. A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns, giving the output power at 230 V. If the current in the primary of the transformer is 5 A, and its efficiency is 90%, the output current would be :

(1)   50 A

(2)   45 A

(3)   25 A

(4)   20 A

Answer: (2)

21. A plane electromagnetic wave of wavelength λ has an intensity I. It is propagating along the positive Y-direction. The allowed expressions for the electric and magnetic fields are given by :

(1)  

(2)  

(3)    

(4)  

Answer: (1)

22. A ray of light is incident at an angle of 60° on one face of a prism of angle 30°. The emergent ray of light makes an angle of 30° with incident ray. The angle made by the emergent ray with second face of prism will be :

(1)   0°

(2)   90°

(3)   45°

(4)   30°

Answer: (2)

23. Unpolarized light of intensity I is incident on a system of two polarizers, A followed by B. The intensity of emergent light is I/2. If a third polarizer C is placed between A and B, the intensity of emergent light is reduced to I/3. The angle between the polarizers A and C is θ. Then :

(1)    

(2)  

(3)    

(4)    

Answer: (2)

24. The de-Broglie wavelength (λB) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state (λG) by :

(1)   λB = 2λG

(2)   λB = 3λG

(3)   λB = λG/2

(4)   λB = λG/3

Answer: (2)

25. Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths λN, λA The ratio  is closest to :

(1)   106

(2)   10

(3)   1010

(4)   101

Answer: (1)

26. At some instant, a radioactive sample S1 having an activity 5 μCi has twice the number of nuclei as another sample S2 which has an activity of 10 μCi. The half lives of S1 and S2 are :

(1)   20 years and 5 years, respectively

(2)   20 years and 10 years, respectively

(3)   5 years and 20 years, respectively

(4)   10 years and 20 years, respectively

Answer: (1)

27. In the given circuit, the current through zener diode is :

(1)   5.5 mA

(2)   6.7 mA

(3)   2.5 mA

(4)   3.3 mA

Answer: (4)

28. A carrier wave of peak voltage 14 V is used for transmitting a message signal. The peak voltage of modulating signal given to achieve a modulation index of 80% will be :

(1)   7 V

(2)   28 V

(3)   11.2 V

(4)   22.4 V

Answer: (3)

29. In a circuit for finding the resistance of a galvanometer by half deflection method, a 6 V battery and a high resistance of 11 kΩ are used. The figure of merit of the galvanometer is 60 μA/division. In the absence of shunt resistance, the galvanometer produces a deflection of θ = 9 divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of θ/2, is closest to :

(1)   550 Ω

(2)   220Ω

(3)   55Ω

(4)   110Ω

Answer: (4)

30. The end correction of a resonance column is 1 cm. If the shortest length resonating with the tuning fork is 10 cm, the next resonating length should be :

(1)   28 cm

(2)   32 cm

(3)   36 cm

(4)   40 cm

Answer: (2)

CHEMISTRY

31. An unknown chlorohydrocarbon has 3.55% of chlorine. If each molecule of the hydrocarbon has one chlorine atom only; chlorine atoms present in 1 g of chlorohydrocarbon are :

(Atomic wt. of Cl=35.5 u; Avogadro constant=6.023 × 1023 mol−1)

(1)   6.023 × 1020

(2)   6.023 × 109

(3)   6.023 × 1021

(4)   6.023 × 1023

Answer: (1)

32. The gas phase reaction 2NO2(g) → N2O4(g) is an exothermic reaction. The decomposition of N2O4, in equilibrium mixture of NO2(g) and N2O4(g), can be increased by :

(1)   lowering the temperature.

(2)   increasing the pressure.

(3)   addition of an inert gas at constant volume.

(4)   addition of an inert gas at constant pressure.

Answer: (4)

33. Assuming ideal gas behaviour, the ratio of density of ammonia to that of hydrogen chloride at same temperature and pressure is : (Atomic wt. of Cl=35.5 u)

(1)   1.46

(2)   0.46

(3)   1.64

(4)   0.64

Answer: (2)

34. When 9.65 ampere current was passed for 1.0 hour into nitrobenzene in acidic medium, the amount of p-aminophenol produced is :

(1)   9.81 g

(2)   10.9 g

(3)   98.1 g

(4)   109.0 g

Answer: (1)

35. For which of the following processes, ΔS is negative ?

(1)   H2(g) → 2H(g)

(2)   N2(g, 1 atm) → N2(g, 5 atm)

(3)   C(diamond) → C(graphite)

(4)   N2(g, 273 K) → N2(g, 300 K)

Answer: (2)

36. Which one of the following is not a property of physical adsorption ?

(1)   Higher the pressure, more the adsorption

(2)   Lower the temperature, more the adsorption

(3)   Greater the surface area, more the adsorption

(4)   Unilayer adsorption occurs

Answer: (4)

37. If 50% of a reaction occurs in 100 second and 75% of the reaction occurs in 200 second, the order of this reaction is :

(1)   Zero

(2)   1

(3)   2

(4)   3

Answer: (2)

38. Which of the following statements is false ?

(1)   Photon has momentum as well as wavelength.

(2)   Splitting of spectral lines in electrical field is called Stark effect.

(3)   Rydberg constant has unit of energy.

(4)   Frequency of emitted radiation from a black body goes from a lower wavelength to higher wavelength as the temperature increases.

Answer: (4)

39. At 320 K, a gas A2 is 20% dissociated to A(g). The standard free energy change at 320 K and 1 atm in J mol−1 is approximately : (R=8.314 JK−1 mol−1; ln 2=0.693; ln 3=1.098)

(1)   4763

(2)   2068

(3)   1844

(4)   4281

Answer: (1)

40. The mass of a non-volatile, non-electrolyte solute (molar mass=50 g mol−1) needed to be dissolved in 114 g octane to reduce its vapour pressure to 75%, is :

(1)   37.5 g

(2)   75 g

(3)   150 g

(4)   50 g

Answer: (3)

41. The incorrect statement is :

(1)   Cu2+ salts give red coloured borax bead test in reducing flame.

(2)   Cu2+ and Ni2+ ions give black precipitate with H2S in presence of HCl solution.

(3)   Ferricion gives blood red colour with potassium thiocyanate.

(4)   Cu2+ ion gives chocolage coloured precipitate with potassium ferrocyanide solution.

Answer: (2)

42. The incorrect geometry is represented by :

(1)   BF3 – trigonal planar

(2)   H2O – bent

(3)   NF3 – trigonal planar

(4)   AsF5 – trigonal bipyramidal

Answer: (3)

43. In Wilkinson’s catalyst, the hybridization of central metal ion and its shape are respectively :

(1)   sp3d, trigonal bipyramidal

(2)   sp3, tetrahedral

(3)   dsp2, square planar

(4)   d2sp3, octahedral

Answer: (3)

44. Among the oxides of nitrogen : N2O3, N2O4 and N2O5 ; the molecule(s) having nitrogen-nitrogen bond is/are :

(1)   Only N2O5

(2)   N­2O3 and N2O5

(3)   N2O4 and N2O5

(4)   N2O3­ and N2O4

Answer: (4)

45. Which of the following complexes will show geometrical isomerism ?

(1)   aquachlorobis(ethylenediamine) cobalt(II) chloride

(2)   pentaaquachlorochromium(III) chloride

(3)   potassium amminetrichloroplatinate (II)

(4)   potassium tris(oxalato)chromate(III)

Answer: (1)

46. In a complexometric titration of metal ion with ligand M(Metal ion)+L(Ligand) → C(Complex) end point is estimated spectrophotometrically (through light absorption). If ‘M’ and ‘C’ do not absorb light and only ‘L’ absorbs, then the titration plot between absorbed light (A) versus volume of ligand ‘L’ (V) would look like :

(1)  

(2) 

(3)  

(4)  

Answer: (2)

47. In the extraction of copper from its sulphide ore, metal is finally obtained by the oxidation of cuprous sulphide with :

(1)   Fe2O3

(2)   Cu2O

(3)   SO2

(4)   CO

Answer: (2)

48. Which of the following conversions involves change in both shape and hybridisation ?

(1)   NH3 → NH4+

(2)   CH4 → C2H6

(3)   H2O → H3O+

(4)   BF­3 → BF4

Answer: (4)

49. A group 13 element ‘X’ reacts with chlorine gas to produce a compound XCl3 . XCl3 is electron deficient and easily reacts with NH3 to form Cl3X ← NH3 adduct; however, XCl3 does not dimerize. X is :

(1)   B

(2)   Al

(3)   Ga

(4)   In

Answer: (1)

50. When XO2 is fused with an alkali metal hydroxide in presence of an oxidizing agent such as KNO3 ; a dark green product is formed which disproportionates in acidic solution to afford a dark purple solution. X is :

(1)   Ti

(2)   V

(3)   Cr

(4)   Mn

Answer: (4)

51. The major product of the following reaction is :

(1)  

(2)  

(3)  

(4)  

Answer: (1)

52. For standardizing NaOH solution, which of the following is used as a primary standard ?

(1)   Ferrous Ammonium Sulfate

(2)   dil. HCl

(3)   Oxalic acid

(4)   Sodium tetraborate

Answer: (3)

53. The most polar compound among the following is :

(1)  

(2)  

(3)  

(4)  

Answer: (1)

54. The correct match between items of List – I and List – II is :

(1)   (A)-(R), (B)-(S), (C)-(P), (D)-(Q)

(2)   (A)-(S), (B)-(R), (C)-(P), (D)-(Q)

(3)   (A)-(S), (B)-(R), (C)-(Q), (D)-(P)

(4)   (A)-(R), (B)-(S), (C)-(Q), (D)-(P)

Answer: (1)

55. Among the following, the incorrect statement is :

(1)   Maltose and lactose has 1, 4-glycosidic linkage.

(2)   Sucrose and amylose has 1, 2-glycosidic linkage.

(3)   Cellulose and amylose has 1, 4-glycosidic linkage.

(4)   Lactose contains β-D-galactose and β-D-glucose.

Answer: (2)

56. Which of the following compounds will most readily be dehydrated to give alkene under acidic condition ?

(1)   1-Pentanol

(2)   4-Hydroxypentan-2-one

(3)   3-Hydroxypentan-2-one

(4)   2-Hydroxycyclopentanone

Answer: (2)

57. Products A and B formed in the following reactions are respectively :

(1)  

(2)   

(3)  

(4)  

Answer: (4)

58. The major product B formed in the following reaction sequence is :

(1)  

(2)  

(3)  

(4)  

Answer: (2)

59. The major product of the following reaction is :

(1)   

(2) 

(3)   

(4) 

Answer: (1)

60. The major product of the following reaction is :

(1)   

(2)   

(3)   

(4)  

Answer: (1)

MATHEMATICS

61. Let N denote the set of all natural numbers. Define two binary relations on N as R1={(x, y) ϵ N × N : 2x + y = 10} and R2={(x, y) ϵ N × N : x + 2y = 10}. Then :

(1)   Range of R1 is {2, 4, 8}.

(2)   Range of R2 is {1, 2, 3, 4}.

(3)   Both R1 and R2 are symmetric relations.

(4)   Both R1 and R2 are transitive relations.

Answer: (2)

62. Let p, q and r be real numbers (p ≠ q, r ≠ 0), such that the roots of the equation  are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to :

(1)     

(2)   p2 + q2

(3)   2(p2 + q2)

(4)   p2 + q2 + r2

Answer: (2)

63. The least positive integer n for which  is

(1)   2

(2)   3

(3)   5

(4)   6

Answer: (2)

64. Let  and B = A20. Then the sum of the elements of the first column of B is :

(1)   210

(2)   211

(3)   231

(4)   251

Answer: (3)

65. The number of values of k for which the system of linear equations,

(k + 2)x + 10y = k

kx + (k + 3)y = k – 1

has no solution, is :

(1)   1

(2)   2

(3)   3

(4)   infinitely many

Answer: (1)

66. The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is not allowed) and are multiple of 3 is :

(1)   24

(2)   30

(3)   36

(4)   48

Answer: (2)

67. The coefficient of x2 in the expansion of the product (2− x2) ⋅ ((1 + 2x + 3x2)6+ (1 − 4x2)6) is :

(1)   107

(2)   106

(3)   108

(4)   155

Answer: (2)

68. Let  (xi ≠ 2 for i = 1, 2, . . . , n) be in A.P. such that x1 = 4 and x21 = 20. If n is the least positive integer for which xn > 50, then  is equal to :

(1)   1/8

(2)   3

(3)   13/8

(4)   13/4

Answer: (4)

69. The sum of the first 20 terms of the series  is :

(1)    

(2)    

(3)    

(4)    

Answer: (1)

70. 

(1)   1/3

(2)   −1/3

(3)   −1/6

(4)   1/6

Answer: (3)

71. If the function f defined as  is continuous at x = 0, then the ordered pair (k, f(0)) is equal to :

(1)   (3, 2)

(2)   (3, 1)

(3)   (2, 1)

(4)   (1/3, 2)

Answer: (2)

72. If  then  is equal to :

(1)   y/x

(2)   x/y

(3)   −y/x

(4)   −x/y

Answer: (3)

73. Let M and m be respectively the absolute maximum and the absolute minimum values of the function, f (x)=2x3 − 9x2 + 12x + 5 in the interval [0, 3]. Then M−m is equal to :

(1)   5

(2)   9

(3)   4

(4)   1

Answer: (2)

74. If  (C is a constant of integration), then the ordered pair (K, A) is equal to :

(1)   (2, 1)

(2)   (−2, 3)

(3)   (2, 3)

(4)   (−2, 1)

Answer: (3)

75. If  then :

(1)   fʹʹʹ(x) + fʹʹ(x) = sin x

(2)   fʹʹʹ(x) + fʹʹ(x) – fʹ(x) = cos x

(3)   fʹʹʹ(x) + fʹ(x) = cos x – 2x sin x

(4)   fʹʹʹ(x) – fʹʹ(x) = cos x – 2x sin x

Answer: (3)

76. If the area of the region bounded by the curves, y = x2, y = 1/x and the lines y = 0 and x = t (t > 1) is 1 sq. unit, then it is equal to :

(1)   e3/2

(2)   4/3

(3)   3/2

(4)   e2/3

Answer: (4)

77. The differential equation representing the family of ellipses having foci either on the x-axis or on the y-axis, centre at the origin and passing through the point (0, 3) is :

(1)   xy yʹʹ + x(yʹ)2 – y yʹ = 0

(2)   x + y yʹʹ = 0

(3)   xy yʹ + y2 – 9 = 0

(4)   xy yʹ – y2 + 9 = 0

Answer: (4)

78. The locus of the point of intersection of the lines,  and   (k is any non-zero real parameter), is :

(1)   an ellipse whose eccentricity is 1/√3.

(2)   an ellipse with length of its major axis 8√2.

(3)   a hyperbola whose eccentricity is √3.

(4)   a hyperbola with length of its transverse axis 8√2.

Answer: (4)

79. If a circle C, whose radius is 3, touches externally the circle, x2 + y2 + 2x − 4y – 4 = 0 at the point (2, 2), then the length of the intercept cut by this circle C, on the x-axis is equal to :

(1)   2√5

(2)   3√2

(3)   √5

(4)   2√3

Answer: (1)

80. Let P be a point on the parabola, x2 = 4y. If the distance of P from the centre of the circle, x2 + y2 + 6x + 8 = 0 is minimum, then the equation of the tangent to the parabola at P, is :

(1)   x + 4y – 2 = 0

(2)   x – y + 3 = 0

(3)   x + y + 1 = 0

(4)   x + 2y = 0

Answer: (3)

81. If the length of the latus rectum of an ellipse is 4 units and the distance between a focus and its nearest vertex on the major axis is 3/2 units, then its eccentricity is :

(1)   1/2

(2)   1/3

(3)   2/3

(4)   1/9

Answer: (2)

82. The sum of the intercepts on the coordinate axes of the plane passing through the point (−2, −2, 2) and containing the line joining the points (1, −1, 2) and (1, 1, 1), is :

(1)   4

(2)   −4

(3)   −8

(4)   12

Answer: (2)

83. If the angle between the lines,  is  then p is  equal to :

(1)   7/2

(2)   2/7

(3)   −7/4

(4)   −4/7

Answer: (1)

84. Let  and a vector  be such that  Then  equals :

(1)   11/3

(2)   11/√3

(3)    

(4)    

Answer: (3)

85. The mean and the standard deviation(s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :

(1)   0

(2)   1

(3)   2

(4)   4

Answer: (3)

86. Let A, B and C be three events, which are pair-wise independent and  denotes the complement of an event E. If P(A ∩ B ∩ C) = 0 and P(C) > 0, then  is equal to :

(1)     

(2)    

(3)    

(4)    

Answer: (1)

87. Two different families A and B are blessed with equal number of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family B is 1/12, then the number of children in each family is :

(1)   3

(2)   4

(3)   5

(4)   6

Answer: (3)

88. If an angle A of a ΔABC satisfies 5 cosA+3=0, then the roots of the quadratic equation, 9x2 + 27x + 20=0 are :

(1)   sec A, cot A

(2)   sin A, sec A

(3)   sec A, tan A

(4)   tan A, cos A

Answer: (3)

89. A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min. for the angle of depression of the car to change from 30° to 45° ; then after this, the time taken (in min.) by the car to reach the foot of the tower, is :

(1)    

(2)    

(3)    

(4)    

Answer: (1)

90. If p→(∼p∨∼q) is false, then the truth values of p and q are respectively :

(1)   F, F

(2)   T, F

(3)   F, T

(4)   T, T

Answer: (4)

JEE Main Online Computer Based Test (CBT) Examination Held on 15-04-2018 Afternoon Question Paper With Answer Key

JEE Main Online Computer Based Test (CBT) Examination Afternoon Held on 15-04-2018,

Timing : 2:30 PM – 5.30 PM

PHYSICS 

1. The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants G, h and c. Which of the following correctly gives the Planck length ?

(1)   G h2 c3

(2)   G2 h c

(3)   G1/2 h2 c

(4) 

Answer: (4)

2. A man in a car at location Q on a straight highway is moving with speed υ. He decides to reach a point P in a field at a distance d from the highway (point M) as shown in the figure. Speed of the car in the field is half to that on the highway. What should be the distance RM, so that the time taken to reach P is minimum ?

(1)   d

(2)   d/√2

(3)   d/2

(4)   d/√3

Answer: (4)

3. A body of mass 2 kg slides down with an acceleration of 3 m/s2 on a rough inclined plane having a slope of 30°. The external force required to take the same body up the plane with the same acceleration will be : (g=10 m/s2)

(1)   14 N

(2)   20 N

(3)   6 N

(4)   4 N

Answer: (2)

4. A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of 90° with respect to each other. The mass of unknown particle is :

(1)   m/2

(2)   m

(3)   m/√3

(4)   2 m

Answer: (2)

5. A disc rotates about its axis of symmetry in a horizontal plane at a steady rate of 3.5 revolutions per second. A coin placed at a distance of 1.25 cm from the axis of rotation remains at rest on the disc. The coefficient of friction between the coin and the disc is : (g=10 m/s2)

(1)   0.5

(2)   0.3

(3)   0.7

(4)   0.6

Answer: (4)

6. A thin uniform bar of length L and mass 8 m lies on a smooth horizontal table. Two point masses m and 2 m are moving in the same horizontal plane from opposite sides of the bar with speeds 2υ and υ respectively. The masses stick to the bar after collision at a distance  respectively from the centre of the abr. If the bar starts rotating about its center of mass as a result of collision, the angular speed of the bar will be :

(1) 

(2) 

(3) 

(4) 

Answer: (2)

7. A thin rod MN, free to rotate in the vertical plane about the fixed end N, is held horizontal. When the end M is released the speed of this end, when the rod makes an angle α with the horizontal, will be proportional to : (see figure)

(1) 

(2)   sin α

(3) 

(4)   cos α

Answer: (1)

8. As shown in the figure, forces of 105 N each are applied in opposite directions, on the upper and lower faces of a cube of side 10 cm, shifting the upper face parallel to itself by 0.5 cm. If the side of another cube of the same material is 20 cm, then under similar conditions as above, the displacement will be :

(1)   0.25 cm

(2)   0.37 cm

(3)   0.75 cm

(4)   1.00 cm

Answer: (1)

9. When an air bubble of radius r rises from the bottom to the surface of a lake, its radius becomes 5r/4. Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature) :

(1)   11.2 m

(2)   8.7 m

(3)   9.5 m

(4)   10.5 m

Answer: (3)

10. Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature T. Engine B receives heat rejected by engine A and in turn rejects it to a reservoir at 100 K. If the efficiencies of the two engines A and B are represented by ηA and ηB, respectively, then what is the value of 

(1)   12/7

(2)   7/12

(3)   12/5

(4)   5/12

Answer: (1)

11. The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms1 : [kB = 1.4 × 1023 J/K; mHe = 7 × 1027 kg]

(1)   1.3 × 104

(2)   1.3 × 103

(3)   1.3× 105

(4)   1.3 × 102

Answer: (2)

12. Two simple harmonic motions, as shown below, are at right angles. They are combined to form Lissajous figures.

         x(t) = A sin (at + δ)

         y(t) = B sin (bt)

Identify the correct match below.

          Parameters                      Curve

(1)   A ≠ B, a = b ; δ = 0            Parabola

(2)   A = B, a = b ; δ = π/2         Line

(3)   A ≠ B, a = b ; δ = π/2         Ellipse

(4)   A = B, a = 2b ; δ = π/2       Circle

Answer: (3)

13. 5 beats/second are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or 1 m. The frequency of the fork will be :

(1)   195 Hz

(2)   150 Hz

(3)   300 Hz

(4)   251 Hz

Answer: (1)

14. A solid ball of radius R has a charge density ρ given by ρ = ρ0(1 – r/R) for 0 ≤ r ≤ The electric field outside the ball is :

(1) 

(2) 

(3) 

(4) 

Answer: (2)

15. A parallel plate capacitor with area 200 cm2 and separation between the plates 1.5 cm, is connected across a battery of emf V. If the force of attraction between the plates is 25×10−6 N, the value of V is approximately :

(1)   250 V

(2)   100 V

(3)   300 V

(4)   150 V

Answer: (1)

16. A copper rod of cross-sectional area A carries a uniform current I through it. At temperature T, if the volume charge density of the rod is ρ, how long will the charges take to travel a distance d ?

(1) 

(2) 

(3) 

(4) 

Answer: (3)

17. A capacitor C1=1.0 μF is charged up to a voltage V=60 V by connecting it to battery B through switch (1). Now C1 is disconnected from battery and connected to a circuit consisting of two uncharged capacitors C2=3.0 μF and C3=6.0 μF through switch (2), as shown in the figure. The sum of final charges on C2 and C3 is :

(1)   40 μC

(2)   36 μC

(3)   20 μC

(4)   54 μC

Answer: (1)

18. A current of 1 A is flowing on the sides of an equilateral triangle of side 4.5×10−2 The magnetic field at the centre of the triangle will be :

(1)   2 ×10−5 Wb/m2

(2)   Zero

(3)   8 ×10−5 Wb/m2

(4)   4 ×10−5 Wb/m2

Answer: (4)

19. At the centre of a fixed large circular coil of radius R, a much smaller circular coil of radius r is placed. The two coils are concentric and are in the same The larger coil carries a current I. The smaller coil is set to rotate with a constant angular velocity ω about an axis along their common diameter. Calculate the emf induced in the smaller coil after a time t of its start of rotation.

(1) 

(2) 

(3) 

(4) 

Answer: (1)

20. 

A copper rod of mass m slides under gravity on two smooth parallel rails, with

separation l and set at an angle of θ with the horizontal. At the bottom, rails are joined by a resistance R. There is a uniform magnetic field B normal to the plane of the rails, as shown in the figure. The terminal speed of the copper rod is :

(1) 

(2) 

(3) 

(4) 

Answer: (3)

21. A plane polarized monochromatic EM wave is traveling in vacuum along z direction such that at t = t1 it is found that the electric field is zero at a spatial point z1. The next zero that occurs in its neighbourhood is at z2. The frequency of the electromagnetic wave is :

(1) 

(2) 

(3) 

(4) 

Answer: (2)

22. A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of 10 cm. The separation between the two lenses is 2 cm. The focal lengths of the component lenses are :

(1)   10 cm, 12 cm

(2)   12 cm, 14 cm

(3)   16 cm, 18 cm

(4)   18 cm, 20 cm

Answer: (4)

23. A plane polarized light is incident on a polariser with its pass axis making angle θ with x-axis, as shown in the figure. At four different values of θ, θ=8°, 38°, 188° and 218°, the observed intensities are same. What is the angle between the direction of polarization and x-axis ?

(1)   98°

(2)   128°

(3)   203°

(4)   45°

Answer: (3)

24. If the de Broglie wavelengths associated with a proton and an α-particle are equal, then the ratio of velocities of the proton and the α-particle will be :

(1)   4 : 1

(2)   2 : 1

(3)   1 : 2

(4)   1 : 4

Answer: (1)

25. Muon (μ) is a negatively charged (|q| = |e|) particle with a mass mμ=200 me, where me is the mass of the electron and e is the electronic charge. If μ is bound to a proton to form a hydrogen like atom, identify the correct statements.

(A)  Radius of the muonic orbit is 200 times smaller than that of the electron.

(B)  The speed of the μ in the nth orbit is 1/200 times that of the electron in the nth orbit.

(C)  The ionization energy of muonic atom is 200 times more than that of an hydrogen atom.

(D)  The momentum of the muon in the nth orbit is 200 times more than that of the electron.

(1)   (A), (B), (D)

(2)   (A), (C), (D)

(3)   (B), (D)

(4)   (C), (D)

Answer: (2)

26. An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The ratio of the radii of the nuclei (assumed to be spherical) is :

(1)   8 : 27

(2)   4 : 9

(3)   3 : 2

(4)   2 : 3

Answer: (3)

27. Truth table for the following digital circuit will be :

(1) 

(2) 

(3) 

(4) 

Answer: (3)

28. The carrier frequency of a transmitter is provided by a tank circuit of a coil of inductance 49 μH and a capacitance of 2.5 nF. It is modulated by an audio signal of 12 kHz. The frequency range occupied by the side bands is :

(1)   13482 kHz − 13494 kHz

(2)   442 kHz − 466 kHz

(3)   63 kHz − 75 kHz

(4)   18 kHz − 30 kHz

Answer: (2)

29. A constant voltage is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be :

(1)   Doubled

(2)   Halved

(3)   Unchanged

(4)   Increased 8 times

Answer: (4)

30. A body takes 10 minutes to cool from 60°C to 50° The temperature of surroundings is constant at 25°C. Then, the temperature of the body after next 10 minutes will be approximately :

(1)   47°C

(2)   41°C

(3)   45°C

(4)   43°C

Answer: (4)

CHEMISTRY

31. For per gram of reactant, the maximum quantity of N2 gas is produced in which of the following thermal decomposition reactions ?

(Given : Atomic wt. – Cr = 52 u, Ba = 137 u)

(1)   (NH4)2Cr2O7(s) → N2(g)+4H2O(g) +Cr2O3(s)

(2)   2NH4NO3(s) → 2 N2(g)+4H2O(g) +O2(g)

(3)   Ba(N3)2(s) → Ba(s)+3N2(g)

(4)   2NH3(g) → N2(g)+3H2(g)

Answer: (4)

32. All of the following share the same crystal structure except :

(1)   LiCl

(2)   NaCl

(3)   RbCl

(4)   CsCl

Answer: (4)

33. The de-Broglie’s wavelength of electron present in first Bohr orbit of ‘H’ atom is :

(1)   0529 Å

(2)   2π × 0.529 Å

(3)