JEE Main Session 2 29th July 2022 Shift 2 Question Paper and Answer Key

JEE Main Session 2 29th July 2022 Shift 2

PHYSICS

Section-A

IMPORTANT INSTRUCTIONS:

(1)   The test is of 3 hours duration:

(2)   The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i)    Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

(ii)   Section-B: This section contains 10 questions. In Section-B, attempt any five questions out of 10. The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and −1 mark for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. Two identical metallic spheres A and B when placed at certain distance in air repel each other with a force of F. Another identical uncharged sphere C is first placed in contact with A and then in contact with B and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be

(A) 3F/2

(B) 3F/4

(C) F

(D) 2F

Answer: (B)

2. 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-III, B-IV, C-II, D-I

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

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

Answer: (B)

3. Two identical thin metal plates has charge q1 and q2 respectively such that q1> q2. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is

Answer: (C)

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

Assertion A: Alloys such as constantan andmanganing are used in making standard resistance coils.

Reason R: Constantan and manganin have very small value of temperature coefficient of resistance.

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)

5. A 1 m long wire is broken into two unequal parts X and Y. The X part of the wire is stretched into another wire W. Length of W is twice the length of X and the resistance of W is twice that of Y. Find the ratio of length of X and Y.

(A) 1:4

(B) 1:2

(C) 4:1

(D) 2:1

Answer: (B)

6. A wire X of length 50 cm carrying a current of 2 A is placed parallel to a long wire Y of length 5 m. The wire Y carries a current of 3 A. The distance between two wires is 5 cm and currents flow in the same direction. The force acting on the wire Y is

(A) 1.2 × 10–5 N directed towards wire X

(B) 1.2 × 10–4 N directed away from wire X

(C) 1.2 × 10–4 N directed towards wire X

(D) 2.4 × 10–5 N directed towards wire X

Answer: (A)

7. A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is

(A) g/2n

(B) g/n

(C) 2gn

(D) g/2n2

Answer: (D)

8. A circuit element X when connected to an a.c. supply of peak voltage 100 V gives a peak current of 5 A which is in phase with the voltage. A second element Y when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by π/2. If X and Y are connected in series to the same supply, what will be the rms value of the current in ampere?

(A) 10/√2

(B) 5/√2

(C) 5√2

(D) 5/2

Answer: (D)

9. An unpolarised light beam of intensity 2I0 is passed through a polaroid P and then through another polaroid Q which is oriented in such a way that its passing axis makes an angle of 30° relative to that of P. The intensity of the emergent light is

(A) I0/4

(B) I0/2

(C) 3I0/4

(D) 3I0/2

Answer: (C)

10. An α particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:

(A) √2 : 1

(B) 2√2 : 1

(C) 4√2 : 1

(D) 8 : 1

Answer: (B)

11. Read the following statements:

(A) Volume of the nucleus is directly proportional to the mass number.

(B) Volume of the nucleus is independent of mass number.

(C) Density of the nucleus is directly proportional to the mass number.

(D) Density of the nucleus is directly proportional to the cube root of the mass number.

(E) Density of the nucleus is independent of the mass number.

Choose the correct option from the following options

(A) (A) and (D) only

(B) (A) and (E) only

(C) (B) and (E) only

(D) (A) and (C) only

Answer: (B)

12. An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be

[If, g = 10 ms–2 and radius of earth = 6400 km]

(A) 48 MJ

(B) 24MJ

(C) 36MJ

(D) 12MJ

Answer: (A)

13. A ball is released from a height h. If t1 and t2 be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between t1 and t2.

(A) t1 = (√2)t2

(B) t1 = (√2 – 1)t2

(C) t2 = (√2 + 1)t1

(D) t2 = (√2 – 1)t1

Answer: (D)

14. Two bodies of masses m1 = 5 kg and m2 = 3 kg are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass m1 will be

[Take g = 10 ms–2]

(A) 30 N

(B) 40 N

(C) 50 N

(D) 60 N

Answer: (B)

15. If momentum of a body is increased by 20%, then its kinetic energy increases by

(A) 36%

(B) 40%

(C) 44%

(D) 48%

Answer: (C)

16. The torque of a force  about the origin is τ. If the force acts on a particle whose position vector is  then the value of τ will be

Answer: (C)

17. A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be

(A) −450 J

(B) 450 J

(C) 900 J

(D) 1350 J

Answer: (B)

18. The vertical component of the earth’s magnetic field is 6 × 10–5 T at any place where the angle of dip is 37°. The earth’s resultant magnetic field at that place will be (Given tan 37° = 3/4)

(A) 8 × 105 T

(B) 6 × 105 T

(C) 5 × 104 T

(D) 1 × 104 T

Answer: (D)

19. The root mean square speed of smoke particles of mass 5 × 1017 in their Brownian motion in air at NTP is approximately. [Given k = 1.38 × 1023 JK1]

(A) 60 mm s1

(B) 12mm s1

(C) 15mm s1

(D) 36mm s1

Answer: (C)

20. Light enters from air into a given medium at an angle of 45° with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of 15° from its original direction. The refractive index of the medium is

(A) 1.732

(B) 1.333

(C) 1.414

(D) 2.732

Answer: (C)

SECTION-B

21. A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity x√F rad s1.

Answer: (4)

22. Nearly 10% of the power of a 110 W light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of 1 m from the bulb to a distance of 5 m is a × 10–2m2. The value of ‘a’ will be _____.

Answer: (84)

23. A metal wire of length 0.5 m and cross-sectional area 10–4 m2 has breaking stress 5 × 108 Nm–2. A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _____ ms–1.

Answer: (50)

24. The velocity of a small ball of mass 0.3 g and density 8 g/cc when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3 g/cc, then the value of viscous force acting on the ball will be x × 10–4 The value of x is _______. [use g = 10 m/s2]

Answer: (25)

25. A modulating signal 2sin (6.28 × 106) t is added to the carrier signal 4sin(12.56 × 109) t for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passed through a band pass filter. The bandwidth of the output signal of band pass filter will be ______MHz.

Answer: (2)

26. The speed of a transverse wave passing through a string of length 50 cm and mass 10 g is 60 ms–1. The area of cross-section of the wire is 2.0 mm2 and its Young’s modulus is 1.2 × 1011 Nm–2. The extension of the wire over its natural length due to its tension will be x × 10–5 The value of x is _____.

Answer: (15)

27. The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is 10 s. If the metallic bob is immersed in water, then the new time period becomes 5√x s. The value of x will be _____.

Answer: (5)

28. A 8 V Zener diode along with a series resistance R is connected across a 20 V supply (as shown in the figure). If the maximum Zener current is 25 mA, then the minimum value of R will be ____ Ω.

Answer: (480)

29. Two radioactive materials A and B have decay constants 25λ and 16λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be ‘e’ after a time 1/aλ. The value of a is _____.

Answer: (9)

30. A capacitor of capacitance 500 μF is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. The maximum current in the LC circuit will be ______A.

Answer: (10)

CHEMISTRY

SECTION-A

1. Consider the reaction

4HNO3(l) + 3KCl(s) → Cl2(g) + NOCl(g) + 2H2O(g) + 3KNO3(s)

The amount of HNO3 required to produce 110.0 g of KNO3is :

(Given : Atomic masses of H, O, N and K are 1, 16, 14 and 39, respectively.)

(A) 32.2 g

(B) 69.4 g

(C) 91.5 g

(D) 162.5 g

Answer: (C)

2. Given below are the quantum numbers for 4 electrons.

(A)n = 3, l = 2, m1 = 1, ms = +1/2 

(B)n = 4, l = 1, m1 = 0, ms = +1/2 

(C)n = 4, l = 2, m1 = –2, ms = –1/2 

(D)n = 3, l = 1, m1 = –1, ms = +1/2 

The correct order of increasing energy is :

(A) D < B < A < C

(B) D < A < B < C 

(C) B < D < A < C

(D) B < D < C < A

Answer: (B)

3. C(s) + O2(g) → CO2(g) + 400 kJ

When coal of purity 60% is allowed to burn in presence of insufficient oxygen, 60% of carbon is converted into ‘CO’ and the remaining is converted into ‘CO2‘. 

The heat generated when 0.6 kg of coal is burnt is ______.

(A) 1600 kJ

(B) 3200 kJ

(C) 4400 kJ

(D) 6600 kJ

Answer: (D)

4. 200 mL of 0.01 M HCl is mixed with 400 mL of 0.01M H2SO4. The pH of the mixture is ____.

(A) 1.14

(B) 1.78

(C) 2.32

(D) 3.02

Answer: (B)

5. Given below are the critical temperatures of some of the gases :

The gas showing least adsorption on a definite amount of charcoal is :

(A) He

(B) CH4

(C) CO2

(D) NH3

Answer: (A)

6. In liquation process used for tin (Sn), the metal :

(A) is reacted with acid 

(B) is dissolved in water  

(C) is brought to molten form which is made to flow on a slope 

(D) is fused with NaOH.

Answer: (C)

7. Given below are two statements.

Statement I:Stannane is an example of a molecular hydride. 

Statement II:Stannane is a planar molecule. In the light of the above statement, choose the 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 is true but Statement II is false. 

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

Answer: (C)

8. Portland cement contains ‘X’ to enhance the setting time. What is ‘X’?

(A) 

(B) CaSO4.2H2O

(C) CaSO­4

(D) CaCO3

Answer: (B)

9. When borax is heated with CoO on a platinum loop, blue coloured bead formed is largely due to :

(A) B2O3

(B) Co(BO2)2

(C) CoB4O7

(D) Co[B4O5(OH)4]

Answer: (B)

10. Which of the following 3d-metal ion will give the lowest enthalpy of hydration (∆hydH) when dissolved in water ?

(A) Cr2+

(B) Mn2+

(C) Fe2+

(D) Co2+

Answer: (B)

11. Octahedral complexes of copper (II) undergo structural distortion (Jahn-Teller). Which one of the given copper (II) complexes will show the maximum structural distortion ?

(en–ethylenediamine; H2N-CH2-CH2-NH2)

(A) [Cu(H2O)6]SO4

(B) [Cu(en)(H2O)4]SO4

(C) cis-[Cu(en)2Cl2]

(D) trans-[Cu(en)2Cl2]

Answer: (A)

12. Dinitrogen is a robust compound, but reacts at high altitude to form oxides. The oxide of nitrogen that can damage plant leaves and retard photosynthesis is :

(A) NO

(B) NO3

(C) NO2

(D) NO2

Answer: (C)

13. Correct structure of γ-methylcyclohexanecarbaldehyde is :

Answer: (A)

14. Compound ‘A’ undergoes following sequence of reactions to give compound ‘B’. The correct structure and chirality of compound ‘B’ is:

[where Et is –C2H5

Answer: (C)

15. Given below are two statements.

Statement I: The compound  is optically active.

Statement II:  is mirror image of above compound A.

In the light of the above statement, 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)

16. When enthanol is heated with conc. H2SO4, a gas is produced. The compound formed, when this gas is treated with cold dilute aqueous solution of Baeyer’s reagent, is :

(A) Formaldehyde

(B) Formic acid 

(C)Glycol

(D) Ethanoic acid

Answer: (C)

17. The Hinsberg reagent is :

Answer: (A)

18. Which of the following is NOT a natural polymer?

(A) Protein  

(B) Starch 

(C) Rubber  

(D) Rayon

Answer: (D)

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

Assertion A : Amylose is insoluble in water. 

Reason R : Amylose is a long linear molecule with more than 200 glucose units. 

In the light of the above statements, choose the correct 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: (D)

20. A compound ‘X’ is a weak acid and it exhibits colour change at pH close to the equivalence point during neutralization of NaOH with CH3 Compound ‘X’ exists in ionized form in basic medium. The compound ‘X’ is :

(A) methyl orange

(B) methyl red 

(C) phenolphthalein

(D) erichrome Black T

Answer: (C)

SECTION-B

21. ‘x’ g of molecular oxygen (O2) is mixed with 200 g of neon (Ne). The total pressure of the nonreactive mixture of O2 and Ne in the cylinder is 25 bar. The partial pressure of Ne is 20 bar at the same temperature and volume. The value of ‘x’ is_____. [Given: Molar mass of O2 = 32 g mol–1.  Molar mass of Ne = 20 g mol–1]

Answer: (80)

22. Consider, PF5, BrF5, PCl3, SF6, [ICl4], ClF3 and IF5.

Amongst the above molecule(s)/ion(s), the number of molecule(s)/ion(s) having sp3d2 hybridisation is____.

Answer: (4)

23. 1.80 g of solute A was dissolved in 62.5 cm3 of ethanol and freezing point of the solution was found to be 155.1 K. The molar mass of solute A is _______ g mol–1.

[Given: Freezing point of ethanol is 156.0 K. Density of ethanol is 0.80 g cm–3.

Freezing point depression constant of ethanol is 2.00 K kg mol–1

Answer: (80)

24. For a cell, Cu(s) |Cu2+(0.001M| |Ag+(0.01M)| Ag(s) the cell potential is found to be 0.43 V at 298 K. The magnitude of standard electrode potential for Cu2+/Cu is _______ × 10–2 V.

Answer: (34)

25. Assuming 1μg of trace radioactive element X with a half life of 30 years is absorbed by a growing tree. The amount of X remaining in the tree after 100 years is______ × 10–1μ

[Given :ln 10 = 2.303; log2 = 0.30]

Answer: (1)

26. Sum of oxidation state (magnitude) and coordination number of cobalt in Na[Co(bpy)Cl4] is_______.

Answer: (9)

27. Consider the following sulphure based oxoacids. H2SO3, H2SO4, H2S2O8 and H2S2O7.

Amongst these oxoacids, the number of those with peroxo(O-O) bond is______.

Answer: (1)

28. A 1.84 mg sample of polyhydric alcoholic compound ‘X’ of molar mass 92.0 g/mol gave 1.344 mL of H2 gas at STP. The number of alcoholic hydrogens present in compound ‘X’ is____.

Answer: (3)

29. The number of stereoisomers formed in a reaction of (±) Ph(C=O) C(OH)(CN)Ph with HCN is_____.

Answer: (3)

30. The number of chlorine atoms in bithionol is____.

Answer: (4)

MATHEMATICS

SECTION-A

1. If z ≠ 0 be a complex number such that  then the maximum value of |z| is

(A) √2

(B) 1

(C) √2 − 1

(D) √2 + 1

Answer: (D)

2. Which of the following matrices can NOT be obtained from the matrix  by a single elementary row operation?

Answer: (C)

3. If the system of equations

x + y + z = 6

2x + 5y + αz = β

x + 2y + 3z = 14

has infinitely many solutions, then α + β is equal to

(A) 8

(B) 36

(C) 44

(D) 48

Answer: (C)

4. Let the function  be continuous at x = 0.

The α is equal to :

(A) 10

(B) −10

(C) 5

(D) −5

Answer: (D)

5. If [t] denotes the greatest integer ≤ t, then the value of  is

Answer: (A)

6. Let  be a sequence such that a0 = a1 = 0 and an+2 = 3an+1 – 2an + 1, ∀ n ≥

Then a25 a23 – 2 a25 a22 – 2 a23 a24 + 4 a22 a24 is equal to:

(A) 483

(B) 528

(C) 575

(D) 624

Answer: (B)

7. is equal to:

(A) 22! – 21!

(B) 22! – 2(21!)

(C) 21! – 2(20!)

(D) 21! – 20!

Answer: (B)

8. For  then

Answer: (A)

9. If the solution curve of the differential equation  passes through the points (2, 1) and (k + 1, 2), k > 0, then

Answer: (A)

10. Let y = y(x) be the solution curve of the differential equation  x >−1 which passes through the point (0, 1). Then y(1) is equal to

(A) 1/2

(B) 3/2

(C) 5/2

(D) 7/2

Answer: (B)

11. Let m1, m2 be the slopes of two adjacent sides of a square of side a such that  If one vertex of the square is (10 (cos α – sin α), 10(sin α + cos α)), where α ∈ (0, π/2) and the equation of one diagonal is (cosα – sin α)x + (sin α + cosα) y = 10, then 72(sin4α + cos4α) + a2 – 3a + 13 is equal to

(A) 119

(B) 128

(C) 145

(D) 155

Answer: (B)

12. The number of elements in the set 

(A) 1

(B) 3

(C) 0

(D) infinite

Answer: (A)

13. Let A(α, −2), B(α, 6) and C(α/4, −2) be vertices of a ΔABC. If (5, α/4) is the circumcentre of ΔABC, then which of the following is NOT correct about ΔABC?

(A) Area is 24

(B) Perimeter is 25

(C) Circumradius is 5

(D) Inradius is 2

Answer: (B)

14. Let Q be the foot of perpendicular drawn from the point P(1, 2, 3) to the plane x + 2y + z = 14. If R is a point on the plane such that ∠PRQ = 60°, then the area of ΔPQR is equal to :

(A) √3/2

(B) √3

(C) 2√3

(D) 3

Answer: (B)

15. If (2, 3, 9), (5, 2, 1), (1, λ, 8) and (λ, 2, 3) are coplanar, then the product of all possible values of λ is :

(A) 21/2

(B) 59/8

(C) 57/8

(D) 95/8

Answer: (D)

16. Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is :

(A) 4/9

(B) 5/18

(C) 1/6

(D) 3/10

Answer: (B)

17. S = {z = x + iy: |z – 1 + i| ≥ |z|, |z| < 2, |z + i| = |z – 1|}.Then the set of all values of x, for which w = 2x + iy∈ S for some y ∈ R is

Answer: (B)

18. Let  be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and  then  is equal to :

(A) 10

(B) 14

(C) 16

(D) 18

Answer: (C)

19. The domain of the function  is:

(A) [1, ∞)

(B) [−1, 2]

(C) [−1, ∞)

(D)  (−∞, 2]

Answer: (C)

20. The statement (p ⇒ q) ∨ (p ⇒ r) is NOT equivalent to

(A) (p∧ (~r)) ⇒ q

(B) (~q) ⇒ ((~r) ∨ p)

(C) p⇒ (q ∨ r)

(D) (p∧ (~q)) ⇒ r

Answer: (B)

SECTION-B

21. The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number of trials in the binomial distribution is _______.

Answer: (96)

22. Let α, β(α > β) be the roots of the quadratic equation x2 – x – 4 = 0. If Pn = αn – βn, n ∈ℕ then  is equal to ______.

Answer: (16)

23. Let  For k∈ N, if X’AkX = 33, then k is equal to _______.

Answer: (10)

24. The number of natural numbers lying between 1012 and 23421 that can be formed using the digits 2, 3, 4, 5, 6 (repetition of digits is not allowed) and divisible by 55 is _______.

Answer: (6)

25. If  then L is equal to _____.

Answer: (221)

26. If [t] denotes the greatest integer ≤ t, then the number of points, at which the function  is not differentiable in the open interval (–20, 20), is ________.

Answer: (79)

27. If the tangent to the curve y = x3 – x2 + x at the point (a, b) is also tangent to the curve y = 5x2 + 2x – 25 at the point (2, –1), then |2a + 9b| is equal to ________.

Answer: (195)

28. Let AB be a chord of length 12 of the circle  If tangents drawn to the circle at points A and B intersect at the point P, then five times the distance of point P from chord AB is equal to _______.

Answer: (72)

29. Let  be two vectors such that and  Then  is equal to _______.

Answer: (14)

30. Let

S = {(x, y) ∈ℕ×ℕ : 9(x – 3)2 + 16(y – 4)2≤ 144}

and

T = {(x, y)∈ℝ×ℝ : (x – 7)2 + (y – 4)2≤ 36}.

Then n(S ⋂ T) is equal to ______.

Answer: (27)

JEE Main Session 2 28th July 2022 Shift 2 Question Paper and Answer Key

JEE Main Session 2 28th July 2022 Shift 2

PHYSICS

Section-A

IMPORTANT INSTRUCTIONS:

(1)   The test is of 3 hours duration:

(2)   The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i)    Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

(ii)   Section-B: This section contains 10 questions. In Section-B, attempt any five questions out of 10. The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and −1 mark for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. Consider the efficiency of Carnot engine is given by where α and β are constants. If T is temperature, k is Boltzmann constant, θ is angular displacement, and x has the dimensions of length. Then, choose the incorrect option

(A) Dimensions of βis same as that of force. 

(B) Dimensions of α–1 x is same as that of energy. 

(C) Dimensions of η–1sinθ is same as that of αβ

(D) Dimensions of α is same as that of β

Answer: (D)

2. At time t = 0 a particle starts travelling from a height  in a plane keeping z coordinate constant. At any instant of time it’s position along the  directions are defined at 3t and 5t3 At t = 1 s acceleration of the particle will be

Answer: (B)

3. A pressure-pump has a horizontal tube of cross sectional area 10 cm2 for the outflow of water at a speed of 20 m/s. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is

[given: density of water = 1000 kg/m3]

(A) 300 N

(B) 500 N

(C) 250 N

(D) 400 N

Answer: (D)

4. A uniform metal chain of mass m and length ‘L’ passes over a massless and frictionless pully. It is released from rest with a part of its length ‘l’ is hanging on one side and rest of its length ‘L – l’ is hanging on the other side of the pully. At a certain point of time, when l = L/x, the acceleration of the chain is g/2. The value of x is ______.

(A) 6

(B) 2

(C) 1.5

(D) 4

Answer: (D)

5. A bullet of mass 200 g having initial kinetic energy 90 J is shot inside a long swimming pool as shown in the figure. If it’s kinetic energy reduces to 40 J within 1s, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is

(A) 45 m

(B) 90 m

(C) 125 m

(D) 25 m

Answer: (A)

6. Assume there are two identical simple pendulum Clocks-1 is placed on the earth and Clock-2 is placed on a space station located at a height h above the earth surface. Clock-1 and Clock-2 operate at time periods 4s and 6s respectively. Then the value of h is –

(consider radius of earth RE = 6400 km and g on earth 10 m/s2)

(A) 1200 km

(B) 1600km

(C) 3200km

(D) 4800km

Answer: (C)

7. Consider a cylindrical tank of radius 1 m is filled with water. The top surface of water is at 15 m from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of 5 m from the bottom. A force of 5 × 105 N is applied an the top surface of water using a piston. The speed of efflux from the hole will be:

(given atmospheric pressure PA = 1.01 × 105 Pa, density of water ρw = 1000 kg/m3 and gravitational acceleration g = 10 m/s2)

(A) 11.6 m/s

(B) 10.8m/s

(C) 17.8m/s

(D) 14.4m/s

Answer: (C)

8. A vessel contains 14 g of nitrogen gas at a temperature of 27°C. The amount of heat to be transferred to the gap to double the r.m.s. speed of its molecules will be : (Take R = 8.32 J mol–1k–1)

(A) 2229 J

(B) 5616 J

(C) 9360 J

(D) 13,104 J

Answer: (C)

9. A slab of dielectric constant K has the same cross-sectional area as the plates of a parallel plate capacitor and thickness  where d is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be :

(Given Co = capacitance of capacitor with air as medium between plates.)

Answer: (A)

10. A uniform electric field E = (8m/e) V/m is created between two parallel plates of length 1 m as shown in figure, (where m = mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of 2 m/s. The angle of the deviation (θ) of the path of the electron as it comes out of the field will be_______.

(A) tan1 (4)

(B) tan1 (2)

(C) tan1 (1/3)

(D) tan1 (3)

Answer: (B)

11. Given below are two statements :

Statement I : A uniform wire of resistance 80Ω  is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be 5Ω. 

Statement II : Two resistance 2R and 3R are connected in parallel in a electric circuit. The value of thermal energy developed in 3R and 2R will be in the ratio 3 : 2. 

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)

12. A triangular shaped wire carrying 10 A current is placed in a uniform magnetic field of 0.5 T, as shown in figure. The magnetic force on segment CD is (Given BC = CD = BD = 5 cm).

(A) 0.126 N

(B)  0.312 N

(C) 0.216 N

(D) 0.245 N

Answer: (C)

13. The magnetic field at the center of current carrying circular loop is B1. The magnetic field at a distance of √3 times radius of the given circular loop from the center on its axis is B2. The value of B1/B2 will be

(A) 9 : 4

(B)12 : √5

(C) 8 : 1

(D) 5 :√3

Answer: (C)

14. A transformer operating at primary voltage 8 kV and secondary voltage 160 V serves a load of 80 kW. Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be

(A) 800 Ω and 1.06 Ω

(B) 10 Ω and 500 Ω

(C) 800 Ω and 0.32 Ω

(D) 1.0 Ω and 500 Ω

Answer: (C)

15. Sun light falls normally on a surface of area 36 cm2 and exerts an average force of 7.2 × 10–9 N within a time period of 20 minutes. Considering a case of complete absorption, the energy flux of incident light is

(A) 25.92 × 102 W/cm2

(B) 8.64 × 106 W/cm2

(C) 6.0 W/cm2

(D) 0.06 W/cm2

Answer: (D)

16. The power of a lens (biconvex) is 1.25 m–1 in particular medium. Refractive index of the lens is 1.5, and the radii of curvature are 20 cm and 40 cm, respectively. The refractive index of surrounding medium

(A) 1.0

(B) 9/7

(C) 3/2

(D) 4/3

Answer: (B)

17. Two streams of photons, possessing energies equal to five and ten times the work function of metal are incident on the metal surface successively. The ratio of maximum velocities of the photoelectron emitted, in the two cases respectively, will be

(A) 1 : 2

(B) 1 : 3

(C) 2 : 3

(D) 3 : 2

Answer: (C)

18. A radioactive sample decays 7/8 times its original quantity in 15 minutes. The half-life of the sample is

(A) 5 min

(B) 7.5min

(C) 15min

(D) 30min

Answer: (A)

19. An npn transistor with current gain β = 100 in common emitter configuration is shown in the figure. The output voltage of the amplifier will be

(A) 0.1 V

(B) 1.0 V

(C) 10 V

(D) 100 V

Answer: (B)

20. A FM Broad cast transmitter, using modulating signal of frequency 20 kHz has a deviation ratio of 10. The Bandwidth required for transmission is

(A) 220 kHz

(B) 180kHz

(C) 360kHz

(D) 440kHz

Answer: (D)

SECTION-B

21. A ball is thrown vertically upwards with a velocity of 19.6 ms–1 from the top of a tower. The ball strikes the ground after 6 s. The height from the ground up to which the ball can rise will be (k/5) m. The value of k is ______ (use g = 9.8 m/s2)

Answer: (392)

22. The distance of centre of mass from end A of a one dimensional rod (AB) having mass density and length L (in meter) is  The value of α is ______. (where x is the distance from end A)

Answer: (8)

23. A string of area of cross-section 4mm2 and length 0.5 m is connected with a rigid body of mass 2 kg. The body is rotated in a vertical circular path of radius 0.5 m. The body acquires a speed of 5 m/s at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is ______×10–5.

(use young’s modulus 1011 N/m2 and g = 10 m/s2)

Answer: (30)

24. At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be ______ J.

Answer: (750)

25. The potential energy of a particle of mass 4 kg in motion along the x-axis is given by U = 4 (1–cos 4x) J. The time period of the particle for small oscillation (sin θ≃θ) is  The value of K is __________

Answer: (2)

26. An electrical bulb rated 220 V, 100 W, is connected in series with another bulb rated 220 V, 60 W. If the voltage across combination is 220 V, the power consumed by the 100 W bulb will be about ____________ W.

Answer: (14)

27. For the given circuit the current through battery of 6 V just after closing the switch ‘S’ will be __________ A.

Answer: (1)

28. An object ‘o’ is placed at a distance of 100 cm in front of a concave mirror of radius of curvature 200 cm as shown in the figure. The object starts moving towards the mirror at a speed 2 cm/s. The position of the image from the mirror after 10s will be at _______ cm.

Answer: (400)

29. In an experiment with a convex lens, the plot of the image distance (ν′) against the object distance (μ′) measured from the focus gives a curve ν′μ′ = 225. If all the distances are measured in cm. The magnitude of the focal length of the lens is _______ cm.

Answer: (15)

30. In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0.5 s is measured from time of 100 oscillations with a watch of 1 s resolution. If measured value of length is 10 cm known to 1 mm accuracy, the accuracy in the determination of g is found to be x %. The value of x is _________.

Answer: (5)

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 : Zero orbital overlap is an out of phase overlap. 

Reason : It results due to different orientation/ direction of approach of orbitals. 

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. The correct decreasing order for metallic character is

(A) Na > Mg > Be > Si > P  

(B) P > Si > Be > Mg > Na 

(C) Si > P > Be > Na > Mg 

(D) Be > Na > Mg > Si > P

Answer: (A)

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

Assertion A : The reduction of a metal oxide is easier if the metal formed is in liquid state than solid state. 

Reason R : The value of ∆Gbecomes more on negative side as entropy is higher in liquid state than solid state. 

In the light of the above statements. Choose the most appropriate answer from the options given below

(A) Both A and R are correct and R is the correct explanation of A 

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

(C) A is correct but R is not correct 

(D) A is not correct but R is correct

Answer: (A)

4. The products obtained during treatment of hard water using Clark’s method are:

(A) CaCO3 and MgCO3

(B) Ca(OH)2 and Mg(OH)2

(C) CaCO3 and Mg(OH)2

(D) Ca(OH)2 and MgCO3

Answer: (C)

5. Statement I: An alloy of lithium and magnesium is used to make aircraft plates.

Statement II: The magnesium ions are important for cell-membrane integrity. 

In the light 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: (B)

6. White phosphorus reacts with thionyl chloride to give

(A) PCl5, SO2 and S2Cl2

(B) PCl3, SO2 and S2Cl2

(C) PCl3, SO2 and Cl2

(D) PCl5, SO2 and Cl2

Answer: (B)

7. Concentrated HNO3 reacts with Iodine to give

(A) HI, NO2 and H2O

(B) HIO2, N2O and H2

(C) HIO3, NO2 and H2O

(D) HIO4, N2O and H2O

Answer: (C)

8. Which of the following pair is not isoelectronic species?

(At. no.Sm, 62; Er, 68: Yb, 70: Lu, 71; Eu, 63: Tb, 65; Tm, 69)

(A) Sm2+ and Er3+

(B) Yb2+ and Lu3+

(C) Eu2+ and Tb4+

(D) Tb2+ and Tm4+

Answer: (D)

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

Assertion A: Permanganate titrations are not performed in presence of hydrochloric acid. 

Reason R: Chlorine is formed as a consequence of oxidation of hydrochloric acid.

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)

10. Match List I with List II

Choose the correct answer from the options given below:

(A) A-IV, B-I, C-III, D-II 

(B) A-I. B-IV, C-III, D-II 

(C) A-I. B-IV, C-II, D-III 

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

Answer: (B)

11. Dinitrogen and dioxygen. the main constituents of air do not react with each other in atmosphere to form oxides of nitrogen because

(A) N2 is unreactive in the condition of atmosphere. 

(B) Oxides of nitrogen are unstable. 

(C) Reaction between them can occur in the presence of a catalyst. 

(D) The reaction is endothermic and require very high temperature.

Answer: (D)

12. The major product in the given reaction is

Answer: ()

13. Arrange the following in increasing order of reactivity towards nitration  

(A) p-xylene         (B) bromobenzene

(C)mesitylene       (D) nitrobenzene 

(E)benzene

Choose the correct answer from the options given below

(A) C < D < E < A < B 

(B) D < B < E < A < C 

(C) D < C < E < A < B  

(D) C < D < E < B < A

Answer: (B)

14. Compound I is heated with Conc. HI to give a hydroxy compound A which is further heated with Zn dust to give compound B. Identify A and B.

Answer: (D)

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

Assertion A: Aniline on nitration yields ortho, meta&para nitro derivatives of aniline. 

Reason R: Nitrating mixture is a strong acidic mixture.

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)

16. 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-III, B-II, C-IV, D-I 

(C) A-III, B-I, C-IV, D-II 

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

Answer: (B)

17. Two statements in respect of drug-enzyme interaction are given below

Statement I: Action of an enzyme can be blocked only when an inhibitor blocks the active site of the enzyme.

Statement II: An inhibitor can form a strong covalent bond with the enzyme.

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: (D)

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

Assertion A: Thin layer chromatography is an adsorption chromatography. 

Reason: A thin layer of silica gel is spread over a glass plate of suitable size in thin layer chromatography which acts as an adsorbent. 

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)

19. The formulas of A and B for the following reaction sequence are

(A) A = C7H14O8, B = C6H14

(B) A = C7H13O7, B = C7H14O

(C) A = C7H12O8, B = C6H14

(D) A = C7H14O8, B = C6H14O6

Answer: (A)

20. 

Find out the major product for the above reaction.

Answer: (C)

SECTION-B

21. 2L of 0.2 M H2SO4 is reacted with 2L of 0.1 M NaOH solution, the molarity of the resulting product Na2SO4 in the solution is ____ millimolar. (Nearest integer).

Answer: (25)

22. Metal M crystallizes into a FCC lattice with the edge length of 4.0×10−8 The atomic mass of the metal is ______ g/mol.

(Nearest integer).  (Use : NA = 6.02×1023 mol−1, density of metal, M = 9.03 g cm−3)

Answer: (87)

23. If the wavelength for an electron emitted from Hatom is 3.3×1010 m, then energy absorbed by the electron in its ground state compared to minimum energy required for its escape from the atom, is _____times. (Nearest integer).

[Given : h = 6.626 ×1034Js,                Mass of electron = 9.1×101]

Answer: (2)

24. A gaseous mixture of two substances A and B, under a total pressure of 0.8 atm is in equilibrium with an ideal liquid solution. The mole fraction of substance A is 0.5 in the vapour phase and 0.2 in the liquid phase. The vapour pressure of pure liquid A is _______ atm. (Nearest integer)

Answer: (2)

25. At 600K, 2 mol of NO are mixed with 1 mol of O2.

2NO(g) + O2(g) ⇄ 2NO2(g)

The reaction occurring as above comes to equilibrium under a total pressure of 1 atom. Analysis of the system shows that 0.6 mol of oxygen are present at equilibrium. The equilibrium constant for the reaction is _______. (Nearest integer).

Answer: (2)

26. A sample of 0.125 g of an organic compound when analysed by Duma’s method yields 22.78 mL of nitrogen gas collected over KOH solution at 280K and 759 mm Hg. The percentage of nitrogen in the given organic compound is ____. (Nearest integer).

(a) The vapour pressure of water at 280 K is 14.2 mm Hg

(b) R = 0.082 L atm K–1mol–1

Answer: (22)

27. On reaction with stronger oxidizing agent like KIO4, hydrogen peroxide oxidizes with the evolution of O2. The oxidation number of I in KIO4changes to ______.

Answer: (5)

28. For a reaction, given below is the graph of ln k vs 1/T. The activation energy for the reaction is equal to ________ cal mol1. (Nearest integer).

(Given : R = 2 cal K1 mol1)

Answer: (8)

29. Among the following the number of curves not in accordance with Freundlich adsorption isotherm is ______.

Answer: (3)

30. Among the following the number of state variable is ______.

Internal energy (U) 

Volume (V) 

Heat (q) 

Enthalpy (H)

Answer: (3)

MATHEMATICS

SECTION-A

1. Let  and T = {x ∈Z : x2 – 7|x| + 9 ≤ 0}. Then the number of elements in S ∩ T is

(A) 7

(B) 5

(C) 4

(D) 3

Answer: (D)

2. Let α, β be the roots of the equation x2 – √2x + √6 = 0 and  be the roots of the equation x2 + ax + b = 0 . Then the roots of the equation x2 – (a + b – 2)x + (a + b + 2) = 0 are

(A) Non-real complex number

(B) Real and both negative

(C) Real and both positive

(D) Real and exactly one of them is positive

Answer: (B)

3. Let A and B be any two 3 × 3 symmetric and skew symmetric matrices, respectively. Then which of the following is NOT true?

(A) A4 – B4 is a symmetric matrix

(B) AB – BA is a symmetric matrix

(C) B5 – A5 is a skew-symmetric matrix

(D) AB + BA is a skew-symmetric matrix

Answer: (C)

4. Let f(x) = ax2 + bx + c be such that f(1) = 3, f(-2) = λ and f(3) = 4. If f(0) + f(1) + f(-2) + f(3) = 14, then λ is equal to

(A) −4

(B) 13/2

(C) 23/2

(D) 4

Answer: (D)

5. The function f: ℝ → ℝ defined by  is continuous for all x in

(A) ℝ − {−1}

(B) ℝ − {−1, 1}

(C) ℝ − {1}

(D) ℝ − {0}

Answer: (B)

6. The function f(x) = xex(1x), x ∈ ℝ is

(A) Increasing in (−1/2, 1)

(B) Decreasing in (1/2, 2)

(C) Increasing in (−1, −1/2)

(D) Decreasing in (−1/2, 1/2)

Answer: (A)

7. The sum of the absolute maximum and absolute minimum values of the function f(x) = tan1 (sin x – cos x) in the interval [0, π] is

(A) 0

(B) 

(C) 

(D) –π/12

Answer: (C)

8. Let  and  Then  is equal to

(A) −2√2/3

(B) 2/3

(C) 1/3

(D) −2/3

Answer: (D)

9. Let  n = 1, 2, 3, ….. Then

(A) 50I6 – 9I5 = xI′5

(B) 50I6 – 11I5 = xI′5

(C) 50I6 – 9I5 = I′5

(D) 50I6 – 11I5=  I′5

Answer: (A)

10. The area enclosed by the curves y = loge (x + e2),  and x = loge2, above the line y = 1 is

(A) 2 + e – loge 2

(B) 1 + e – loge 2

(C) e– loge 2

(D) 1 + loge 2

Answer: (B)

11. Let y = y(x) be the solution curve of the differential equation  passing through the point  Then √7 (8) is equal to

(A) 11 + 6loge 3

(B) 19

(C) 12 – 2loge 3

(D) 19 – 6loge 3

Answer: (D)

12. The differential equation of the family of circles passing through the points (0, 2) and (0, –2) is

Answer: (A)

13. Let the tangents at two points A and B on the circle x2 + y2 – 4x + 3 = 0 meet at origin O(0, 0). Then the area of the triangle OAB is

(A) 3√3/2

(B) 3√3/4

(C) 3/2√3

(D) 3/4√3

Answer: (B)

14. Let the hyperbola  pass through the point (2√2, −2√2). A parabola is drawn whose focus is same as the focus of H with positive abscissa and the directrix of the parabola passes through the other focus of H. If the length of the latus rectum of the parabola is e times the length of the latus rectum of H, where e is the eccentricity of H, then which of the following points lies on the parabola?

(A) (2√3, 3√2)

(B) (3√3, −6√2)

(C) (√3, −√6)

(D) (3√6, 6√2)

Answer: (B)

15. Let the lines  and  be coplanar and P be the plane containing these two lines. Then which of the following points does NOT lie on P?

(A) (0, −2, −2)

(B) (−5, 0, −1)

(C) (3, −1, 0)

(D) (0, 4, 5)

Answer: (D)

16. A plane P is parallel to two lines whose direction rations are –2, 1, –3 and –1, 2, –2 and it contains the point (2, 2, –2). Let P intersect the co-ordinate axes at the points A, B, C making the intercepts α, β, γ. If V is the volume of the tetrahedron OABC, where O is the origin and p = α + β + γ, then the ordered pair (V, p) is equal to :

(A) (48, –13)

(B) (24, –13)

(C) (48, 11)

(D) (24, –5)

Answer: (B)

17. Let S be the set of all a∈ R for which the angle between the vectors  and  is acute. Then S is equal to

(A) (−∞, −4/3)

(B) Φ

(C) (−4/3, 0)

(D) (12/7, ∞)

Answer: (C)

18. A horizontal park is in the shape of a triangle OAB with AB = 16. A vertical lamp post OP is erected at the point O such that ∠PAO = ∠PBO = 15° and ∠PCO = 45°, where C is the midpoint of AB. Then (OP)2 is equal to

Answer: (B)

19. Let A and B be two events such that  and  Consider

(S1) P(A′ ∪ B) = 5/6,

(S2) P(A′ ∩ B′) = 1/18. Then

(A) Both (S1) and (S2) are true

(B) Both (S1) and (S2) are false

(C) Only (S1) is true

(D) Only (S2) is true

Answer: (A)

20. Let

p : Ramesh listens to music.

q :Ramesh is out of his village.

r : It is Sunday.

s : It is Saturday.

Then the statement “Ramesh listens to music only if he is in his village and it is Sunday or Saturday” can be expressed as

(A) ((~q) ∧ (r ∨ s)) ⇒ P

(B) (q∧ (r ∨ s)) ⇒ P

(C) p⇒ (q ∧ (r ∨ s))

(D) p⇒ ((~q)∧ (r ∨ s))

Answer: (D)

SECTION-B

21. Let the coefficients of the middle terms in the expansion of  and  respectively form the first three terms of an A.P. If d is the common difference of this A.P., then  is equal to _______

Answer: (57)

22. A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168, then b + 3 g is equal to ______.

Answer: (17)

23. Let the tangents at the points P and Q on the ellipse  meet at the point R(√2, 2√2 – 2). If S is the focus of the ellipse on its negative major axis, then SP2 + SQ2is equal to ________.

Answer: (13)

24. If 1 + (2 + 49C1 + 49C2 + … 49C49) (50C2 + 50C4 + … 50C50) is equal to 2n. m, where m is odd, then n + m is equal to ______.

Answer: (99)

25. Two tangent lines l1 and l2 are drawn from the point (2, 0) to the parabola 2y2 = – x. If the lines l1 and l2 are also tangent to the circle (x – 5)2 + y2 = r, then 17r is equal to _________.

Answer: (9)

26. If  where m is odd, then m.n is equal to ______

Answer: (12)

27. Let  Then the number of elements in the set

A = {θ∈S : tan θ(1 + √5 tan(2θ)) = √5 – tan(2θ)} is ______

Answer: (5)

28. Let z = a + ib, b≠ 0 be complex numbers satisfying  Then the least value of n ∈ N, such that zn = (z + 1)n, is equal to _____.

Answer: (6)

29. A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If σ2 is the variance of X, then 100 σ2 is equal to ____.

Answer: (56)

30. The value of the integral  is equal to _______

Answer: (104)

JEE Main Session 2 27th July 2022 Shift 2 Question Paper and Answer Key

JEE Main Session 2 27th July 2022 Shift 2

PHYSICS

SECTION-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

(ii) Section-B: This section contains 10 questions. In Section-B, attempt any five questions out of 10. The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and −1 mark for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. An expression of energy density is given by  where α, β are constants, x is displacement, k is Boltzmann constant and t is the temperature. The dimensions of β will be

(A)  [ML2T2θ1]

(B)  [M0L2T2]

(C)  [M0L0T0]

(D)  [M0L2T0]

Answer: (D)

2. A body of mass 10 kg is projected at an angle of 45° with the horizontal. The trajectory of the body is observed to pass through a point (20, 10). If T is the time of flight, then its momentum vector, at time t = T/√2, is

[Take g = 10 m/s2]

Answer: (D)

3. A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is θ. The magnitude of the contact force will be :

(A)  Mg

(B)  Mg cosθ

(C) 

(D) 

Answer: (A)

4. A block ‘A’ takes 2 s to slide down a frictionless incline of 30° and length ‘l’, kept inside a lift going up with uniform velocity ‘v’. If the incline is changed to 45°, the time taken by the block, to slide down the incline, will be approximately:

(A)  2.66 s

(B)  0.83 s

(C)  1.68 s

(D)  0.70 s

Answer: (C)

5. The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is:

(A)  2.0

(B)  1.0

(C)  0.5

(D)  1.5

Answer: (C)

6. A body of mass m is projected with velocity λvein vertically upward direction from the surface of the earth into space. It is given that evis escape velocity and λ< 1. If air resistance is considered to the negligible, then the maximum height from the centre of earth, to which the body can go, will be (R : radius of earth)

Answer: (B)

7. A steel wire of length 3.2 m (Ys = 2.0 × 1011 Nm2) and a copper wire of length 4.4 m (Yc = 1.1 × 1011 Nm2), both of radius 1.4 mm are connected end to end. When stretched by a load, the net elongation is found to be 1.4 mm. The load applied, in Newton, will be:

(Given π = 22/7)

(A)  360

(B)  180

(C)  1080

(D)  154

Answer: (D)

8. In 1st case, Carnot engine operates between temperatures 300 K and 100 K. In 2nd case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in 2nd case) will be:

(A) Same as the 1st case

(B) Always greater than the 1st case

(C) Always less than the 1st case

(D) May increase or decrease with respect to the 1st case

Answer: (C)

9. Which statements are correct about degrees of freedom?

(A) A molecule with n degrees of freedom has n2 different ways of storing energy.

(B) Each degree of freedom is associated with (1/2)RT average energy per mole.

(C) A monatomic gas molecule has 1 rotational degree of freedom whereas diatomic molecule has 2 rotational degrees of freedom.

(D) CH4 has a total of 6 degrees of freedom.

Choose the correct answer from the option given below:

(A) (B) and (C) only

(B) (B) and (D) only

(C) (A) and (B) only

(D) (C) and (D) only

Answer: (B)

10. A charge of 4 μC is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be:

(A) 1 μC and 3 μC

(B) 2 μC and 2 μC

(C) 0 and 4 μC

(D) 1.5 μC and 2.5 μC

Answer: (B)

11. (A) The drift velocity of electrons decreases with the increase in the temperature of conductor.

(B) The drift velocity is inversely proportional to the area of cross-section of given conductor.

(C) The drift velocity does not depend on the applied potential difference to the conductor.

(D) The drift velocity of electron is inversely proportional to the length of the conductor.

(E) The drift velocity increases with the increase in the temperature of conductor.

Choose the correct answer from the options given below

(A) (A) and (B) only

(B) (A) and (D) only

(C) (B) and (E) only

(D) (B) and (C) only

Answer: (A)

12. A compass needle of oscillation magnetometer oscillates 20 times per minute at a place P of dip 30°. The number of oscillations per minute become 10 at another place Q of 60° dip. The ratio of the total magnetic field at the two places (BQ: BP) is

(A)  √3 : 4

(B)  4 :√3

(C)  √3 : 2

(D)  2 :√3

Answer: (A)

13. A cyclotron is used to accelerate protons. If the operating magnetic field is 1.0 T and the radius of the cyclotron ‘dees’ is 60 cm, the kinetic energy of the accelerated protons in MeV will be

(Use mp = 1.6 × 1027 kg, e = 1.6 × 1019 C]

(A)  12

(B)  18

(C)  16

(D)  32

Answer: (B)

14. A series LCR circuit has L = 0.01 H, R = 10 Ω and C = 1 μF and it is connected to ac voltage of amplitude (Vm) 50 V. At frequency 60% lower than resonant frequency, the amplitude of current will be approximately :

(A)  466 mA

(B)  312mA

(C)  238mA

(D)  196mA

Answer: (C)

15. Identify the correct statements from the following descriptions of various properties of electromagnetic waves.

(A) In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field.

(B) The energy in electromagnetic wave is divided equally between electric and magnetic fields.

(C) Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave.

(D) The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other.

(E) The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light.

Choose the most appropriate answer from the options given below

(A) (D) only

(B) (B) & (D) only

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

(D) (A), (B) & (E) only

Answer: (B)

16. Two coherent sources of light interfere. The intensity ratio of two sources is 1 : 4. For this interference pattern if the value of  is equal to  will be:

(A)  1.5

(B)  2

(C)  0.5

(D)  1

Answer: (B)

17. With reference to the observations in photo-electric effect, identify the correct statements from below:

(A) The square of maximum velocity of photoelectrons varies linearly with frequency of incident light.

(B) The value of saturation current increases on moving the source of light away from the metal surface.

(C) The maximum kinetic energy of photo-electrons decreases on decreasing the power of LED (Light emitting diode) source of light.

(D) The immediate emission of photo-electrons out of metal surface can not be explained by particle nature of light/electromagnetic waves.

(E) Existence of threshold wavelength can not be explained by wave nature of light/electromagnetic waves.

Choose the correct answer from the options given below.

(A) (A) & (B) only

(B) (A) & (E) only

(C) (C) & (E) only

(D) (D) & (E) only

Answer: (B)

18. The activity of a radioactive material is 6.4 × 104 Its half life is 5 days. The activity will become 5 × 106 curie after

(A) 7 days

(B) 15 days

(C) 25 days

(D) 35 days

Answer: (D)

19. For a constant collector-emitter voltage of 8 V, the collector current of a transistor reached to the value of 6 mA from 4 mA, whereas base current changed from 20 μA to 25 μA value. If transistor is in active state, small signal current gain (current amplification factor) will be

(A)  240

(B)  400

(C)  0.0025

(D)  200

Answer: (B)

20. A square wave of the modulating signal is shown in the figure. The carrier wave is given by C(t) = 5 sin(8πt) Volt. The modulation index is

(A)  0.2

(B)  0.1

(C)  0.3

(D)  0.4

Answer: (A)

SECTION-B

21. In an experiment to determine the Young’s modulus, steel wires of five different lengths (1, 2, 3, 4 and 5 m) but of same cross section (2 mm2) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young’s modulus of given steel wires is x × 1011 Nm–2, then the value of x is ______.

Answer: (2)

22. In the given figure of meter bridge experiment, the balancing length AC corresponding to null deflection of the galvanometer is 40 cm. The balancing length, if the radius of the wire AB is doubled, will be ________ cm.

Answer: (40)

23. A thin prism of angle 6º and refractive index for yellow light (nY)1.5 is combined with another prism of angle 5º and nY = 1.55. The combination produces no dispersion. The net average deviation (δ) produced by the combination is (1/x)°. The value of x is _______

Answer: (4)

24. A conducting circular loop is placed in X -Y plane in presence of magnetic field  in SI unit. If the radius of the loop is 1 m, the induced emf in the loop, at time t = 2 s is nπV. The value of n is ______.

Answer: (12)

25. As show in the figure, in the steady state, the charge stored in the capacitor is _________ × 10–6 C.

Answer: (10)

26. A parallel plate capacitor with width 4 cm, length 8 cm and separation between the plates of 4 mm is connected to a battery of 20 V. A dielectric slab of dielectric constant 5 having length 1 cm, width 4 cm and thickness 4 mm is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be _______ ε0 (Where ε0 is the permittivity of free space)

Answer: (240)

27. A wire of length 30 cm, stretched between rigid supports, has it’s nth and (n + 1)th harmonics at 400 Hz and 450 Hz, respectively. If tension in the string is 2700 N, its linear mass density is _____ kg/m.

Answer: (3)

28. A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of the another single soap bubble of radius r cm. The value of r is ________

Answer: (2)

29. A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding the strings to achieve a speed of 4 m/s, is ________ cm. (Take g = 10 m/s2).

Answer: (120)

30. Two inclined planes are placed as shown in figure. A block is projected from the point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top point B at a height 10 m. After reaching the point B the block sides down on inclined plane BC. Time it takes to reach to the point C from point A is t(√2 + 1) s. The value of t is ______. (Use g = 10 m/s2)

Answer: (2)

CHEMISTRY

SECTION-A

1. The correct decreasing order of energy, for the orbitals having, following set of quantum numbers:

(A) n = 3, l = 0, m = 0 

(B) n = 4, l = 0, m = 0 

(C) n = 3, l = 1, m = 0 

(D) n = 3, l = 2, m = 1

(A) (D) > (B) > (C) > (A) 

(B) (B) > (D) > (C) > (A) 

(C) (C) > (B) > (D) > (A) 

(D) (B) > (C) > (D) > (A)

Answer: (A)

2. Match List-I with List-II

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

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

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

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

Answer: (C)

3. The Plot of pH-metric titration of weak base NH4OH vs strong acid HCl looks like:

Answer: (A)

4. Given below are two statements:

Statement I: For KI, molar conductivity increases steeply with dilution. 

Statement II: For carbonic acid, molar conductivity increases slowly with dilution.

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: (B)

5. Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R)

Assertion (A): Dissolved substances can be removed from a colloidal solution by diffusion through a parchment paper.  Reason (R): Particles in a true solution cannot pass through parchment paper but the collodial particles can pass through the parchment paper.  In the light of the above statements, choose the correct answer from the options given below:

(A) Both (A) and (R) are correct and (R) is the correct explanation of (A)  

(B) Both (A) and (R) are correct but (R) is not the correct explanation of (A) 

(C) (A) is correct but (R) is not correct

(D) (A) is not correct but (R) is correct

Answer: (C)

6. Outermost electronic configurations of four elements A, B, C, D are given below:

(A) 3s2  (B) 3s23p1 (C) 3s23p3  (D) 3s23p4  The correct order of first ionization enthalpy for them is:

(A) (A) < (B) < (C) < (D) 

(B) (B) < (A) < (D) < (C)  

(C) (B) < (D) < (A) < (C) 

(D) (B) < (A) < (C) < (D)

Answer: (B)

7. An element A of group 1 shows similarity to an element B belonging to group 2. If A has maximum hydration enthalpy in group 1 then B is:

(A)  Mg

(B)  Be

(C)  Ca

(D)  Sr

Answer: (A)

8. Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R)

Assertion (A): Boron is unable to form BF63

Reason (R): Size of B is very small. 

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: (B)

9. In neutral or alkaline solution, MnO4 oxidises thiosulphate to:

(A)  S2O72

(B)  S2O82

(C)  SO32

(D)  SO42

Answer: (D)

10. Low oxidation state of metals in their complexes are common when ligands:

(A) have good π-accepting character 

(B) have good σ-donor character 

(C) arehavind good π-donating ability 

(D) arehavind poor σ-donating ability

Answer: (A)

11. Given below are two statements:

Statement I: The non bio-degradable fly ash and slag from steel industry can be used by cement industry.

Statement II: The fuel obtained from plastic waste is lead free.

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)

12. The structure of A in the given reaction is:

Answer: (C)

13. Major product ‘B’ of the following reaction sequence is:

Answer: (B)

14. Match List-I with List-II.

List-II

(I) Gatterman Koch reaction 

(II) Etard reaction 

(III) Stephen reaction 

(IV) Rosenmundreaction  Choose the correct answer from the options given below:

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

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

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

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

Answer: (A)

15. Match List-I with List-II.

Choose the correct answer from the option given below:

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

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

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

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

Answer: (A)

16. An organic compound ‘A’ contains nitrogen and chlorine. It dissolves readily in water to give a solution that turns litmus red. Titration of compound ‘A’ with standard base indicates that the molecular weight of ‘A’ is 131± When a sample of ‘A’ is treated with aq. NaOH, a liquid separates which contains N but not Cl. Treatment of the obtained liquid with nitrous acid followed by phenol gives orange precipitate. The compound ‘A’ is :

Answer: (D)

17. Match List-I with List-II

List-I 

(A) Glucose + HI 

(B) Glucose + Br2 water 

(C) Glucose + acetic anhydride 

(D) Glucose + HNO3

List-II 

(I) Gluconic acid 

(II) Glucose pentacetate

(III) Saccharic acid 

(IV) Hexane  

Choose the correct answer from the options given below:

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

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

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

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

Answer: (A)

18. Which of the following enhances the lathering property of soap?

(A)  Sodium stearate 

(B) Sodium carbonate  

(C) Sodium rosinate

(D) Trisodium phosphate 

Answer: (C)

19. Match List-I with List-II

List-I (Mixture) 

(A) Chloroform& Aniline 

(B) Benzoic acid &Napthalene

(C) Water & Aniline 

(D) Napthalene& Sodium chloride  

List-II (Purification Process) 

(I) Steam distillation 

(II) Sublimation 

(III) Distillation 

(IV) Crystallisation

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

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

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

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

Answer: (D)

20. Fe3+cation gives a prussian blue precipitate on addition of potassium ferrocyanide solution due to the formation of:

(A)  [Fe(H2O)6]2 [Fe(CN)6]

(B)  Fe2[Fe(CN)6]2

(C)  Fe3[Fe(OH)2(CN)4]2

(D)  Fe4[Fe(CN)6]3          

Answer: (D)

SECTION-B

21. The normality of H2SO4 in the solution obtained on mixing 100 mL of 0.1 M H2SO4 with 50 mL of 0.1 M NaOH is_______×10–1 (Nearest Integer)

Answer: (1)

22. For a real gas at 25°C temperature and high pressure (99 bar) the value of compressibility factor is 2, so the value of Vander Waal’s constant ‘b’ should be_________×10–2 L mol–1 (Nearest integer) (Given R = 0.083 L bar K–1mol–1)

Answer: (25)

23. A gas (Molar mass = 280 g mol–1) was burnt in excess O2 in a constant volume calorimeter and during combustion the temperature of calorimeter increased from 298.0 K to 298.45 K. If the heat capacity of calorimeter is 2.5 kJ K–1 and enthalpy of combustion of gas is 9 kJ mol–1 then amount of gas burnt is _______ g. (Nearest Integer)

Answer: (35)

24. When a certain amount of solid A is dissolved in 100 g of water at 25°C to make a dilute solution, the vapour pressure of the solution is reduced to one-half of that of pure water. The vapour pressure of pure water is 23.76 mmHg. The number of moles of solute A added is________. (Nearest Integer)

Answer: (3)

25. 

If formation of compound [B] follows the first order of kinetics and after 70 minutes the concentration of [A] was found to be half of its initial concentration. Then the rate constant of the reaction is x × 106 s1. The value of x is______.

(Nearest Integer)

Answer: (165)

26. Among the following ores Bauxite, Siderite, Cuprite, Calamine, Haematite, Kaolinite, Malachite, Magnetite, Sphalerite, Limonite, Cryolite, the number of principal ores if (of) iron is_______.

Answer: (4)

27. The oxidation state of manganese in the product obtained in a reaction of potassium permanganate and hydrogen peroxide in basic medium is ______.

Answer: (4)

28. The number of molecule(s) or ion(s) from the following having non-planar structure is______.

Answer: (6)

29. The spin only magnetic moment of the complex present in Fehling’s reagent is______ B.M. (Nearest integer).

Answer: (2)

30. 

In the above reaction, 5 g of toluene is converted into benzaldehyde with 92% yield. The amount of benzaldehyde produced is ______×102 g. (Nearest integer)

Answer: (530)

MATHEMATICS

SECTION-A

1. The domain of the function f(x) = sin1[2x2 – 3] + log2(log1/2(x2 – 5x + 5)), where [t] is the greatest integer function, is:

Answer: (C)

2. Let S be the set of (α, β), π < α, β < 2π, for which the complex number  is purely imaginary and  is purely real. Let Zαβ = sin 2α + icos 2β, (α, β) ∈

Then  is equal to:

(A)  3

(B)  3i

(C)  1

(D)  2 – i

Answer: (C)

3. If α, β are the roots of the equation  then the equation, whose roots are  is

(A) 3x2 – 20x – 12 = 0

(B) 3x2 – 10x – 4 = 0

(C) 3x2 – 10x + 2 = 0

(D) 3x2 – 20x + 16 = 0

Answer: (B)

4. Let  If A2 + γA + 18I = 0, then det (A) is equal to ______.

(A)  −18

(B)  18

(C)  −50

(D)  50

Answer: (B)

5. If for p ≠ q ≠ 0, the function  is continuous at x = 0, then:

(A)  7pq f(0) – 1 = 0

(B)  63q f(0) – p2 = 0

(C)  21q f(0) – p2 = 0

(D)  7pq f(0) – 9 = 0

Answer: (B)

6. Let f(x) = 2 + |x| – |x – 1| + |x + 1|, x ∈ Consider

Then,

(A) Both (S1) and (S2) are correct

(B) Both (S1) and (S2) are wrong

(C) Only (S1) is correct

(D) Only (S2) is correct

Answer: (D)

7. Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5. Let the sum of its first five terms be 98/25. Then the sum of the first 21 terms of an AP, whose first term is 10ar, nth term is an and the common difference is 10ar2, is equal to

(A)  21a11

(B)  22a11

(C)  15a16

(D)  14a16

Answer: (A)

8. The area of the region enclosed by y ≤ 4x2, x2≤ 9y and y ≤ 4, is equal to

(A)  40/3

(B)  56/3

(C)  112/3

(D)  80/3

Answer: (D)

9. where [t] is the greatest integer function, is equal to

(A)  7/6

(B)  19/12

(C)  31/12

(D)  3/2

Answer: (B)

10. Consider a curve y = y(x) in the first quadrant as shown in the figure. Let the area A1 is twice the area A2. Then the normal to the curve perpendicular to the line 2x – 12y = 15 does NOT pass through the point.

(A)  (6, 21)

(B)  (8, 9)

(C)  (10, −4)

(D)  (12, −15)

Answer: (C)

11. The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0, x + py = 39 and x – y = 3, respectively and P(2, 3) is its circumcentre. Then which of the following is NOT true?

(A)  (AC)2 =9p

(B)  (AC)2 + p2 = 136

(C)  32 < area (∆ABC) < 36

(D)  34 < area (∆ABC) < 38

Answer: (D)

12. A circle C1 passes through the origin O and has diameter 4 on the positive x-axis. The line y = 2x gives a chord OA of circle C1. Let C2 be the circle with OA as a diameter. If the tangent to C2 at the point A meets the x-axis at P and y-axis at Q, then QA : AP is equal to

(A)  1 : 4

(B)  1 : 5

(C)  2 : 5

(D)  1 : 3

Answer: (A)

13. If the length of the latus rectum of a parabola, whose focus is (a, a) and the tangent at its vertex is x + y = a, is 16, then |a| is equal to :

(A)  2√2

(B)  2√3

(C)  4√2

(D)  4

Answer: (C)

14. If the length of the perpendicular drawn from the point P(a, 4, 2), a> 0 on the line  is 2√6 units and Q(α1, α2, α3) is the image of the point P in this line, then  is equal to :

(A)  7

(B)  8

(C)  12

(D)  14

Answer: (B)

15. If the line of intersection of the planes ax + by = 3 and ax + by + cz = 0, a> 0 makes an angle 30° with the plane y – z + 2 = 0, then the direction cosines of the line are :

Answer: (B)

16. Let X have a binomial distribution B(n, p) such that the sum and the product of the mean and variance of X are 24 and 128 respectively. If  then k is equal to

(A)  528

(B)  529

(C)  629

(D)  630

Answer: (B)

17. A six faced die is biased such that3 × P (a prime number) = 6 × P (a composite number) = 2 × P (1).Let X be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of X is :

(A)  3/11

(B)  5/11

(C)  7/11

(D)  8/11

Answer: (D)

18. The angle of elevation of the top P of a vertical tower PQ of height 10 from a point A on the horizontal ground is 45°, Let R be a point on AQ and from a point B, vertically above R, the angle of elevation of P is 60°. If ∠BAQ = 30°, AB = d and the area of the trapezium PQRB is α, then the ordered pair (d, α) is :

Answer: (A)

19. Let  Then

(A)  S = {π/12}

(B)  S = {2π/3}

(C) 

(D) 

Answer: (C)

20. If the truth value of the statement

(P ∧ (~R)) → ((~R) ∧ Q)

is F, then the truth value of which of the following is F?

(A)  P ∨ Q → ~R

(B)  R ∨ Q → ~ P

(C)  ~ (P ∨ Q) → ~R

(D)  ~ (R ∨ Q) → ~ P

Answer: (D)

SECTION-B

21. Consider a matrix  where α, β, γ are three distinct natural numbers. If  then the number of such 3 – tuples (α, β, γ) is ________.

Answer: (42)

22. The number of functions f, from the set A = {x ∈N : x2 – 10x + 9 ≤ 0} to the set B = {n2 : n ∈ N} such that f(x) ≤ (x – 3)2 + 1, for every x ∈ A, is ___________.

Answer: (1440)

23. Let for the 9th term in the binomial expansion of (3 + 6x)n, in the increasing powers of 6x, to be the greatest for x = 3/2, the least value of n is n0. If k is the ratio of the coefficient of x6 to the coefficient of x3, then k + n0 is equal to :

Answer: (24)

24. is equal to _________.

Answer: (120)

25. A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is  Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is 4 meters, is __________.

Answer: (5)

26. For the curve C : (x2 + y2 – 3) + (x2 – y2 – 1)5 = 0, the value of 3y’ – y3y”, at the point (α, α), α> 0, on C, is equal to __________.

Answer: (16)

27. Let f(x) = min{[x – 1], [x – 2], …, [x – 10]} where [t] denotes the greatest integer ≤ Then  is equal to _______.

Answer: (385)

28. Let f be a differential function satisfying  and f(1) = √ If y = f(x) passes through the point (α, 6), then α is equal to _______.

Answer: (12)

29. A common tangent T to the curves  does not pass through the fourth quadrant. If T touches C1 at (x1, y1) and C2 at (x2, y2), then |2x1 + x2| is equal to ______.

Answer: (20)

30. Let  be three non-coplanar vectors such that  and  If  then α is equal to __________.

Answer: (36)

JEE Main Session 2 26th July 2022 Shift 2 Question Paper and Answer Key

JEE Main Session 2 26th July 2022 Shift 2

PHYSICS

Section-A

IMPORTANT INSTRUCTIONS:

(1) The test is of 3 hours duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

(ii)  Section-B: This section contains 10 questions. In Section-B, attempt any five questions out of 10. The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and −1 mark for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. Two projectiles are thrown with same initial velocity making an angle of 45° and 30° with the horizontal, respectively. The ratio of their respective ranges will be

(A) 1 :√2

(B) √2 : 1

(C) 2 :√3

(D) √3 : 2

Answer: (C)

2. In aVernierCalipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Verniercalipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and 4th Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to 1 mm. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between 30 and 31 divisions of main scale reading and 6th Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be

(A) 3.02 cm

(B) 3.06cm

(C) 3.10cm

(D) 3.20cm

Answer: (C)

3. A ball of mass 0.15 kg hits the wall with its initial speed of 12 ms–1 and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is 100 N, calculate the time duration of the contact of ball with the wall.

(A) 0.018 s

(B) 0.036s

(C) 0.009s

(D) 0.072s

Answer: (B)

4. A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be

(A) 1 : 1

(B) 2 : 1

(C) 1 : 4

(D) 4 : 1

Answer: (B)

5. Two uniformly charged spherical conductors, A and B of radii 5 mm and 10 mm are separated by a distance of 2 cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitude of the electric fields at surface of the spheres A and B will be

(A) 1 : 2

(B) 2 : 1

(C) 1 : 1

(D) 1 : 4

Answer: (B)

6. The oscillating magnetic field in a plane electromagnetic wave is given by By = 5 × 10–6 sin1000π (5x – 4 × 108t)T. The amplitude of electric field will be:

(A) 15 × 102Vm–1

(B) 5 × 10–6Vm–1

(C) 16 × 1012Vm–1

(D) 4 × 102Vm–1

Answer: (D)

7. Light travels in two media M1 and M2 with speeds 1.5 × 108ms–1 and 2.0 × 108ms–1, respectively. The critical angle between them is:

(A) tan1(3/√7)

(B) tan1(2/3)

(C) cos1(3/4)

(D) sin1(2/3)

Answer: (A)

8. A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be:

(Take radius of earth = 6400 km and g = 10 ms–2)

(A) 800 km

(B) 1600 km

(C) 2133 km

(D) 4800 km

Answer: (A)

9. The maximum and minimum voltage of an amplitude modulated signal are 60 V and 20 V, respectively. The percentage modulation index will be:

(A) 0.5%

(B) 50%

(C) 2%

(D) 30%

Answer: (B)

10. A nucleus of mass M at rest splits into two parts having masses  The ratio of de Broglie wavelength of two parts will be:

(A) 1 : 2

(B) 2 : 1

(C) 1 : 1

(D) 2 : 3

Answer: (C)

11. An ice cube of dimensions 60 cm × 50 cm × 20 cm is placed in an insulation box of wall thickness 1 cm. The box keeping the ice cube at 0°C of temperature is brought to a room of temperature 40°C. The rate of melting of ice is approximately.

(Latent heat of fusion of ice is 3.4 × 105 J kg–1 and thermal conducting of insulation wall is 0.05 Wm–1°C–1)

(A) 61 × 103 kgs1

(B) 61 × 105 kgs1

(C) 208 kgs1

(D) 30 × 105 kgs1

Answer: (B)

12. A gas has n degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be

Answer: (A)

13. A transverse wave is represented by y = 2sin(ωt – kx) cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be

(A) 4π

(B) 2π

(C) π

(D) 2

Answer: (A)

14. A battery of 6 V is connected to the circuit as shown below. The current I drawn from the battery is

(A) 1A

(B) 2A

(C) 

(D) 

Answer: (A)

15. A source of potential difference V is connected to the combination of two identical capacitors as shown in the figure. When key ‘K’ is closed, the total energy stored across the combination is E1. Now key ‘K’ is opened and dielectric of dielectric constant 5 is introduced between the plates of the capacitors. The total energy stored across the combination is now E2. The ratio E1/E2 will be

(A) 1/10

(B) 2/5

(C) 5/13

(D) 5/26

Answer: (C)

16. Two concentric circular loops of radii r1 = 30 cm and r2 = 50 cm are placed in X–Y plane as shown in the figure. A current I = 7 A is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately

Answer: (B)

17. A velocity selector consists of electric field  and magnetic field  with B = 12 mT. The value of E required for an electron of energy 728 eV moving along the positive x-axis to pass undeflected is

(Given, mass of electron = 9.1 × 10–31 kg)

(A) 192 kVm1

(B) 192 mVm1

(C) 9600kVm1

(D) 16kVm1

Answer: (A)

18. Two masses M1 and M2 are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass M2 is twice that of M1, the acceleration of the system is a1. When the mass M2 is thrice that of M1, the acceleration of the system is a2. The ratio a1/a2 will be

(A) 1/3

(B) 2/3

(C) 3/2

(D) 1/2

Answer: (B)

19. Mass numbers of two nuclei are in the ratio of 4 : 3. Their nuclear densities will be in the ratio of

(A) 4 : 3

(B) (3/4)1/3

(C) 1 : 1

(D) (4/3)1/3

Answer: (C)

20. The area of cross section of the rope used to lift a load by a crane is 2.5 × 10–4 m2. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, The required area of cross section of the rope should be

(take g = 10 ms–2)

(A) 6.25 × 10–4 m2

(B) 10 × 10–4 m2

(C) 1 × 10–4 m2

(D) 1.67 × 10–4 m2

Answer: (A)

SECTION-B

21. If  The magnitude of component of vector  will be _________ m.

Answer: (2)

22. The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be _________m.

Given the length of the rod is 10√3 m.

Answer: (5)

23. In the given figure, the face AC of the equilateral prism is immersed in a liquid of refractive index ‘n‘. For incident angle 60° at the side AC the refracted light beam just grazes along face AC. The refractive index of the liquid  The value of x is _______.

(Given refractive index of glass = 1.5)

Answer: (27)

24. Two lighter nuclei combine to from a comparatively heavier nucleus by the relation given below:

The binding energies per nucleon for are 1.1 MeV and 7.6 MeV respectively. The energy released in the process is ______ MeV.

Answer: (26)

25. A uniform heavy rod of mass 20 kg, cross sectional area 0.4 m2 and length 20 m is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is x × 10–9 The value of x is ________

(Given Young’s modulus Y = 2 × 1011 Nm–2 andg = 10 ms–2)

Answer: (25)

26. The typical transfer characteristics of a transistor in CE configuration is shown in figure. A load resistor of 2 kΩ is connected in the collector branch of the circuit used. The input resistance of the transistor is 0.50 kΩ. The voltage gain of the transistor is ________.

Answer: (200)

27. Three point charges of magnitude 5 μC, 0.16μC and 0.3μC are located at the vertices, B, C of a right angled triangle whose sides are AB = 3 cm, BC = 3√2 cm and CA = 3 cm and point A is the right angle corner. Charge at point A, experiences ______N of electrostatic force due to the other two charges.

Answer: (17)

28. In a coil of resistance 8Ω, the magnetic flux due to an external magnetic field varies with time as . The value of total heat produced in the coil, till the flux becomes zero, will be ______ J.

Answer: (2)

29. A potentiometer wire of length 300 cm is connected in series with a resistance 780 Ω and a standard cell of emf 4V. A constant current flows through potentiometer wire. The length of the null point for cell of emf20 mV is found to be 60 cm. The resistance of the potentiometer wire is _____ Ω.

Answer: (20)

30. As per given figures, two springs of spring constants k and 2k are connected to mass m. If the period of oscillation in figure (a)is 3s, then the period of oscillation in figure (b) will be √x s. The value of x is _______

Answer: (2)

CHEMISTRY

SECTION-A

1. Hemoglobin contains 0.34% of iron by mass. The number of Fe atoms in 3.3 g of hemoglobin is : (Given : Atomic mass of Fe is 56 u, NA in 6.022 × 1023mol–1)

(A) 1.21 × 105

(B) 12.0 × 1016

(C) 1.21 × 1020

(D) 3.4 × 1022

Answer: (C)

2. Arrange the following in increasing order of their covalent character.

(A) CaF2  (B) CaCl2    (C) CaBr2  (D) CaI2   Choose the correct answer from the options given below.

(A)  B < A < C < D

(B) A < B < C < D 

(C) A < B < D < C

(D) A < C < B < D

Answer: (B)

3. Class XII students were asked to prepare one litre of buffer solution of pH 8.26 by their chemistry teacher. The amount of ammonium chloride to be dissolved by the student in 0.2 M ammonia solution to make one litre of the buffer is (Given pKb (NH3) = 4.74; Molar mass of NH3 = 17 g mol1; Molar mass of NH4Cl = 53.5 g mol–1)

(A) 53.5 g

(B) 72.3 g

(C) 107.0 g

(D) 126.0 g

Answer: (C)

4. At 30°C, the half life for the decomposition of AB2 is 200 s and is independent of the initial concentration of AB2. The time required for 80% of the AB2 to decompose is (Given: log 2 = 0.30; log 3 = 0.48)

(A) 200 s

(B) 323 s

(C) 467 s

(D) 532 s

Answer: (C)

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

Assertion A : Finest gold is red in colour, as the size of the particles increases, it appears purple then blue and finally gold.

Assertion R : The colour of the colloidal solution depends on the wavelength of light scattered by the dispersed particles.

In the light of the above statements, choose the most appropriate 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)

6. The metal that has very low melting point and its periodic position is closer to a metalloid is :

(A) Al

(B) Ga

(C) Se

(D) In

Answer: (B)

7. The metal that is not extracted from its sulphide ore is :

(A) Aluminium

(B) Iron

(C) Lead

(D) Zinc

Answer: (A)

8. The products obtained from a reaction of hydrogen peroxide and acidified potassium permanganate are

(A) Mn4+, H2O only

(B) Mn2+, H2O only   

(C) Mn4+, H2O, O2 only

(D) Mn2+, H2O, O2 only

Answer: (D)

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

Assertion A :LiF is sparingly soluble in water. 

Reason R : The ionic radius of Li+ ion is smallest among its group members, hence has least hydration enthalpy. 

In the light of the above statements, choose the most appropriate 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: (C)

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

Assertion A : Boric acid is a weak acid

Reason R : Boric acid is not able to release H+ ion on its own. It receives OH ion from water and releases H+ ion. 

In the light of the above statements, choose the most appropriate answer from the options given below.

(A) Both A and R are correct and R is the correct explanation of A 

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

(C) A is correct but R is not correct 

(D) A is not correct but R is correct 

Answer: (A)

11. The metal complex that is diamagnetic is (Atomic number : Fe, 26; Cu, 29)

(A) K3[Cu(CN)4

(B) K2[Cu(CN)4]  

(C) K3[Fe(CN)4

(D) K4[FeCl6

Answer: (A)

12. Match List I with List II.

Choose the correct answer from the options given below :

(A) A-II, B-III, C-IV, D-I 

(B) A-II, B-I, C-IV, D-III 

(C) A-I, B-IV, C-II, D-III 

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

Answer: (A)

13. The correct decreasing order of priority of functional groups in naming an organic compound as per IUPAC system of nomenclature is :

Answer: (B)

14. Which of the following is not an example of benzenoidcompound ?

Answer: (B)

15. Hydrolysis of which compound will give carbolic acid ?

(A) Cumene

(B) Benzenediazonium chloride  

(C) Benzal chloride 

(D) Ethylene glycol ketal

Answer: (B)

16. 

Consider the above reaction and predict the major product.

Answer: (A)

17. The correct sequential order of the reagents for the given reaction is :

(A) HNO2, Fe/H+, HNO2, KI, H2O/H+

(B) HNO2, KI, Fe/H+, HNO2, H2O/warm 

(C) HNO2, KI, HNO2, Fe/H+, H2O/H+

(D) HNO2, Fe/H+, KI, HNO2, H2O/warm 

Answer: (B)

18. Vulcanization of rubber is carried out by heating a mixture of :

(A) isoprene and styrene 

(B) neoprene and sulphur  

(C) isoprene and sulphur 

(D) neoprene and styrene

Answer: (C)

19. Animal starch is the other name of :

(A) amylose

(B) maltose

(C) glycogen

(D) amylopectin

Answer: (C)

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

Assertion A :Phenolphthalein is a pH dependent indicator, remains colourless in acidic solution and gives pink colour in basic medium 

Reason R : Phenolphthalein is a weak acid. It doesn’t dissociate in basic medium. 

In the light of the above statements, choose the most appropriate 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: (C)

SECTION-B

21. A 10 g mixture of hydrogen and helium is contained in a vessel of capacity 0.0125 m3 at 6 bar and 27°C. The mass of helium in the mixture is _______ g. (nearest integer) Given : R = 8.3 JK–1mol–1 (Atomic masses of H and He are 1u and 4u, respectively)

Answer: (8)

22. Consider an imaginary ion  The nucleus contains ‘a’% more neutrons than the number of electrons in the ion. The value of ‘a’ is ______. [nearest integer]

Answer: (4)

23. For the reaction

H2F2(g) → H2(g) + F2(g)

∆U = –59.6 kJ mol–1 at 27°C.

The enthalpy change for the above reaction is (–) ______ kJ mol–1 [nearest integer] Given : R = 8.314 JK–1mol–1.

Answer: (57)

24. The elevation in boiling point for 1 molal solution of non-volatile solute A is 3K. The depression in freezing point for 2 molalsolution of A in the same solvent is 6 K. The ratio of Kb and Kfe., Kb/Kf is 1 : X. The value of X is [nearest integer]

Answer: (1)

25. 20 mL of 0.02 M hypo solution is used for the titration of 10 mL of copper sulphate solution, in the presence of excess of KI using starch as an indicator. The molarity of Cu2+ is found to be _____ × 102 M [nearest integer]

Given : 2Cu2+ + 4I→ Cu2I2 + I2I2 + 2S2O32−→ 2I + S4O62−

Answer: (4)

26. The number of non-ionisable protons present in the product B obtained from the following reaction is _____. C2H5OH + PCl3→ C2H5Cl + A

A + PCl3→ B

Answer: (2)

27. The spin-only magnetic moment value of the compound with strongest oxidizing ability among MnF4, MnF3 and MnF2 is ______ B.M. [nearest integer]

Answer: (5)

28. Total number of isomers (including stereoisomers) obtained on monochlorination of methylcyclohexane is ________.

Answer: (12)

29. A 100 mL solution of CH3CH2MgBr on treatment with methanol produces 2.24 mL of a gas at STP. The weight of gas produced is _______ mg. [nearest integer]

Answer: (3)

30. How many of the following drugs is/are example(s) of broad spectrum antibiotic ?Ofloxacin, Penicillin G, Terpineol, Salvarsan

Answer: (1)

MATHEMATICS

SECTION-A

1. The minimum value of the sum of the squares of the roots of x2 + (3 – a)x + 1 = 2a is:

(A) 4

(B) 5

(C) 6

(D) 8

Answer: (C)

2. If z = x + iy satisfies | z | – 2 = 0 and |z – i| – | z + 5i| = 0, then

(A) x + 2y – 4 = 0

(B) x2 + y – 4 = 0

(C) x + 2y + 4 = 0

(D) x2 – y + 3 = 0

Answer: (C)

3. Let  then the value of A’BA is

(A) 1224

(B) 1042

(C) 540

(D) 539

Answer: (D)

4. is equal to

(A) 22n2nCn

(B) 22n – 1 2n – 1Cn – 1

(C) 

(D) 2n – 1  +2n – 1Cn

Answer: (B)

5. Let P and Q be any points on the curves (x – 1)2 + (y + 1)2 = 1 and y = x2, respectively. The distance between P and Q is minimum for some value of the abscissa of P in the interval

(A) (0, 1/4)

(B) (1/2, 3/4)

(C) (1/4, 1/2)

(D) (3/4, 1)

Answer: (C)

6. If the maximum value of a, for which the functionfa(x) = tan12x – 3ax + 7 is non-decreasing in  is equal to

Answer: (A)

7. Let  for some α ∈ ℝ. Then the value of α + β is :

(A) 14/5

(B) 3/25

(C) 5/2

(D) 7/2

Answer: (C)

8. The value of  is

(A) −2√2

(B) 2√2

(C) −4

(D) 4

Answer: (D)

9. is equal to :-

(A) 10(π + 4)

(B) 10(π + 2)

(C) 20(π – 2)

(D) 20(π + 2)

Answer: (D)

10. Let the solution curve y = f(x) of the differential equation pass through the origin. Then 

Answer: (B)

11. The acute angle between the pair of tangents drawn to the ellipse 2x2 + 3y2 = 5 from the point (1, 3) is

Answer: (B)

12. The equation of a common tangent to the parabolas y = x2 and y = –(x – 2)2 is

(A) y = 4(x – 2)

(B) y = 4(x – 1)

(C) y = 4(x + 1)

(D) y = 4(x + 2)

Answer: (B)

13. Let the abscissae of the two points P and Q on a circle be the roots of x2 – 4x – 6 = 0 and the ordinates of P and Q be the roots of y2 + 2y – 7 = 0. If PQ is a diameter of the circle x2 + y2 + 2ax + 2by + c = 0, then the value of (a + b – c) is

(A) 12

(B) 13

(C) 14

(D) 16

Answer: (A)

14. If the line x – 1 = 0 is a directrix of the hyperbola kx2 – y2 = 6, then the hyperbola passes through the point

(A) (−2√5, 6)

(B) (−√5, 3)

(C) (√5, −2)

(D) (2√5, 3√6)

Answer: (C)

15. A vector  is parallel to the line of intersection of the plane determined by the vectors and the plane determined by the vectors The obtuse angle between  is

(A) 3π/4

(B) 2π/3

(C) 4π/5

(D) 5π/6

Answer: (A)

16. If  then a value of  is

Answer: (B)

17. Negation of the Boolean expression p⇔ (q ⇒ p) is

(A) (~ p) ∧q

(B) p∧ (~ q)

(C) (~ p) ∨ (~ q)

(D) (~ p) ∧ (~ q)

Answer: (D)

18. Let X be a binomially distributed random variable with mean 4 and variance 4/3. Then, 54 P(X ≤ 2) is equal to

(A) 73/27

(B) 146/27

(C) 146/81

(D) 126/81

Answer: (B)

19. The integral  is equal to

Answer: (A)

20. The area bounded by the curves y = |x2 – 1| and y = 1 is

Answer: (D)

SECTION-B

21. Let A = {1, 2, 3, 4, 5, 6, 7} and B = {3, 6, 7, 9}. Then the number of elements in the set {C ⊆ A : C ∩ B ≠ϕ} is ________

Answer: (112)

22. The largest value of a, for which the perpendicular distance of the plane containing the lines  and  from the point (2, 1, 4) is √3, is _________.

Answer: (20)

23. Numbers are to be formed between 1000 and 3000, which are divisible by 4, using the digits 1, 2, 3, 4, 5 and 6 without repetition of digits. Then the total number of such numbers is ______________.

Answer: (30)

24. If  where m and n are co-prime, them m + n is equal to

Answer: (166)

25. If the sum of solutions of the system of equations 2sin2θ – cos2θ = 0 and 2cos2θ + 3sinθ = 0 in the interval [0, 2π] is kπ, then k is equal to _______.

Answer: (3)

26. The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If σ is the standard deviation of the data after omitting the two wrong observations from the data, then 38σ2 is equal to ___________.

Answer: (238)

27. The plane passing through the line L :ℓx – y + 3(1 – ℓ) z = 1, x + 2y – z = 2 and perpendicular to the plane 3x + 2y + z = 6 is 3x – 8y + 7z = 4. If θ is the acute angle between the line L and the y-axis, then 415 cos2θ is equal to ________.

Answer: (125)

28. Suppose y = y(x) be the solution curve to the differential equation  such that  is finite. If a and bare respectively the x – and y – intercepts of the tangent to the curve at x = 0, then the value of a – 4b is equal to _______.

Answer: (3)

29. Different A.P.’s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the common differences of all such A.P.’s having at least 3 terms and at most 33 terms is ________.

Answer: (53)

30. The number of matrices where a, b, c, d ∈ {−1, 0, 1, 2, 3,………..,10}, such that A = A1, is _______.

Answer: (50)

JEE Main Session 2 25th July 2022 Shift 2 Question Paper and Answer Key

JEE Main Session 2 25th July 2022 Shift 2

PHYSICS

SECTION-A

IMPORTANT INSTRUCTIONS:

(1)   The test is of 3 hours duration:

(2)   The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i)    Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

(ii)   Section-B: This section contains 10 questions. In Section-B, attempt any five questions out of 10. The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and −1 mark for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. In AM modulation, a signal is modulated on a carrier wave such that maximum and minimum amplitudes are found to be 6 V and 2 V, respectively. The modulation index is

(A)  100%

(B)  80%

(C)  60%

(D)  50%

Answer: (D)

2. The electric current in a circular coil of 2 turns produces a magnetic induction B1 at its centre. The coil is unwound and is rewound into a circular coil of 5 turns and the same current produces a magnetic induction B2 at its centre. The ratio of B2/B1 is

(A)  5/2

(B)  25/4

(C)  5/4

(D)  25/2

Answer: (B)

3. A drop of liquid of density ρ is floating half immersed in a liquid of density σ and surface tension 7.5 × 10–4 N  cm–1. The radius of drop in cm will be (g = 10 ms–2)

Answer: (A)

4. Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 ms–1 collide and rebound with the same speed. If the time duration of contact is t = 0.005 s, then what is the force exerted on the ball due to each other?

(A)  100 N

(B)  200 N

(C)  300 N

(D)  400 N

Answer: (B)

5. For a free body diagram shown in the figure, the four forces are applied in the ‘x’ and ‘y’ directions. What additional force must be applied and at what angle with positive x-axis so that net acceleration of body is zero?

(A)  √2 N, 45°

(B)  √2 N, 135°

(C) 

(D)  2 N, 45°

Answer: (A)

6. Capacitance of an isolated conducting sphere of radius R1 becomes n times when it is enclosed by a concentric conducting sphere of radius R2 connected to earth. The ratio of their radii (R2/R1) is:

Answer: (A)

7. The ratio of wavelengths of proton and deuteron accelerated by potential Vp and Vd is 1 : √2. Then, the ratio of Vp to Vd will be:

(A)  1 : 1

(B)  √2 : 1

(C)  2 : 1

(D)  4 : 1

Answer: (D)

8. For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a screen placed at a distance 12 cm form the lens. A glass plate of refractive index 1.5 and thickness 1 cm is introduced between lens and screen such that the glass plate plane faces parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screen?

(A)  0.8 m

(B)  3.2 m

(C)  1.2 m

(D)  5.6 m

Answer: (B)

9. Light wave traveling in air along x-direction is given by Ey = 540 sin π × 104 (x – ct)Vm–1. Then, the peak value of magnetic field of wave will be (Given c = 3 × 108ms–1)

(A) 18 × 10–7 T

(B) 54 × 10–7 T

(C) 54 × 10–8 T

(D) 18 × 10–8 T

Answer: (A)

10. When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on:

(A) Electromagnetic induction

(B) Resonance in ac circuits

(C) Mutual induction in ac circuits

(D) Interference of electromagnetic waves

Answer: (B)

11. An electron with energy 0.1 keV moves at right angle to the earth’s magnetic field of 1 × 10–4Wbm–2. The frequency of revolution of the electron will be

(Take mass of electron = 9.0 × 10–31 kg)

(A) 1.6 × 105 Hz

(B) 5.6 × 105 Hz

(C) 2.8 × 106 Hz

(D) 1.8 × 106 Hz

Answer: (C)

12. A current of 15 mA flows in the circuit as shown in figure. The value of potential difference between the points A and B will be

(A)  50 V

(B)  75 V

(C)  150 V

(D)  275 V

Answer: (D)

13. The length of a seconds pendulum at a height h = 2R from earth surface will be

(Given R = Radius of earth and acceleration due to gravity at the surface of earth, g = π2ms–2)

(A)  2/9 m

(B)  4/9 m

(C)  8/9 m

(D)  1/9 m

Answer: (D)

14. Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is √2 times the speed of sound, then the value of n will be

(A)  1

(B)  2

(C)  3

(D)  4

Answer: (B)

15. Let η1 is the efficiency of an engine at T1 = 447°C and T2 = 147°C while η2 is the efficiency at T1 = 947°C and T2 = 47°C. The ratio η1/ η2 will be

(A)  0.41

(B)  0.56

(C)  0.73

(D)  0.70

Answer: (B)

16. An object is taken to a height above the surface of earth at a distance (5/4)R from the centre of the earth. Where radius of earth, R = 6400 km. The percentage decrease in the weight of the object will be

(A)  36%

(B)  50%

(C)  64%

(D)  25%

Answer: (A)

17. A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed 10 ms–1 gets embedded in it, then loss of kinetic energy will be

(A)  4.9 J

(B)  9.8 J

(C)  14.7 J

(D)  19.6 J

Answer: (B)

18. A ball is projected from the ground with a speed 15 ms–1 at an angle θ with horizontal so that its range and maximum height are equal, then ‘tan θ’ will be equal to

(A)  1/4

(B)  1/2

(C)  2

(D)  4

Answer: (D)

19. The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 1%, 2% and 3% respectively. The maximum percentage error in the detection of the dissipated heat will be

(A)  2

(B)  4

(C)  6

(D)  8

Answer: (D)

20. Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength λ. The value of principal quantum number ‘n’ of the excited state will be, (R: Rydberg constant)

Answer: (B)

SECTION-B

21. A particle is moving in a straight line such that its velocity is increasing at 5 ms–1 per meter. The acceleration of the particle is _______ms–2 at a point where its velocity is 20 ms–1.

Answer: (100)

22. Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be √x m. The value of x is ________.

Answer: (2)

23. A block of ice of mass 120 g at temperature 0°C is put in 300 g of water at 25°C. The x g of ice melts as the temperature of the water reaches 0°C. The value of x is _______.

[Use specific heat capacity of water = 4200 Jkg–1K–1, Latent heat of ice = 3.5 ×105Jkg–1]

Answer: (90)

24. is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its

(i) Third permitted energy level to the second level and

(ii) The highest permitted energy level to the second permitted level.

The value of x will be ______.

Answer: (5)

25. In a potentiometer arrangement, a cell of emf 1.20 V gives a balance point at 36 cm length of wire. This cell is now replaced by another cell of emf 1.80 V. The difference in balancing length of potentiometer wire in above conditions will be _______ cm.

Answer: (18)

26. Two ideal diodes are connected in the network as shown is figure. The equivalent resistance between A and B is ________ Ω.

Answer: (25)

27. Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the √3 times of amplitude of individual motions. The phase difference between the two motions is _________ (degree).

Answer: (60)

28. Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18 V. The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric constant 9. The final potential difference across the combination of capacitors will be ________ V.

Answer: (6)

29. A convex lens of focal length 20 cm is placed in front of a convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm. A point object is placed on principal axis at a distance of 60 cm from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is _________ cm.

Answer: (10)

30. Magnetic flux (in weber) in a closed circuit of resistance 20 Ω varies with time t(s) as φ = 8t2 – 9t + 5. The magnitude of the induced current at t = 0.25 s will be _______ mA.

Answer: (250)

CHEMISTRY

SECTION-A

1. Match List I with List II:

(A)  A-II, B-I, C-IV, D-III

(B)  A-II, B-IV, C-III, D-I

(C)  A-IV, B-II, C-III, D-I

(D)  A-IV, B-II, C-I, D-III

Answer: (A)

2. Two solutions A and B are prepared by dissolving 1 g of non-volatile solutes X and Y. respectively in 1 kg of water. The ratio of depression in freezing points for A and B is found to be 1 : 4. The ratio of molar masses of X and Y is :

(A) 1 : 4

(B) 1 : 0.25

(C) 1 : 0.20

(D) 1 : 5

Answer: (B)

3. are the respective ionization constants for the following reactions (a),(b), and (c).

The relationship between  is given as

Answer: (D)

4. The molar conductivity of a conductivity cell filled with 10 moles of 20 mL NaCl solution is Λm1 and that of 20 moles another identical cell heaving 80 mL NaCl solution is Λm2, The conductivities exhibited by these two cells are same. The relationship between Λm2 and Λm1 is

(A)  Λm2 = 2Λm1

(B)  Λm2 = Λm1/2

(C)  Λm2 = Λm1

(D)  Λm2 = 4Λm1

Answer: (A)

5. For micelle formation, which of the following statements are correct?

(A) Micelle formation is an exothermic process.

(B) Micelle formation is an endothermic process.

(C) The entropy change is positive.

(D)The entropy change is negative.

(A) A and D only

(B) A and C only

(C) B and C only

(D) B and D only

Answer: (A)

6. The first ionization enthalpies of Be, B, N and O follow the order

(A) O < N < B < Be

(B) Be < B < N < O

(C) B < Be < N < O

(D) B < Be < O < N

Answer: (D)

7. Given below are two statements.

 Statement I:Pig iron is obtained by heating cast iron with scrap iron.

Statement II:Pig iron has a relatively lower carbon content than that of cast iron. In the light of the above statements, choose the correct answer from the options given below.

(A) Both Statement I and Statement II are correct.

(B) Both Statement I and Statement II are not correct.

(C) Statement I is correct but Statement II is not correct

(D) Statement I is not correct but Statement II is correct.

Answer: (B)

8. High purity (>99.95%) dihydrogen is obtained by

(A) reaction of zinc with aqueous alkali.

(B) electrolysis of acidified water using platinum electrodes.

(C) electrolysis of warm aqueous barium hydroxide solution between nickel electrodes.

(D) reaction of zinc with dilute acid.

Answer: (C)

9. The correct order of density is

(A) Be > Mg >Ca>Sr

(B) Sr>Ca> Mg > Be

(C) Sr> Be > Mg >Ca

(D) Be >Sr> Mg >Ca

Answer: (C)

10. The total number of acidic oxides from the : NO, N2O, B2O3, N2O5 , CO, SO3 , P4O10

(A)  3

(B)  4

(C)  5

(D)  6

Answer: (B)

11. The correct order of energy of absorption for the following metal complexes is

A: [Ni(en)3 ]2+, B: [Ni(NH3)6 ]2+, C: [Ni(H2 O)6 ]2+

(A) C < B < A

(B) B < C < A

(C) C < A < B

(D) A < C < B

Answer: (A)

12. 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-IV, B-III, C-II, D-I

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

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

Answer: (C)

13. Major product of the following reaction is

Answer: (D)

14. What is the major product of the following reaction?

Answer: (B)

15. Arrange the following in decreasing acidic strength.

(A) A > B > C > D

(B) B > A > C > D

(C) D > C > A > B

(D) D > C > B > A

Answer: (A)

16. 

The correct structure of C is

Answer: (A)

17. Match List I with List II:

Choose the correct answer from the options given below:

(A) A–III, B-I, C-IV, D-II

(B) A–III, B-IV, C-I, D-II

(C) A–II, B-I, C-IV, D-III

(D) A–II, B-IV, C-I, D-III

Answer: (B)

18. Glycosidic linkage between C1 of a-glucose and C2 of b-fructose is found in

(A) maltose

(B) sucrose

(C) lactose

(D) amylose

Answer: (B)

19. Some drugs bind to a site other than, the active site of an enzyme. This site is known as

(A) non-active site

(B) allosteric site

(C) competitive site

(D) therapeutic site

Answer: (B)

20. In base vs. Acid titration, at the end point methyl orange is present as

(A) quinonoid form

(B) heterocyclic form

(C) phenolic form

(D) benzenoid form

Answer: (A)

SECTION-B

21. 56.0 L of nitrogen gas is mixed with excess of hydrogen gas and it is found that 20 L of ammonia gas is produced. The volume of unused nitrogen gas is found to be______ L.

Answer: (46)

22. A sealed flask with a capacity of 2 dm3 contains 11 g of propane gas. The flask is so weak that it will burst if the pressure becomes 2 MPa. The minimum temperature at which the flask will burst is _______ °C. [Nearest integer]

(Given: R = 8.3 J K–1mol–1. Atomic masses of C and H are 12u and 1u respectively.) (Assume that propane behaves as an ideal gas.)

Answer: (1655)

23. When the excited electron of a H atom from n = 5 drops to the ground state, the maximum number of emission lines observed are _____

Answer: (10)

24. While performing a thermodynamics experiment, a student made the following observations,

HCl + NaOH→NaCl + H2O ∆H = –57.3 kJ mol–1 CH3COOH + NaOH→ CH3COONa + H2O ∆H = –55.3 kJ mol–1. The enthalpy of ionization of CH3 COOH as calculated by the student is ______ kJ mol–1. (nearest integer)

Answer: (2)

25. For the decomposition of azomethane. CH3N2CH3(g) → CH3CH3(g) + N2(g) a first order reaction, the variation in partial pressure with time at 600 K is given as

The half life of the reaction is _____ × 10–5s. [Nearest integer]

Answer: (2)

26. The sum of number of lone pairs of electrons present on the central atoms of XeO3, XeOF4 and XeF6 is ___________

Answer: (3)

27. The spin-only magnetic moment value of M3+ ion (in gaseous state) from the pairs Cr3+/Cr2+, Mn3+/Mn2, Fe3+/Fe2+ and Co3+/Co2+ that has negative standard electrode potential, is B.M. [Nearest integer]

Answer: (4)

28. A sample of 4.5 mg of an unknown monohydric alcohol, R–OH was added to methylmagnesium iodide. A gas is evolved and is collected and its volume measured to be 3.1 mL. The molecular weight of the unknown alcohol is ____ g/mol. [Nearest integer]

Answer: (33)

29. The separation of two coloured substances was done by paper chromatography. The distances travelled by solvent front, substance A and substance B from the base line are 3.25 cm. 2.08 cm and 1.05 cm. respectively. The ratio of Rf values of A to B is ______

Answer: (2)

30. The total number of monobromo derivatives formed by the alkanes with molecular formula C5H12 is (excluding stereo isomers) _____

Answer: (8)

MATHEMATICS

SECTION-A

1. z ∈ ℂ if the minimum value of (|z – 3√2| + |z – p√2i|) is 5√2, then a value of p is _________.

(A)  3

(B)  7/2

(C)  4

(D)  9/2

Answer: (C)

2. The number of real values of λ, such that the system of linear equations

2x – 3y + 5z = 9

x + 3y – z = –18

3x – y + (λ2 – | λ |)z = 16

has no solutions, is

(A)  0

(B)  1

(C)  2

(D)  4

Answer: (C)

3. The number of bijective functions f : {1, 3, 5, 7, …, 99} → {2, 4, 6, 8, ….., 100} such that f(3) ≥ f(9) ≥ f(15) ≥ f(21) ≥ … ≥ f(99) is _________.

(A)  50P17

(B)  50P33

(C)  33! × 17!

(D)  50!/2

Answer: (B)

4. The remainder when (11)1011 + (1011)11 is divided by 9 is

(A)  1

(B)  4

(C)  6

(D)  8

Answer: (D)

5. The sum  is equal to

(A)  7/87

(B)  7/29

(C)  14/87

(D)  21/29

Answer: (B)

6. is equal to

(A)  14

(B)  7

(C)  14√2

(D)  7√2

Answer: (A)

7. is equal to

(A)  1/2

(B)  1

(C)  2

(D)  −2

Answer: (C)

8. If A and B are two events such that P(A) = 1/3, P(B) = 1/5 and (A ∪ B) = 1/2, then P(A|B’) + P(B|A’|) is equal to

(A)  3/4

(B)  5/8

(C)  5/4

(D)  7/8

Answer: (B)

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

(A) 

(B)  52/e

(C) 

(D)  104/e

Answer: (B)

10. Let the point P(α, β) be at a unit distance from each of the two lines L1 : 3x – 4y + 12 = 0 and L2 : 8x + 6y + 11 = 0. If P lies below L1 and above L2, then 100(α + β) is equal to

(A)  −14

(B)  42

(C)  −22

(D)  14

Answer: (D)

11. Let a smooth curve y = f(x) be such that the slope of the tangent at any point (x, y) on it is directly proportional to (-y/x). If the curve passes through the points (1, 2) and (8, 1), then |y(1/8)| is equal to

(A)  2 loge2

(B)  4

(C)  1

(D)  4 loge2

Answer: (B)

12. If the ellipse  meets the line  on the x-axis and the line  on the y-axis, then the eccentricity of the ellipse is

(A)  5/7

(B)  2√6/7

(C)  3/7

(D)  2√5/7

Answer: (A)

13. The tangents at the points A(1, 3) and B(1, –1) on the parabola y2 – 2x – 2y = 1 meet at the point P. Then the area (in unit2) of the triangle PAB is :

(A)  4

(B)  6

(C)  7

(D)  8

Answer: (D)

14. Let the foci of the ellipse  and the hyperbola coincide. Then the length of the latus rectum of the hyperbola is :

(A)  32/9

(B)  18/5

(C)  27/4

(D)  27/10

Answer: (D)

15. A plane E is perpendicular to the two planes 2x – 2y + z = 0 and x – y + 2z = 4, and passes through the point P(1, –1, 1). If the distance of the plane E from the point Q(a, a, 2) is 3√2, then (PQ)2 is equal to

(A)  9

(B)  12

(C)  21

(D)  33

Answer: (C)

16. The shortest distance between the lines  is

(A)  2√29

(B)  1

(C) 

(D)  √29/2

Answer: (A)

17. Let  be a vector such that  Then the projection of  on the vector  is :-

Answer: (A)

18. If the mean deviation about median for the number 3, 5, 7, 2k, 12, 16, 21, 24 arranged in the ascending order, is 6 then the median is

(A)  11.5

(B)  10.5

(C)  12

(D)  11

Answer: (D)

19. is equal to

(A)  3/16

(B)  1/16

(C)  1/32

(D)  9/32

Answer: (B)

20. Consider the following statements :

P :Ramu is intelligent.

Q :Ramu is rich.

R :Ramu is not honest.

The negation of the statement “Ramu is intelligent and honest if and only if Ramu is not rich” can be expressed as :

(A) ((P ∧ (~ R)) ∧ Q) ∧ ((~ Q) ∧ ((~ P) ∨ R))

(B) ((P ∧ R) ∧ Q) ∨ ((~ Q) ∧ ((~ P) ∨ (~ R)))

(C) ((P ∧ R) ∧ Q) ∧ ((~ Q) ∧ (( ~ P) ∨ (~ R)))

(D) ((P ∧ (~ R)) ∧ Q) ∨ ((~ Q) ∧ ((~ P) ∧ R))

Answer: (D)

SECTION-B

21. Let A = {1, 2, 3, 4, 5, 6, 7}. Define B = {T ⊆A : either ∉ T or 2 ∈ T} and C = T ⊆ A : T The sum of all the elements of T is prime number}.Then the number of elements in the set B ∪ C is ______.

Answer: (107)

22. Let f(x) be a quadratic polynomial with leading coefficient 1 such that f(0) = p, p ≠ 0, and f(1) = 1/3 . If the equations f(x) = 0 and fofofo f(x) = 0 have a common real root, then f(–3) is equal to ______.

Answer: (25)

23. Let  If for some n ∈ N,  then n + a + b is equal to ________

Answer: (24)

24. The sum of the maximum and minimum values of the function f(x) = |5x – 7| + [x2 + 2x] in the interval [5/4, 2], where [t] is the greatest integer ≤ t, is ______.

Answer: (15)

25. Let y = y(x) be the solution of the differential equation  If for some n ∈ N, y(2) ∈ [n – 1, n), then n is equal to _________.

Answer: (3)

26. Let f be a twice differentiable function on R. If f’(0) = 4 and  then (2a + 1)5 a2 is equal to _________

Answer: (8)

27. Let  for n ∈ Then the sum of all the elements of the set {n ∈ N : an∈ (2, 30)} is ______

Answer: (5)

28. If the circles x2 + y2 + 6x + 8y + 16 = 0 and x2 + y2 + 2(3 – √3)x + x + 2(4 – √6)y = k + 6√3 + 8√6, k > 0, touch internally at the point P(α, β), then (α + √3)2 + (β + √6)2 is equal to _________

Answer: (25)

29. Let the area enclosed by the x-axis, and the tangent and normal drawn to the curve 4x3 – 3xy2 + 6x2 – 5xy – 8y2 + 9x + 14 = 0 at the point (–2, 3) be A. Then 8A is equal to _______.

Answer: (170)

30. Let x = sin(2tan1α) and  If S = {α∈ R : y2 = 1 – x}, then  is equal to _______

Answer: (130)

JEE Main Session 2 29th June 2022 Shift 2 Question Paper and Answer Key

JEE Main Session 2 29th June 2022 Shift 2

PHYSICS

SECTION-A

IMPORTANT INSTRUCTIONS:

(1)   The test is of 3 hours duration:

(2)   The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i)    Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

(ii)   Section-B: This section contains 10 questions. In Section-B, attempt any five questions out of 10. The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and −1 mark for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10 m in t s, the distance travelled by the toy in the next t s will be :

(A)  10 m

(B)  20 m

(C)  30 m

(D)  40 m

Answer: (C)

2. At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm? Both the diameters have been measured at room temperature (27°C).

(Given: coefficient of linear thermal expansion of gold αL = 1.4 × 10–5 K–1)

(A) 125.7°C

(B) 91.7°C

(C) 425.7°C

(D) 152.7°C

Answer: (D)

3. Two point charges Q each are placed at a distance d apart. A third point charge q is placed at a distance x from mid-point on the perpendicular bisector. The value of x at which charge q will experience the maximum Coulombs force is :

(A)  x = d

(B)  x = d/2

(C)  x = d/√2

(D)  x = d/2√2

Answer: (D)

4. The speed of light in media ‘A’ and ‘B’ are 2.0 × 1010 cm/s and 1.5 × 1010 cm/s respectively. A ray of light enters from the medium B to A at an incident angle ‘θ’. If the ray suffers total internal reflection, then

Answer: (D)

5. In the following nuclear reaction,  Mass number of D is 182 and atomic number is 74. Mass number and atomic number of D4, respectively, will be ________.

(A) 174 and 71

(B) 174 and 69

(C) 172 and 69

(D) 172 and 71

Answer: (A)

6. The electric field at a point associated with a light wave is given by

E = 200[sin(6 × 1015)t + sin(9 × 1015)t] Vm–1

Given : h = 4.14 × 10–15eVs

If this light falls on a metal surface having a work function of 2.50 eV, the maximum kinetic energy of the photoelectrons will be

(A) 1.90 eV

(B) 3.27 eV

(C) 3.60 eV

(D) 3.42 eV

Answer: (D)

7. A capacitor is discharging through a resistor R. Consider in time t1, the energy stored in the capacitor reduces to half of its initial value and in time t2, the charge stored reduces to one eighth of its initial value. The ratio t1/t2 will be

(A)  1/2

(B)  1/3

(C)  1/4

(D)  1/6

Answer: (D)

8. Starting with the same initial conditions, an ideal gas expands from volume V1 to V2 in three different ways. The work done by the gas is W1 if the process is purely isothermal, W2, if the process is purely adiabatic and W3 if the process is purely isobaric. Then, choose the correct option.

(A) W1< W2< W3

(B) W2< W3< W1

(C) W3< W1< W2

(D) W2< W1< W3

Answer: (D)

9. Two long current carrying conductors are placed parallel to each other at a distance of 8 cm between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is 30 μT. The equal current flowing in the two conductors is:

(A) 30 A in the same direction

(B) 30 A in the opposite direction

(C) 60 A in the opposite direction

(D) 300 A in the opposite direction

Answer: (B)

10. The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be

(A) 40 hours

(B) 36 hours

(C) 30 hours

(D) 25 hours

Answer: (B)

11. The TV transmission tower at a particular station has a height of 125 m. For doubling the coverage of its range, the height of the tower should be increased by

(A) 125 m

(B) 250 m

(C) 375 m

(D) 500 m

Answer: (C)

12. The motion of a simple pendulum executing S.H.M. is represented by the following equation. y = A sin(πt + φ), where time is measured in second. The length of pendulum is

(A) 97.23 cm

(B) 25.3 cm

(C) 99.4 cm

(D) 406.1 cm

Answer: (C)

13. A vessel contains 16 g of hydrogen and 128 g of oxygen at standard temperature and pressure. The volume of the vessel in cm3 is:

(A) 72 × 105

(B) 32 × 105

(C) 27 × 104

(D) 54 × 104

Answer: (C)

14. Given below are two statements:

Statement I: The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle.

Statement II: The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field.

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)

15. A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over frictionless pulley as shown below.

The coefficient of kinetic friction between the surface and block is 0.02. The acceleration of block is (Given g = 10 ms–2.)

(A)  1 ms2

(B)  1/5ms2

(C)  4/5ms2

(D)  8/11ms2

Answer: (D)

16. In the given figure, the block of mass m is dropped from the point ‘A’. The expression for kinetic energy of block when it reaches point ‘B’ is

(A) 

(B) 

(C)  mg(y – y0)

(D)  mgy0

Answer: (D)

17. A block of mass M placed inside a box descends vertically with acceleration ‘a’. The block exerts a force equal to one-fourth of its weight on the floor of the box.

The value of ‘a’ will be

(A)  g/4

(B)  g/2

(C)  3g/4

(D)  g

Answer: (C)

18. If the electric potential at any point (x, y, z)m in space is given by V = 3x2 The electric field at the point (1, 0, 3)m will be

(A) 3 Vm–1, directed along positive x-axis

(B) 3 Vm–1, directed along negative x-axis

(C) 6 Vm–1, directed along positive x-axis

(D) 6 Vm–1, directed along negative x-axis

Answer: (D)

19. The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of 2 Ω. The value of internal resistance of each cell is

(A) 2 Ω

(B) 4 Ω

(C) 6 Ω

(D) 8 Ω

Answer: (A)

20. A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?

(A)  25 m

(B)  50 m

(C)  100 m

(D)  200 m

Answer: (B)

SECTION-B

21. The vernier constant of Vernier callipers is 0.1 mm and it has zero error of (–0.05) cm. While measuring diameter of a sphere, the main scale reading is 1.7 cm and coinciding vernier division is 5. The corrected diameter will be ________× 10–2

Answer: (180)

22. A small spherical ball of radius 0.1 mm and density 104 kg m–3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of h will be ______ m.

(Given g = 10 ms–2, viscosity of water = 1.0 × 10–5 N-sm–2).

Answer: (20)

23. In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms–1. The third resonance is observed when the air column has a length of ______ cm.

Answer: (104)

24. Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance 2000 Ω is used to measure the potential difference across 500 Ω resistor, the reading of the voltmeter will be _____ V.

Answer: (8)

25. A potential barrier of 0.4 V exists across a p-n junction. An electron enters the junction from the n-side with a speed of 6.0 × 105ms–1. The speed with which electrons enters the p side will be  the value of x is ________.

(Give mass of electron = 9 × 10–31 kg, charge on electron = 1.6 × 10–19 C)

Answer: (14)

26. The displacement current of 4.425 μA is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of 106 Vs–1. The area of each plate of the capacitor is 40 cm2. The distance between each plate of the capacitor x × 10–3 The value of x is,

(Permittivity of free space, E0 = 8.85 × 10–12 C2 N–1 m–2)

Answer: (8)

27. The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I1. The same rod is bent into a ring and its moment of inertia about a diameter is I2. If  then the value of x will be _________.

Answer: (8)

28. The half life of a radioactive substance is 5 years. After x years, a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The value of x is ________.

Answer: (20)

29. In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by 5 × 10–2 m towards the slits, the change in fringe width is 3 × 10–3 If the distance between the slits is 1 mm, then the wavelength of the light will be _______ nm.

Answer: (600)

30. An inductor of 0.5 mH, a capacitor of 200 μF and a resistor of 2 Ω are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ______ × 102

Answer: (5)

CHEMISTRY

SECTION-A

1. Using the rules for significant figures, the correct answer for the expression  will be

(A)  0.005613

(B)  0.00561

(C)  0.0056

(D)  0.006

Answer: (B)

2. Which of the following is the correct plot for the probability density ψ2(r) as a function of distance ‘r’ of the electron from the nucleus for 2s orbital?

Answer: (B)

3. Consider the species CH4, NH4+ and BH4.

Choose the correct option with respect to these species.

(A) They are isoelectronic and only two have tetrahedral structures

(B) They are isoelectronic and all have tetrahedral structures.

(C) Only two are isoelectronic and all have tetrahedral structures.

(D) Only two are isoelectronic and only two have tetrahedral structures.

Answer: (B)

4. 4.0 moles of argon and 5.0 moles of PCl5 are introduced into an evacuated flask of 100 litre capacity at 610 K. The system is allowed to equilibrate. At equilibrium, the total pressure of mixture was found to be 6.0 atm. The Kp for the reaction is [Given : R = 0.082 L atm K–1mol–1]

(A)  2.25

(B)  6.24

(C)  12.13

(D)  15.24

Answer: (A)

5. A 42.12% (w, v) solution of NaCl causes precipitation of a certain sol in 10 hours. The coagulating value of NaCl for the sol is

[Given : Molar mass : Na = 23.0 g mol–1; Cl = 35.5 g mol–1]

(A) 36 mmol L–1

(B) 36 mol L–1

(C) 1440 mol L–1

(D) 1440 mmol L–1

Answer: (D)

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

Assertion A: The first ionization enthalpy for oxygen is lower than that of nitrogen.

Reason R: The four electrons in 2p orbitals of oxygen experience more electron-electron repulsion.

In the light of the above statements, choose the correct answer from the options given below.

(A) Both A and R are correct and Rj is the correct explanation of A

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

(C) A is correct but R is not correct

(D) A is not correct but R is correct

Answer: (B)

7. 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-III, B-IV, C-II, D-I

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

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

Answer: (A)

8. Given below are two statements.

Statement-I: In CuSO4.5H2O, Cu-O bonds are present.

Statement-II: In CuSO4.5H2O, ligands coordinating with Cu(II) ion are O-and S-based ligands.

In the light of the above statements, choose the correct 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)

9. Amongst baking soda, caustic soda and washing soda, carbonate anion is present in

(A) Washing soda only

(B) Washing soda and caustic soda only

(C) Washing soda and baking soda only

(D) Baking soda, caustic soda and washing soda

Answer: (A)

10. Number of lone pair(s) of electrons on central atom and the shape of BrF3 molecule respectively, are

(A) 0, triangular planar

(B) 1, pyramidal

(C) 2, bent T-shape

(D) 1, bent T-shape

Answer: (C)

11. Aqueous solution of which of the following boron compounds will be strongly basic in nature?

(A) NaBH4

(B) LiBH4

(C) B2H6

(D) Na2B4O7

Answer: (D)

12. Sulphur dioxide is one of the components of polluted air. SO2 is also a major contributor to acid rain. The correct and complete reaction to represent acid rain caused by SO2 is

(A) 2SO2 + O2 → 2SO3

(B) SO2 + O3 → SO3 + O2

(C) SO2 + H2O2 → H2SO4

(D) 2SO2 + O2 + 2H2O → 2H2SO4

Answer: (D)

13. Which of the following carbocations is most stable?

Answer: (D)

14. 

The stable carbocation formed in the above reaction is

Answer: (C)

15. Two isomers (A) and (B) with Molar mass 184 g/mol and elemental composition C, 52.2%; H, 4.9 % and Br 42.9% gave benzoic acid and p-bromobenzoic acid, respectively on oxidation with KMnO4. Isomer ‘A’ is optically active and gives a pale yellow precipitate when warmed with alcoholic AgNO3. Isomers ‘A’ and ‘B’ are, respectively.

Answer: (C)

16. In Friedel-Crafts alkylation of aniline, one gets

(A) Alkylated product with ortho and para substitution.

(B) Secondary amine after acidic treatment.

(C) An amide product.

(D) Positively charged nitrogen at benzene ring.

Answer: (D)

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

Assertion A: Dacron is an example of polyester polymer.

Reason R: Dacron is made up of ethylene glycol and terephthalic acid monomers.

In the light of the above statements, choose the most appropriate answer from the options given below.

(A) Both A and R are correct and R is the correct explanation of A.

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

(C) A is correct but R is not correct.

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

Answer: (A)

18. The structure of protein that is unaffected by heating is

(A) Secondary Structure

(B) Tertiary Structure

(C) Primary Structure

(D) Quaternary Structure

Answer: (C)

19. The mixture of chloroxylenol and terpineol is an example of

(A) Antiseptic

(B) Pesticide

(C) Disinfectant

(D) Narcotic analgesic

Answer: (A)

20. A white precipitate was formed when BaCl2 was added to water extract of an inorganic salt. Further, a gas ‘X’ with characteristic odour was released when the formed white precipitate was dissolved in dilute HCl. The anion present in the inorganic salt is

(A)  I

(B)  SO32

(C)  S2

(D)  NO2

Answer: (B)

SECTION-B

21. A box contains 0.90 g of liquid water in equilibrium with water vapour at 27°C. The equilibrium vapour pressure of water at 27°C is 32.0 Torr. When the volume of the box is increased, some of the liquid water evaporates to maintain the equilibrium pressure. If all the liquid water evaporates, then the volume of the box must be ______ litre. [nearest integer]

(Given : R = 0.082 L atm K–1mol–1]

(Ignore the volume of the liquid water and assume water vapours behave as an ideal gas.)

Answer: (29)

22. 2.2 g of nitrous oxide (N2O) gas is cooled at a constant pressure of 1 atm from 310 K to 270 K causing the compression of the gas from 217.1 mL to 167.75 mL. The change in internal energy of the process, ΔU is ‘–x’ J. The value of ‘x’ is ____. [nearest integer]

(Given : atomic mass of N = 14 g mol–1 and of O = 16 g mol–1

Molar heat capacity of N2O is 100 J K–1mol–1)

Answer: (195)

23. Elevation in boiling point for 1.5 molalsolution of glucose in water is 4 K. The depression in freezing point for 4.5 molalsolution of glucose in water is 4 K. The ratio of molal elevation constant to molal depression constant (Kb/Kf) is _______.

Answer: (3)

24. The cell potential for the given cell at 298 K

Pt | H2 (g, 1 bar) | H+ (aq) || Cu2+ (aq) | Cu(s)

is 0.31 V. The pH of the acidic solution is found to be 3, whereas the concentration of Cu2+ is 10–x M. The value of x is _________.

(Given:  and 

Answer: (7)

25. The equation k = (6.5 × 1012s–1)e–26000K/T is followed for the decomposition of compound A. The activation energy for the reaction is ______ kJ mol–1. [nearest integer]

(Given : R = 8.314 J K–1mol–1]

Answer: (216)

26. Spin only magnetic moment of [MnBr6]4– is ________ B.M. [round off to the closest integer]

Answer: (6)

27. For the reaction given below:

CoCl3∙ xNH3 + AgNO3(aq) →

If two equivalents of AgCl precipitate out, then the value of x will be_______.

Answer: (5)

28. The number of chiral alcohol(s) with molecular formula C4H10O is ________.

Answer: (1)

29. In the given reaction,

the number of sp2 hybridised carbon(s) in compound ‘X’ is _____.

Answer: (8)

30. In the given reaction,

The number of π electrons present in the product ‘P’ is_______.

Answer: (4)

MATHEMATICS

SECTION-A

1. Let α be a root of the equation 1 + x2 + x4 = 0. Then the value of α1011 + α2022 – α3033 is equal to

(A)  1

(B)  α

(C)  1 + α

(D)  1 + 2α

Answer: (A)

2. Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z – 1) – arg(z + 1) = π/4 intersect

(A) exactly at one point

(B) exactly at two points

(C) nowhere

(D) at infinitely many points

Answer: (C)

3. Let . If B = I – 5C1(adjA) + 5C2(adjA)2 – …. – 5C5(adjA)5, then the sum of all elements of the matrix B is

(A)  –5

(B)  –6

(C)  –7

(D)  –8

Answer: (C)

4. The sum of the infinite series  is equal to

(A)  425/216

(B)  429/216

(C)  288/125

(D)  280/125

Answer: (C)

5. The value of  is equal to

(A)  π2/6

(B)  π2/3

(C)  π2/2

(D)  π2

Answer: (D)

6. Let f : R → R be a function defined by;

Then, which of the following is NOT true?

(A) For n1 = 3, n2 = 4, there exists α ∈ (3, 5) where f attains local maxima.

(B) For n1 = 4, n2 = 3, there exists α ∈ (3, 5) where f attains local minima.

(C) For n1 = 3, n2 = 5, there exists α ∈ (3, 5) where f attains local maxima.

(D) For n1 = 4, n2 = 6, there exists α ∈ (3, 5) where f attains local maxima.

Answer: (C)

7. Let f be a real valued continuous function on [0, 1] and . Then, which of the following points (x, y) lies on the curve y = f(x)?

(A) (2, 4)

(B) (1, 2)

(C) (4, 17)

(D) (6, 8)

Answer: (D)

8. If 

Answer: (C)

9. If y = y (x) is the solution of the differential equation  and y(0) = 0, then 6(y'(0) + (y(loge√3))2) is equal to:

(A)  2

(B)  −2

(C)  −4

(D)  −1

Answer: (C)

10. Let P : y2 = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P make an angle of π/4 with the line y = 3x + 5 touch the parabola P at A and B. Then the value of a for which A, B and S are collinear is

(A)  8 only

(B)  2 only

(C)  1/4 only

(D)  any a > 0

Answer: (D)

11. Let a triangle ABC be inscribed in the circle x2 – √2(x + y) + y2 = 0 such that ∠BAC= π/2. If the length of side AB is √2, then the area of the ΔABC is equal to :

Answer: (*)

12. Let  lie on the plane px – qy + z = 5, for some p, q ∈ℝ. The shortest distance of the plane from the origin is :

Answer: (B)

13. The distance of the origin from the centroid of the triangle whose two sides have the equations x – 2y + 1 = 0 and 2x – y – 1 = 0 and whose orthocenter is (7/3, 7/3) is :

(A)  √2

(B)  2

(C)  2√2

(D)  4

Answer: (C)

14. Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y + 2z = 16. Let T be a plane passing through the point Q and contains the line  Then, which of the following points lies on T?

(A) (2, 1, 0)

(B) (1, 2, 1)

(C) (1, 2, 2)

(D) (1, 3, 2)

Answer: (B)

15. Let A, B, C be three points whose position vectors respectively are

If α is the smallest positive integer for which  are non collinear, then the length of the median, in ΔABC, through A is:

(A)  √82/2

(B)  √62/2

(C)  √69/2

(D)  √66/2

Answer: (A)

16. The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to

(A)  5/16

(B)  9/16

(C)  11/16

(D)  13/16

Answer: (A)

17. The number of values of a ∈ℕ such that the variance of 3, 7, 12, a, 43 – a is a natural number is :

(A)  0

(B)  2

(C)  5

(D)  Infinite

Answer: (A)

18. From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60°. The pole subtends an angle 30° at the top of the tower. Then the height of the tower is :

(A) 15√3

(B) 20√3

(C) 20 + 10√3

(D) 30

Answer: (D)

19. Negation of the Boolean statement (p ∨ q) ⇒ ((~ r) ∨ p) is equivalent to

(A) p∧ (~ q) ∧ r

(B) (~ p) ∧ (~ q) ∧ r

(C) (~p) ∧ q ∧ r

(D) p∧ q ∧ (~ r)

Answer: (C)

20. Let n ≥ 5 be an integer. If 9n – 8n – 1 = 64α and 6n – 5n – 1 = 25β, then α – β is equal to

(A)  1 + nC2(8 – 5) + nC3(82 – 52) + … + nCn(8n1 – 5n1)

(B)  1 + nC2(8 – 5) + nC4(82 – 52) + … + nCn(8n2 – 5n2)

(C)  nC3(8 – 5) + nC4(82 – 52)+ … + nCn(8n2 – 5n2)

(D)  nC4(8 – 5) + nC5(82 – 52)+ … + nCn(8n3 – 5n3)

Answer: (C)

SECTION-B

21. Let  be a vector such that  Then, the value of  is equal to _______.

Answer: (*)

22. Let y = y(x), x > 1, be the solution of the differential equation  with  then the value of α + β is equal to ________.

Answer: (14)

23. Let 3, 6, 9, 12, …upto 78 terms and 5, 9, 13, 17, … upto 59 terms be two series. Then, the sum of terms common to both the series is equal to _________.

Answer: (2223)

24. The number of solutions of the equation sin x = cos2 x in the interval (0, 10) is _____.

Answer: (4)

25. For real number a, b (a > b > 0), let

and

 

Then the value of (a – b)2 is equal to _____.

Answer: (12)

26. Let f and g be twice differentiable even functions on (–2, 2) such that  f(1) = 1 and  g(1) = 2 Then, the minimum number of solutions of f(x)g′′(x) + f′(x)g′(x) = 0 in (–2, 2) is equal to_____.

Answer: (4)

27. Let the coefficients of x–1 and x–3 in the expansion of  be m and n respectively. If r is a positive integer such that mn2 = 15Cr∙ 2r then the value of r is equal to ________.

Answer: (5)

28. The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to _______.

Answer: (1086)

29. Let  where α is a non-zero real number an  If (I – M2)N = −2I, then the positive integral value of α is ________.

Answer: (1)

30. Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x)) = 8x2 – 2x and g(f(x)) = 4x2 + 6x + 1, then the value of f(2) + g(2) is ____________ .

Answer: (18)

JEE Main Session 2 28th June 2022 Shift 2 Question Paper and Answer Key

JEE Main Session 2 28th June 2022 Shift 2

PHYSICS

Section-A

IMPORTANT INSTRUCTIONS:

(1)   The test is of 3 hours duration:

(2)   The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i)    Section-A: This section contains 20 multiple choice questions which have only one correct answer. each question carries 4 marks for correct answer and −1 mark for wrong answer.

(ii)   Section-B: This section contains 10 questions. In Section-B, attempt any five questions out of 10. The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and −1 mark for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as  Here m and n are constants. The relations for distance and time in two systems respectively are :

Answer: (A)

2. A ball is spun with angular acceleration α = 6t2 – 2t, where t is in second and α is in rads–2. At t = 0, the ball has angular velocity of 10 rads–1 and angular position of 4 rad. The most appropriate expression for the angular position of the ball is :

Answer: (B)

3. A block of mass 2 kg moving on a horizontal surface with speed of 4 ms–1 enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by F = –kx where k = 12 Nm–1. The speed of the block as it just crosses the rough surface will be :

(A) Zero

(B) 1.5 ms–1

(C) 2.0 ms–1

(D) 2.5 ms–1

Answer: (C)

4. A √(34) m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If Ff and Fw are the reaction forces of the floor and the wall, then ratio of Fw/Ff will be:

(Use g = 10 m/s2)

(A)  6/√110

(B)  3/√113

(C)  3/√109

(D)  2/√109

Answer: (C)

5. Water falls from a 40 m high dam at the rate of 9 × 104 kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydro electric energy number of 100 W lamps, that can be lit, is :

(Take g = 10 ms2)

(A)  25

(B)  50

(C)  100

(D)  18

Answer: (B)

6. Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be

vertical-align: middle; margin-bottom: 1px;

Answer: (C)

7. A water drop of radius 1 μm falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is 1.8 × 10–5 Nsm–2 and its density is negligible as compared to that of water (106gm–3). Terminal velocity of the water drop is

(Take acceleration due to gravity = 10 ms–2)

(A) 145.4 × 10–6ms–1

(B) 118.0 × 10–6ms–1

(C) 132.6 × 10–6ms–1

(D) 123.4 × 10–6ms–1

Answer: (D)

8. A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work of 50 J is done on the gas during the part BC. The internal energy of the gas at A is 1560 J. The work done by the gas during the part CA is:

(A)  20 J

(B)  30 J

(C)  −30 J

(D)  −60 J

Answer: (B)

9. What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

(A) The velocity of atomic oxygen remains same

(B) The velocity of atomic oxygen doubles

(C) The velocity of atomic oxygen becomes half

(D) The velocity of atomic oxygen becomes four times

Answer: (B)

10. Two point charges A and B of magnitude +8 × 10–6 C and –8 × 10–6 C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6.4 × 104 NC–1. The distance ‘d’ between the point charges A and B is:

(A)  2.0 m

(B)  3.0 m

(C)  1.0 m

(D)  4.0 m

Answer: (B)

11. Resistance of the wire is measured as 2 Ω and 3 Ω at 10°C and 30°C respectively. Temperature co-efficient of resistance of the material of the wire is:

(A) 0.033°C–1

(B) –0.033°C–1

(C) 0.011°C–1

(D) 0.055°C–1

Answer: (A)

12. The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to 1.2 × 10–5. What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?

(A) 1.2 × 10–5

(B) 1.2 × 10–3

(C) 1.8 × 10–3

(D) 2.4 × 10–5

Answer: (A)

13. Two parallel, long wires are kept 0.20 m apart in vacuum, each carrying current of x A in the same direction. If the force of attraction per meter of each wire is 2 × 10–6 N, then the value of x is approximately:

(A)  1

(B)  2.4

(C)  1.4

(D)  2

Answer: (C)

14. A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be:

(Assume the coil to be short circuited.)

(A) Halved

(B) Quadrupled

(C) The same

(D) Doubled

Answer: (D)

15. An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y-direction has maximum magnitude of 60 Vm–1. Choose the correct equations for electric and magnetic field if the EM wave is propagating in vacuum:

Answer: (B)

16. In Young’s double slit experiment performed using a monochromatic light of wavelength λ, when a glass plate (μ = 1.5) of thickness xλ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of x will be:

(A)  3

(B)  2

(C)  1.5

(D)  0.5

Answer: (B)

17. Let K1 and K2 be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength λ1 and λ2, respectively are incident on a metallic surface. If λ1 = 3λ2 then:

(A)  K1> K2/3

(B)  K1< K2/3

(C)  K1 = K2/3

(D)  K2 = K1/3

Answer: (B)

18. Following statements related to radioactivity are given below:

(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.

(B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time.

(C) Slope of the graph of loge (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time (τ).

(D) Product of decay constant (λ) and half-life time (T1/2) is not constant.

Choose the most appropriate answer from the options given below:

(A) (A) and (B) only

(B) (B) and (D) only

(C) (B) and (C) only

(D) (C) and (D) only

Answer: (C)

19. In the given circuit the input voltage Vin is shown in figure. The cut-in voltage of p–n junction diode (D1 or D2) is 0.6 V. Which of the following output voltage (V0) waveform across the diode is correct?

Answer: (D)

20. Amplitude modulated wave is represented by VAM = 10[1 + 0.4 cos(2π × 104t] cos(2π × 107t). The total bandwidth of the amplitude modulated wave is:

(A) 10 kHz

(B) 20 MHz

(C) 20 kHz

(D) 10 MHz

Answer: (C)

SECTION-B

21. A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 mm, 1.23 mm, 1.19 mm and 1.20 mm. The percentage error is . Then value of x is _______.

Answer: (150)

22. A zener of breakdown voltage VZ = 8 V and maximum Zener current, IZM = 10 mA is subjected to an input voltage Vi = 10 V with series resistance R = 100 Ω. In the given circuit RL represents the variable load resistance. The ratio of maximum and minimum value of RL is __________.

Answer: (2)

23. In a Young’s double slit experiment, an angular width of the fringe is 0.35° on a screen placed at 2 m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index 7/5, is 1/α. The value of α is _________.

Answer: (4)

24. In the given circuit, the magnitude of VL and VC are twice that of VR. Given that f = 50 Hz, the inductance of the coil is 1/(Kπ) mH. The value of K is ________.

Answer: (0)

25. All resistances in figure are 1 Ω each. The value of current ‘I‘ is (a/5) A. The value of a is _________.

Answer: (8)

26. A capacitor C1 of capacitance 5 μF is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor C2 of capacitance 10 μF as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor C2 is ____ μC.

Answer: (100)

27. A tuning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is ____ cm.

(Vel