FIITJEE · 2020. 8. 28. · FIITJEE Ltd., FIITJEE House, 29 -A, Kalu Sarai, Sarvapriya Vihar, New Delhi 110016, Ph 46106000, 26569493, Fax 26513942 website: . FIITJEE Solutions to

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com.

FIITJEE Solutions to JEE(Main)-2020

PHYSICS, CHEMISTRY & MATHEMATICS

Time Allotted: 3 Hours

Maximum Marks: 300

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

Important Instructions:

1. The test is of 3 hours duration. 2. This Test Paper consists of 75 questions. The maximum marks are 300. 3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics

having 25 questions in each part of equal weightage out of which 20 questions are MCQs and 5 questions are numerical value based. Each question is allotted 4 (four) marks for correct response.

4. (Q. No. 01 – 20, 26 – 45, 51 – 70) contains 60 multiple choice questions which have only one correct

answer. Each question carries +4 marks for correct answer and –1 mark for wrong answer. 5. (Q. No. 21 – 25, 46 – 50, 71 – 75) contains 15 Numerical based questions with answer as numerical

value. Each question carries +4 marks for correct answer. There is no negative marking. 6. Candidates will be awarded marks as stated above in instruction No.3 for correct response of each

question. One mark will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer box.

7. There is only one correct response for each question. Marked up more than one response in any

question will be treated as wrong response and marked up for wrong response will be deducted accordingly as per instruction 6 above.

Paper - 1

Test Date: 9th January 2020 (First Shift)

http://www.fiitjee.com.

JEE-MAIN-2020 (9th Jan-First Shift)-PCM-2


PART – A (PHYSICS) 1. Two particles of equal mass ‘m’ have respective initial velocities û i and

ˆ î ju .2

They

collide completely inelastically. The energy lost in the process is:

(A) 21mu3

(B) 21mu8

(C) 22 mu3

(D) 23 mu4

2. Radiation, with wavelength 6561 Å falls on a metal surface to produce photoelectrons.

The electrons are made to enter a uniform magnetic field of 3 × 10–4 T. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to:

(A) 0.8 eV (B) 1.6 eV (C) 1.8 eV (D) 1.1 eV 3. Water flows in a horizontal tube (see figure). The

pressure of water changes by 700 Nm–2 between A and B where the area of cross section are 40 cm2 and 20 cm2, respectively. Find the rate of flow of water through the tube. (density of water = 1000 kg m–3)

(Fig.)

(A) 1810 cm3/s (B) 2420 cm3/s (C) 2720 cm3/s (D) 3020 cm3/s 4. The aperture diameter of a telescope is 5m. The separation between the moon and the

earth is 4 × 105 km. With light of wavelength of 5500 Ä, the minimum separation between objects on the surface of moon, so that they are just resolved, is close to:

(A) 200 m (B) 600 m (C) 60 m (D) 20 m 5. A body A of mass m is moving in a circular orbit of radius R about a planet. Another

body B of mass m2

collides with A with a velocity which is half v2

the instantaneous

velocity v

of A. The collision is completely inelastic. Then, the combined body: (A) starts moving in an elliptical orbit around the planet. (B) continues to move in a circular orbit. (C) Escapes from the Planet’s Gravitational field. (D) Falls vertically downwards towards the planet. 6. Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas

A are rigid, and have a mass m. Molecules of the gas B have an additional vibrational

mode and have mass m .4

The ratio of the specific heats A BV V(C and C ) of gas A and B,

respectively is (A) 3 : 5 (B) 5 : 7 (C) 7 : 9 (D) 5 : 9




7. Three harmonic waves having equal frequency v and same intensity I0, have phase

angles 0, and4 4

respectively. When they are superimposed the intensity of the

resultant wave is close to: (A) 3I0 (B) I0 (C) 0.2I0 (D) 5.8I0

8. A quantity f is given by 5hcf

G where c is speed of light, G universal gravitational

constant and h is the Planck’s constant. Dimension of f is that of: (A) energy (B) momentum (C) area (D) volume 9. If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main

scale. If there are 50 divisions on the circular scale the least count of the screw gauge is

(A) 0.001 cm (B) 0.001 mm (C) 0.01 cm (D) 0.02 mm 10. Three solid spheres each of mass m and diameter d

are stuck together such that the lines connecting the centres form an equilateral triangle of side of length d. The ratio I0/IA of moment of inertia I0 of the system about an axis passing the centroid and about center of any of the spheres IA and perpendicular to the plane of the triangle is

(A) 1513

(B) 1315

(C) 2313

(D) 1323

11. Consider a force ˆ ˆF xi yj

. The work done by this

force in moving a particle from point A(1, 0) to B(0, 1) along the line segment is: (all quantities are in SI units)

(A) 2 (B) 1

2

(C) 1 (D) 32

12. A vessel of depth 2h is half filled with a liquid of refractive index 2 2 and the upper half with another liquid of refractive index 2. The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be

(A) h2

(B) h2( 2 1)

(C) 3 h 24

(D) h3 2




13. A particle moving with kinetic energy E has de Broglie wavelength . If energy E ;is added to its energy, the wavelength become /2. Value of E, is:

(A) E (B) 3E (C) 2E (D) 4E 14. In the given circuit diagram, a wire is joining

points B and D. The current in this wire is: (A) zero (B) 2A (C) 0.4 A (D) 4A

15. A long, straight wire of radius a carries a current distributed uniformly over its cross-

section. The ratio of the magnetic fields due to the wire at distance a3

and 2a,

respectively from the axis of the wire is:

(A) 23

(B) 12

(C) 2 (D) 32

16. The electric fields of two plane electromagnetic plane waves in vacuum are given by 1 0

Ê E j cos( t kx)

and 2 0

Ê E k cos( t ky)

At t = 0, a particle of charge q is at origin with velocity ˆv 0.8 cj

(c is the speed of light in vaccum). The instantaneous force experienced by the particle is:

(A) 0ˆ ˆ Ê q 0.8i j 0.4k (B) 0

ˆ ˆ Ê q 0.4i 3 j 0.8k

(C) 0ˆ ˆ Ê q 0.8i j 0.2k (D) 0

ˆ ˆ Ê q 0.8i j k

17. An electric dipole of moment 29ˆ ˆ ˆp ( i 3 j 2k) 10 cm

is at the origin (0, 0, 0). The

electric field due to this dipole at ˆ ˆ ˆr i 3 j 5k

(note that r p 0)

is parallel to: (A) ˆ ˆ ˆ( i 3 j 2k) (B) ˆ ˆ ˆ( i 3 j 2k) (C) ˆ ˆ ˆ( i 3 j 2k) (D) ˆ ˆ ˆ( i 3 j 2k) 18. A charged particle of mass ‘m’ and charge ‘q’ moving

under the influence of uniform electric field E i

and a uniform magnetic field Bk

follows a trajectory from

point P to Q as shown in figure. The velocities at P and Q are respectively, v i and 2v j

. Then which of

the following statements (A, B, C, D) are the correct? (Trajectory shown is schematic and not to scale)

(a) 23 mvE

4 qa




(b) Rate of work done by the electric field at P is 33 mv

4 a

(c) Rate of work done by both the fields at Q is zero. (d) The difference between the magnitude of angular momentum of the particle at P and

Q is 2 mav. (A) (b), (c), (d) (B) (a), (b), (c) (C) (a), (c), (d) (D) (a), (b), (c), (d) 19. Consider a sphere of radius R which carries a uniform

charge density . If a sphere of radius R2

is carved out of it,

as shown the ratio A

B

E

E

of magnitude of electric field AE

and

BE ,

respectively, at point A and B due to the remaining portion is:

(A) 1834

(B) 1754

(C) 1854

(D) 2134

20. Which of the following is an equivalent cyclic

process corresponding to the thermodynamic cyclic given in the figure? Where, 1 2 is adiabatic. (Graphs are schematic and are not to scale)

(A)

(B)

(C)

(D)

21. Both the diodes used in the circuit

shown are assumed to be ideal and have negligible resistance when these are forward biased. Built in potential in each diode is 0.7 V. For the input voltages shown in the figure, the voltage (in Volts) at point A is __________.




22. One end of a straight uniform 1 m long bar is pivoted on horizontal table. It is released from rest when it makes an angle 30ۤ° from the horizontal (see figure). Its angular speed when it hits the table is given as 1n s , where n is an integer. The value of n is __________.

23. In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced

when the choke current changes uniformly from 0.25 A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be __________.

24. A body of mass m = 10 kg is attached to one end of a wire of length 0.3 m. The

maximum angular speed (in rad s–1) with which it can be rotated about its other end in space station is (Breaking stress of wire = 4.8 × 107 Nm–2 and area of cross-section of the wire = 10–2 cm2) is

25. The distance x covered by a particle in one dimensional motion varies with time t as

x2 = at2 + bt + c. If the acceleration of the particle depends on x as x–n, where n is an integer, the value of n is __________.




PART –B (CHEMISTRY) 26. If the magnetic moment of a dioxygen species is 1.73 B.M, it may be: (A) 2 2 2O ,O or O (B) 2 2O or O

(C) 2 2O O (D) 2 2O or O 27. The compound that cannot act both as oxidising and reducing agent is: (A) H2O2 (B) H2SO3 (C) HNO2 (D) H3PO4 28. [Pd(F)(Cl)(Br)(I)]2– has n number of geometrical isomers. Then, the spin-only magnetic

moment and crystal field stabilisation energy [CFSE] of [Fe(CN)6]n –6, respectively, are: [Note: Ignore the pairing energy] (A) 2.84 BM and –1.6 0 (B) 1.73 BM and –2.0 0 (C) 5.92 BM and 0 (D) 0 BM and –2.4 0 29. The electronic configurations of bivalent europium and trivalent cerium are: (atomic

number: Xe = 54, Ce = 58, Eu = 63) (A) [Xe] 4f7 6s2 and [Xe] 4f26s2 (B) [Xe] 4f7 and [Xe] 4f1

(C) [Xe] 4f2 and [Xe] 4f7 (D) [Xe] 4f4 and [Xe] 4f9

30. For following reactions

it was found that the Ea is decreased by 30 kJ/mol in the presence of catalyst. If the rate

remains unchanged, the activation energy for catalysed reaction is (Assume pre exponential factor is same):

(A) 135 kJ/mol (B) 105 kJ/mol (C) 75 kJ/mol (D) 198 kJ/mol 31. The increasing order of basicity for the following intermediates is (from weak to strong)

(A) (v) < (iii) < (ii) < (iv) < (i) (B) (iii) < (i) < (ii) < (iv) < (v) (C) (v) < (i) < (iv) < (ii) < (iii) (D) (iii) < (iv) < (ii) < (i) < (v)




32. 'X' melts at low temperature and is a bad conductor of electricity in both liquid and solid state. X is:

(A) Silicon carbide (B) Mercury (C) Zinc sulphide (D) Carbon tetrachloride

33. The de Broglie wavelength of an electron in the 4th Bohr orbit is: (A) 6a0 (B) 4a0 (C) 2a0 (D) 8a0

34. Identify (A) in the following reaction sequence:

(A)

(B)

(C)

(D)

35. The major product (Y) in the following reactions is:

(A)

(B)

(C)

(D)




36. Complex X of composition Cr(H2O)6Cln has a spin only magnetic moment of 3.83 BM. It reacts with AgNO3 and shows geometrical isomerism. The IUPAC nomenclature of X is: (A) Dichloridotetraaqua chromium (IV) chloride dihydrate (B) Tetraaquadichlorido chromium (III) chloride dihydrate (C) Tetraaquadichlorido chromium (IV) chloride dihydrate (D) Hexaaqua chromium (III) chloride IUPAC name = Tetraaquadichlorido chromium (III) chloride dihydrate

37. The acidic, basic and amphoteric oxides, respectively, are: (A) Cl2O, CaO, P4O10 (B) MgO, Cl2O, Al2O3 (C) Na2O, SO3, Al2O3 (D) N2O3, Li2O, Al2O3 38. The Ksp for the following dissociation is 1.6 10-5

22PbCl s Pb aq 2Cl aq

Which of the following choices is correct for a mixture of 300 mL 0.134 M Pb(NO3)2 and 100 mL 0.4 M NaCl?

(A) Not enough data provided (B) Q > Ksp (C) Q < Ksp (D) Q = Ksp 39. A chemist has 4 samples of artificial sweetener A, B, C and D. To identify these

samples, he performed certain experiments and noted the following observations: (i) A and D both form blue-violet colour with ninhydrin. (ii) Lassaigne extract of C gives positive AgNO3 test and negative Fe4[Fe(CN)6]3 test. (iii) Lassaigne extract of B and D gives positive sodium nitroprusside test. Based on these observations which option is correct? (A) A : Aspartame; B : Alitame; C : Saccharin; D : Sucralose (B) A : Aspartame; B : Saccharin; C : Sucralose; D : Alitame (C) A : Alitame; B : Saccharin; C : Aspartame; D : Sucralose (D) A : Saccharin; B : Alitame; C : Sucralose; D : Aspartame

40. The major product Z obtained in the following reaction scheme is:

(A)

(B)

(C)

(D)




41. Which of these will produce the highest yield in Friedel Crafts reaction?

(A)

(B)

(C)

(D)

42. B has a smaller first ionization enthalpy than Be. Consider the following statements: (i) it is easier to remove 2p electron than 2s electron. (ii) 2p electron of B is more shielded from the nucleus by the inner core of electrons than

the 2s electrons of Be. (iii) 2s electron has more penetration power than 2p electron (iv) atomic radius of B is more than Be (atomic number B = 5, Be = 4) The correct statements are: (A) (i), (iii) and (iv) (B) (i), (ii) and (iii) (C) (i), (ii) and (iv) (D) (ii), (iii) and (iv) 43. The correct order of heat of combustion for following alkadienes is:

(a) (b) (c)

(A) (a) < (b) < (c) (B) (a) < (c) < (b) (C) (c) < (b) < (a) (D) (b) < (c) < (a) 44. If enthalpy of atomisation for Br2(A) is x kJ/mol and bond enthalpy for Br2 is y kJ/mol, the

relation between them: (A) is x = y (B) is x > y (C) does not exist (D) is x < y




45. According to the following diagram, A reduces BO2 when the temperature is:

(A) > 1400 °C (B) < 1400 °C (C) < 1200 °C (D) > 1200 °C but < 1400 °C 46. The molarity of HNO3 in a sample which has density 1.4 g/mL and mass percentage of

63% is (Molecular Weight of HNO3 = 63) 47. The mass percentage of nitrogen in histamine is . 48. How much amount of NaCl should be added to 600 g of water ( = 1.00 g/mL) to

decrease the freezing point of water to –0.2°C ? . (The freezing point depression constant for water = 2 K kg mol-1) 49. 108 g of silver (molar mass 108 g mol-1 ) is deposited at cathode from AgNO3 (aq)

solution by a certain quantity of electricity. The volume (in L) of oxygen gas produced at 273 K and 1 bar pressure from water by the same quantity of electricity is .

50. The hardness of a water sample containing 10-3 M MgSO4 expressed as CaCO3

equivalents (in ppm) is . (molar mass of MgSO4 is 120.38 g/mol)




PART–C (MATHEMATICS)

51. The product 1 1 11

16 48 12842 .4 .8 .16 .......... to is equal to

(A) 122 (B) 2

(C) 1 (D) 142

52. Let the observations ix 1 i 10 satisfy the equation 10

ii 1

x 5 10

and

10 2

ii 1

x 5 40

. If and are the mean and the variance of the observations,

1 2 10x 3,x 3,..............,x 3, then the ordered pair , is equal to: (A) (6, 6) (B) (3, 3) (C) (3, 6) (D) (6, 3)

53. If 1e and 2e are the eccentricities of the ellipse, 2 2x y 1

18 4 and the hyperbola,

2 2x y 19 4 respectively and 1 2e ,e is a point on the ellipse, 2 215x 3y k, then k is

equal to: (A) 16 (B) 14 (C) 17 (D) 15

54. If the matrices 1 1 2

A 1 3 4 ,B adjA1 1 3

and C 3A, then adjB

C is equal to:

(A) 72 (B) 8 (C) 16 (D) 2

55. If

1/32

/3

sin a 2 x sinx;x 0

xf x b ;x 0

x 3x; x 0

x

(A) –2 (B) –1 (C) 0 (D) 1




56. If the number of five digit numbers with distinct digits and 2 at the 10th place is 336 k, then k is equal to:

(A) 6 (B) 7 (C) 4 (D) 8 57. In a box, there are 20 cards, out of which 10 are labeled as A and the remaining 10 are

labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A – card is obtained. The probability that the second A – card appears before the third B – card is:

(A) 916

(B) 1516

(C) 1316

(D) 1116

58. The number of real roots of the equation, 4x 3x 2x xe e 4e e 1 0 is: (A) 2 (B) 4 (C) 3 (D) 1 59. A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness that

melts at a rate of 50 cm3/ min. When the thickness of ice is 5 cm, then the rate (in cm/min) at which of the thickness of ice decreases, is:

(A) 56

(B) 136

(C) 118

(D) 154

60. The value of 2 8

8 80

x sin x dxsin x cos x

is equal to:

(A) 2 (B) 4 (C) 2 (D) 22

61. Let z be a complex number such that z i 1z 2i

and 5z2

. Then the value of

z 3i is:

(A) 154

(B) 2 3

(C) 10 (D) 72

62. Negation of the statement: 5 is an integer or 5 is irrational’ is: (A) 5 is an integer and 5 is irrational (B) 5 is not an integer or 5 is not irrational (C) 5 is not an integer and 5 is not irrational (D) 5 is irrational or 5 is an integer




63. Let C be the centroid of the triangle with vertices (3, –1), (1, 3) AND (2, 4). Let P be the point of intersection of the lines x 3y 1 0 and 3x y 1 0 . Then the line passing through the points C and P also passes through the point:

(A) (–9, –7) (B) (–9, –6) (C) (7, 6) (D) (9, 7) 64. If for some and in R, the intersection of the following three planes x 4y 2z 1 x 7y 5z x 5y z 5 is a line in 3R , then is equal to: (A) 0 (B) 2 (C) 10 (D) –10 65. Let f be any function continuous on a,b and twice differentiable on (a, b). If for all

x a,b ,f ' x 0 and f " x 0 , then for any

f c f ac a,b

f b f c

is greater than:

(A) c ab c

(B) b ab a

(C) b cc a

(D) 1

66. The value of 3 33 3cos .cos sin .sin8 8 8 8

is:

(A) 12

(B) 14

(C) 12

(D) 1

2 2

67. A circle touches the y – axis at the point (0, 4) and passes through the point (2, 0).

Which of the following lines is not a tangent to this circle? (A) 3x 4y 24 0 (B) 3x 4y 6 0 (C) 4x 3y 17 0 (D) 4x 3y 8 0

68. If for all real triplets (a, b, c), 2f x a bx cx ; then 1

0f x dx is equal to:

(A) 1 1f 1 3f2 2

(B) 1 1f 0 f 1 4f

6 2

(C) 1 1f 0 f3 2

(D) 12 3f 1 2f

2




69. If 1f ' x tan sec x tanx , x ,2 2

and f 0 0 , then f 1 is equal to:

(A) 14

(B) 14

(C) 24

(D) 14

70. The integral 8/7 6/7

dxx 4 x 3

is equal to:

(where C is a constant of integration)

(A) 13/71 x 3 C

13 x 4

(B)

1/7x 3 Cx 4

(C) 1/7x 3 C

x 4

(D) 3/71 x 3 C

2 x 4

71. The projection of the line segment joining the points (1, –1, 3) and (2, –4, 11) on the line

joining the points (–1, 2, 3) and (3, –2, 10) is ___________ 72. If the vectors, ˆ ˆ ˆ ˆ ˆ ˆp a 1 i aj ak, q ai a 1 j ak

and

ˆ ˆ ˆr a i aj a 1 k a R

are coplanar and 2 23 p.q r q 0

, then the value of

is _________. 73. If for x 0, y y x is the solution of the differential equation,

2x 1 dy x 1 y 3 dx,y 2 0 , then y 3 is equal to _______________

74. The coefficient of 4x in the expansion of 1021 x x is ______________.

75. The number of distinct solutions of the equation, 1 1

2 2

log sin x 2 log cos x in the

interval 0,2 , is _________.




JEE (Main) – 2020

ANSWERS

PART –A (PHYSICS)

1. B 2. A 3. C 4. C

5. A 6. B 7. D 8. A

9. A 10. D 11. C 12. C

13. B 14. B 15. A 16. C

17. D 18. B 19. A 20. D

21. 12 22. 15 23. 10 24. 4

25. 3

PART –B (CHEMISTRY)

26. D 27. D 28. B 29. B

30. B 31. A 32. D 33. D

34. B 35. B 36. B 37. D

38. B 39. B 40. B 41. B

42. D 43. A 44. B 45. A

46. 14 47. 37.84 48. 0.176 49. 0.568

50. 100

PART–C (MATHEMATICS)

51. B 52. B 53. C 54. B

55. C 56. D 57. D 58. D

59. C 60. C 61. D 62. C

63. B 64. C 65. A 66. D

67. D 68. B 69. B 70. C

71. 8 72. 1 73. 3 74. 615

75. 8




HINTS AND SOLUTIONS PART –A (PHYSICS)

1. B Sol. Conserving momentum

1 2v vˆ ˆ ˆ ˆ ˆmv i m i j 2m (v i v j)2 2

On solving

1 23v vv and v4 4

Change in K.E.

2 2 2

21 1 v 1 9v vmv m 2 (2M)2 2 2 2 16 16

= 2 2 23mv 5mv mv

4 8 8

2. A Sol. KEmax = E –

= 12400(in )Å

– (in eV)

2mKEreB

2 2 2

maxr e BKE

2m (in J)

2 2r eB2m

(in eV)

2 212400 r eB

6561 2m = 1.1 eV

3. C Sol. Using equation of continuity 40 VA = 20 VB 2VA = VB Using Bernoullies equation

2 2A A B B

1 1P V P V2 2

2 2A B B A

1P P V V2

2

2 BB

V1P 1000 V2 4




2B3VP 500

4

B( P) 4 (700) 4V m/s

1500 1500

Volume flow rate = 20 × 100 × VB = 2732 cm3/s 4. C Sol.

1.22

a

Distance = O1O2 = d = 1.22 da

Distance = O1O2 = 10 81.22 5893 10 4 10 57.5 m

5

answer from options = 60 m (minimum distance) 5. A Sol. Conserving momentum

fm v mmv m V2 2 2

f5mV 5VV 3m 64

2

vf < vorb (= v) thus the combined mass will go on to an elliptical path vf < vorb (= v) 6. B

Sol. Molar heat capacity of A at constant volume = 5R2

Molar heat capacity of B at constant volume = 7R2

Dividing both, v A

v B

(C ) 5(c ) 7




7. D Sol.

resA 2 1 A

2

res 0I 2 1 I

= 0 0 s3 2 2 I 5.8 I

8. A Sol. [ML2T–2] [hc] = [ML3T–2] [c] = [LT–1] [G] = [M–1L3T–2] 9. A

Sol. Pitch = 36

= 0.5 mm

L.C. = 0.5 mm 1 mm50 100

= 0.01 mm

= 0.001 cm 10. D

Sol. M. I. about P = 22

22 d d 133 M M Md5 2 103

M. I. about B = 2 2

2 22 d 2 d 232 M M(d ) M Md5 2 5 2 10

Now ratio = 1323

11. C Sol. W F ds

= ˆ ˆ ˆ ˆ( xi yj) (dxi dyj)

= 0 1

1 0

xdx ydy

= 102 2

1 0

x y 1 102 2 2 2

= 1J




12. C Sol. h hd

2 2 2

h 3 3 2 hd2 42

13. B

Sol. h 12(KE)m KE

f

i

KE/ 2 KE

4KEi = KEf E = 4KEi – KEi = 3KE = 3E 14. B Sol.

eff4 6R 25 5

20i 10A2

4i 3i iI 2A5 5 5

15. A Sol.

00 0 0

A 2 2 2

aiir i ia3B6 6 a2 a 2 a a

0B

iB2 (2a)

A

B

B 4 2B 6 3

16. C Sol. Magnetic field vectors associated with this electromagnetic wave are given by




0 01 2

E Eˆ ˆB k cos(kx t) & B i cos(ky t)c c

F qE q(V B)

1 2 1 2q(E E ) q(V (B B ))

By putting the value of 1 2 1 2E ,E , B & B

The net Lorentz force on the charged particle is 0

ˆ ˆ ˆF qE 0.8 cos(kx t)i cos(kx t)j 0.2 cos(ky t)k

At t = 0 and at x = y = 0 0

ˆ ˆ ˆF qE [0.8i j 0.2k]

17. D Sol. Since p r 0

E

must be antiparallel to p

So, E (p)

Where is a arbitrary positive constant Now ˆ ˆ Â ai bj ck

A ||E

a b c k3 2

So, ˆ ˆ Â k( i 3 j 2k)

18. B Sol. (a) By work energy theorem

2 2mag ele

1 1W W m(2v) m(v)2 2

20

30 qE 2a mv2

2

03 mvE4 qa

(b) Rate of work done at A = power of electric force A = qE0V

= 33 mv

4 a

(c) at dwQ, 0dt

for both forces

(d) ˆ ˆL ( m2v2ak) ( mak)

L 3mva




19. A Sol. For a solid sphere

0

rE3

; A0

RE2(3 )

; A0

RE6

Electric field at point B = EB = E1A + E2A

E1A = Electric field due to solid sphere of radius R at point B = 0

R3

E2A = Electric field due to solid sphere of radius R/2 (which having charge density –)

E2A = R/2 = 0

2KQ 4 R

549R

B 1A 2A0 0 0

R R 17 RE E E3 54 54

A

B

E 9E 17

20. D Sol. For process A – B PV = nRT ; as P increases For process B – C PV = Constant TV – 1 = Constant For process C – A ; pressure is constant V = kT 21. 12 Sol.

Let VB = 0 Right diode is reversed biased and left diode is forward biased VE = 12.7 – 0.7 = 12 Volt 22. 15

Sol. 2

o 21 mmg sin 302 2 3

Solving, 2 = 15 ; = 15




23. 10

Sol. 3L(0.25)100 100.025

L = 100 × 10–4 H = 10 mH 24. 4 Sol.

TA …(1)

T = m2 …(2) Solving, = 4 rad/s

25. 3 Sol. x2 = at2 + 2bt + c 2xv = 2at + 2b xv = at + b v2 + ax = a

2at bax a

x

2 2

3a(at 2bt c) (at b)a

x

2

3ac ba

x

; a x–3




PART –B (CHEMISTRY)

26. D Sol. Magnetic moment = 1.73 BM Unpaired electron = 1 2 * 2 2 * 2 2 2 2 * 1 * 1

2 2 x y x yO 1s , 1s , 2s , 2s , 2p , 2p 2p , 2p 2p

Hence 2 2O ,O have one unpaired electron. 27. D Sol. 1 4

2 2 2 3H O H SO

3

25

3 4

HNO

H P O

In H3PO4 phosphorus is in maximum oxidation state so cannot increase its oxidation number.

28. B Sol. Number of geometrical isomers in square planar [PdFClBr]2– are 3 Hence, n = 3 [Fe(CN)6]3– Fe3+ = 3d5, according to CFT configuration planar is 221 00

2g gt e

n n 2 1.73 B.M

CFSE = -0.40 nt2g + 0.60 neq = -0.40 5 = - 2.00 29. B

Sol. Eu2+ [xe]4f2 Ce2+ : [xe]4f2 30. B

Sol. Kcatalyst = K

1 2

1 2

Ea EaRT RTAe Ae

1Ea = energy of activation in presence of catalyst T1 = 500 K T2 = 700 K

1 2

1 2

Ea EaT T

But Ea1 = Ea2 – 30

2 2Ea 30 Ea500 700




5Ea2 = 7Ea2 – 210

Ea2 = 2102

= 105 kJ/mole

31. A Sol. Basicity in inversely proportional to electronegativity.

32. D Sol. CCl4 is a non conductor in solid and liquid phase.

33. D Sol. 2r = n

2 2

0 0

20

0

n nn 4 & r a 2 a nz z

4 a2 41

8 a

34. B Sol.

35. B Sol.




36. B Sol. Cr(H2O)6Cln

(complex)spin = 3.8 B.M n = 3 Cr(H2O)6Cl3 Oxidation number of Cr should be +3 Compound so G.I so it will be [Cr(H2O)4Cl2]Cl.2H2O IUPAC name = Tetraaquadichlorido chromium (III) chloride dihydrate

37. D Sol. Non-metal oxides are acidic in nature Alkali metal oxides are basic in nature Al2O3 is amphoteric. 38. B Sol. Q = [Pb2+][Cl–]2

2

2300 0.134 100 0.4 3 0.134 0.1400 400 4

Q = 1.005 10–3 Q > Ksp 39. B Sol. A – Aspartame

B – Saccharin C – Sucralose D – Alitame

(i) A & D give positive test with ninhydrin because both have free carboxylic and amine group.

(ii) C form precipitate with AgNO3 because it has chlorine atoms. (iii) B & D give positive test because both have S-atom.

40. B

Sol.

41. B Sol. Aniline react lewis acid form anilinium complex. So phenol is most reactive among for

nucleophellic substitution reaction.




42. D Sol. Radius of Boron is less than Radius of Be Hence IV statement is false. Rest are True.

Statement 43. A Sol. In isomers of Hydrocarbon heat of combustion depend upon their stability. Stability

increase heat of combustion decrease. Stability a > b > c Heat of combustion c > b > a 44. B Sol.

45. A Sol. 2 2A BO B AO G = -ve Only above 1400oC 46. 14 Sol. d = 1.4 g/mL 63/w/w

63 1.4Molarity 1000 mole / litre 14 mole / L63 100

47. 37.84 Sol. Structure of Histamine is

Molecular formula = C5H9N3 Molecular mass = 111

% of N = 42 100111

= 37.84%

48. 0.176 Sol. Tf = 0.2 Tf = i Kfm i = 2 for NaCl 0.2 = 2 2 m




w 1000m58.5 600

0.2 = 2 2 w 100058.5 600

0.2 58.5 600 1.2 58.5w 0.1764 1000 40

49. 0.568

Sol. Ag deposit

108n 1 mole108

Ag 1e Ag If charge is required for 1 mole of Ag

2 21H O O 2H 2e2

2F charge deposit = ½ mole 1 F charge deposit = ¼ mole PV = nRT

1 0.83 273V4 1

= 5.675 L

50. 100 Sol. Given: 10–3 M MgSO4 i.e. 10–3 mole MgSO4 present in 1 litre solution

4 3MgSO CaCOn n Mass of CaCO3 = 10–3 100

ppm(in terms of CaCO3) = 3

610 100 10 1001000




PART–C (MATHEMATICS) 51. B

Sol. 1 2 3 ..........4 16 482

1 1 1 ............4 8 162 2

52. B

Sol. Mean i1

x 5x 5 1

10

iMean x 5 2 3

2i i

ix 5 x 5

var x 5 310 10

53. C

Sol. 14 7 7e 1

18 9 3

24 13 13e 19 9 9

2 21 2

7 1315e 3e k k 15 39 9

k 16 54. B

Sol. 1 1 2

A 1 3 4 9 4 1 3 4 2 1 3 13 1 8 61 1 3

2n 1 4 2adjB adjadjA A A 36

3C BA 3 6

3adjB 36 36 8

C 3 6

55. C Sol. LHL = a + 3 f (0) = b

RHL

13

h 0

1 3h 1lim 1

h




a 2 b 1 a 2b 0 56. D Sol. Number of numbers 8 8 7 6 2688 336k k 8 57. D Sol. AA + ABA + BAA + ABBA + BBAA + BABA

1 1 1 1 1 1 114 8 8 16 16 16 16

58. D Sol. Let xe t 0,

Given equation 4 3 2t t 4t t 1 0

22

1 1t t 4 0t t

221 1t t 4 0

tt

Let 1tt

2 2 4 0

2 6 0 3, 2 2 x xe e 2 x 0 only solution 59. C Sol. Let thickness = x cm

Total volume 34v 10 x3

2dv dx4 10 xdt dt

……….(i)

Given 3dv 50 cm / mindt

At x 5cm

2 dx50 4 10 5dt

dx 1 cm / mindt 18




60. C

Sol. 88 8

8 8 8 8 8 80 0

2 x sin xx sin x 2 sin xdx dxsin x cos x sin x cos x sin x cos x

/2 8 8

8 8 8 80

sin x cos x2 dxsin x cos x sin x cos x

/2

2

0

2 1 dx 22

61. D

Sol. 2 22 2x y 1 x y 2 2y 1 4y 4

16y 3 y2

2 2 225 24x y x 64 4

iz 62

25 49z 3i 64 4

7z 3i2

62. C Sol. 5 is not an integer and 5 is not an irrational number ~ p q ~ p ~ q 63. B Sol. D (2, 2)

Point of intersection 1 2P ,5 5

equation of line DP 8x 11y 6 0

64. C

Sol. 1 4 2

0 1 7 5 01 5

7 25 4 10 20 14 0 3 9 0 3

Also z

1 4 1D 0 1 7 0

1 5 5




1 35 5 15 1 4 7 0 13 65. A Sol. Let use LMVT for x a,c

f c f a

f ' , a,cc a

also use LMVT for x c,b

f b f c

f ' , c,bb c

f " x 0 f ' x is decreasing

f ' f '

f c f a f b f c

c a b c

f c f a c af b f c b c

( f (x) is increasing)

66. D

Sol. 3 3 3 3cos 4cos 3cos sin 3sin 4sin8 8 8 8 8 8

6 6 4 44cos 4sin 3cos 3sin8 8 8 8

2 2 4 4 2 2 2 24 cos sin sin cos sin cos 3 cos sin8 8 8 8 8 8 8 8

2 2 1 1 1cos 4 1 sin cos 3 14 8 8 22 2 2

67. D

Sol. Equation of family of circle

2 2x 0 y 4 x 0 passes (2, 0) 4 16 2 0 10 2 2x y 10x 8y 16 0

centre (5, 4). R 25 16 16 5 Check the options. Option (4)

4 5 3 4 8 24 55 5

68. B




Sol. 12 31 2

00

bx cx b ca bx cx dx ax a2 3 2 3

f 1 a b c

f 0 a

1 b cf a2 2 4

Now 1 1 1 b cf 1 f 0 4f a b c a 4 a6 2 6 2 4

1 b c6a 3b 2c a6 2 3

69. B

Sol. 1 1 1 sinxf ' x tan sec x tan x tancos x

2

1 1

x1 cos x 2sin2 4 2tan tan

x xsin x 2sin cos2 4 2 4 2

1 x xtan tan4 2 4 2

xf ' x dx dx4 2

2xf x x c

4 4

2xf 0 c 0 f x x

4 4

So 1f 14

70. C

Sol.

67

2x 3 1 dxx 4 x 4

Let 7x 3 tx 4

,

62

7 dx 7t dtx 4

6 6t t dt t c




71. 8 Sol. Let A 1, 1,3 ,B 2, 4,11

ˆ ˆ ÂB i 3 j 8k

C (–1, 2, 3), D (3, –2, 10) ˆ ˆ ˆCD 4i 4 j 7k

projection of AB

on AB.CDCD

CD

4 12 56 72 8916 16 49

72. 1

Sol.

a 1 a aa a 1 a 0 a 1 a a 0a a a 1

1a3

2 1 1ˆ ˆ ˆP i j k3 3 3

1 ˆ ˆ ˆQ i 2 j k3

1 ˆ ˆ ˆR i j 2k3

i j k

1 1P.Q 1 2 1 i 4 1 j 2 1 k 1 29 9

1 1 2

1 i j k3i 3 j 3k9 3

21 1R Q 3 R Q

3 3

2 23 P Q R Q 0

1 13. . 0 19 3

73. 3

Sol. dy y 31 xdx 1 x

dy 1 3y 1 xdx 1 x 1 x




I.F.

1 dx1 x 1e

1 x

2

d y 31dx 1 x 1 x

1y x 3 1 x c1 x

3y 1 x x c

1 x

at x 2, y 0 0 3 2 1 c c 3 at x = 3, y = 3 74. 615

Sol. General term 210! x! ! !

for coefficient of 4x 2 4

0, 4, 6 10! 2106!4!0 !

1, 2, 7 10! 3607!2!1!

2, 0, 8 10! 458!0!2!

Total = 615 75. 8 Sol. 1/2 1/2log sinx 2 log cosx

1/2log sinxcosx 2

1sin x cos x4

1sin 2x2

Number of solution = 8.


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