FIITJEE RET – 8

RET–8 (CHAMP)

FIITJEE (Hyderabad Classes) Limited., 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad–500 063. Phone: 040-66777000-03 Fax: 040-66777004

FIITJEE RET – 8

(2018– 2020)(2ND

YEAR_CHAMPIONS)

IIT-2017 (P2) DATE: 19.08.2019

Time: 3 hours Maximum Marks: 183

INSTRUCTIONS:

A. General

1. This booklet is your Question Paper containing 54 questions.

2. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets in any form are not allowed to be carried inside the examination hall.

3. Fill in the boxes provided for Name and Enrolment No.

4. The answer sheet, a machine-readable Objective Response (ORS), is provided separately.

5. DO NOT TAMPER WITH / MULTILATE THE ORS OR THE BOOKLET.

B. Filling in the OMR:

6. The instructions for the OMR sheet are given on the OMR itself.

C. Question paper format & Marking Scheme

7. Each part has three sections as detailed in the following table:

Section Question Type

Number of Questions

Category wise Marks Each Question Maximum marks of the section

Full Marks Partial Marks Zero Marks Negative Marks

1 Single Correct Option

7

+3

If only the bubble corresponding to the correct option is darkened

––– 0

If none of the bubbles is darkened

–1

In all other cases

21

2 One or more correct option(s)

7

+4

If only the bubble(s) corresponding to all the correct option(s) is (are) darkened.

+1

For darkening a bubble corresponding to each correct option, provided NO incorrect

option is darkened.

0

If none of the bubbles is darkened.

–2

In all other case.

28

3 Comprehension

4

+3

If only the bubble corresponding to the correct option is darkened

––– 0

In all other case.

––– 12

Don’t write / mark your answers in this question booklet. If you mark the answers in question booklet, you will not be allowed to continue the exam.

NAME:

ENROLLMENT NO.:

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PAPER–II

PART I: PHYSICS SECTION 1 (Maximum Marks: 28)

This section contains SEVEN questions.

Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct.

For each question, darken the bubble corresponding to all the correct option in the ORS.

1. In the plane mirror, the coordinates of image of a charged particle (initially at origin as shown in figure)

after two and a half time periods are (Initial velocity of charge particle is V0 in the xy–plane

and the plane mirror is perpendicular to the x–

axis. A uniform magnetic field B i exists in the

space. P0 is pitch of helix, R0 is radius of helix.)

(A) 7.5 P0, 0, –2R0 (B) 7.5 P0, 0, 2R0

(C) 17.5P0, 0, –2R0 (D) 17.5 P0, 0, 2R0

2. Given figure shows a coil bent with all edges of length 1 m and

carrying a current of 1 A. There exists in space a uniform magnetic field of 2 T in positive y-direction. The net torque on loop is

(in N-m)

(A) 2 k (B) -2 k (C) 2 i (D) None of these

y

3. A circular current loop of radius a is placed in a radial field B as shown.

The net force acting on the loop is

(a = 7 m, 10

i A

, B = 10–1

T, = 30)

(A) 7 3N (B) 14 3N

(C) 7N (D) 14 N

4. An electron is projected with velocity 0v in a uniform electric field E perpendicular to the field. Again it is

projected with velocity 0v perpendicular to a uniform magnetic field B. If r1 is initial radius of curvature just

after entering in the electric field and r2 is initial radius of curvature just after entering in magnetic field then the ratio r1/r2 is equal to.

(A) 2

0Bv

E (B)

B

E (C) 0Ev

B (D) 0Bv

E

space for rough work

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5. Two circular coils X and Y have equal number of turns and carry equal

currents in the same sense and subtend same solid angle at point O. If the smaller coil X is midway between O and Y, then if we represent the

magnetic induction due to bigger coil Y at O as YB and that due to smaller

coil X at O as XB then Y

X

B

B

(A) 1

2 (B) 2

(C) 1

3 (D)

1

4

6. Two long parallel wires are at a distance 2d apart. They carry steady equal current flowing out of the plane

of the paper, as shown in figure. The variation of the magnetic field B along the line XX' is given by

7. A charged particle begins to move from the origin in a region which has a uniform magnetic field in the x–

direction and a uniform electric field in the y–direction. Its speed is v when it reaches the point (x, y, z).

Then, v will depend on (A) x (B) y (C) z (D) none of these


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SECTION 2 (Maximum Marks: 15) This section contains SEVEN questions.

Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four options is(are) correct.

For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS.

For example, if (A), (C) and (D) are all the correct options for a question, darkening all these three will get +4 marks; darkening only (A) and (D) will get +2 marks; and darkening (A) and (B) will get –2 marks, as a wrong option is also darkened.

8. A charged particle of specific charge moves with a velocity oˆv v i in a magnetic field 0B ˆ ˆB ( j k)

2 .

Then (specific charge = charger per unit mass)a (A) Path of the particle is helix (B) Path of the particle is circle

(C) Distance moved by particle in time 0

tB

is 0

0

v

B

(D) Velocity of particle after time 0

tB

is 0 0v vˆ ˆi j

2 2

9. A positively charged particle with velocity ˆ ˆv x i y j moves in a magnetic field ˆ ˆB y i x j both x and y are

constants. The magnitude of magnetic force acting on the particle is F. Which one of the following statement(s) is/are correct:

(A) no force will act on particle if x = y (B) F (x2 – y

2) if x > y

(C) the force will act along z-axis if x > y (D) the force will act along y-axis if y >x 10. Three infinitely long conductors A, B and C are carrying

current as shown in figure. The position of the point lying in the straight line AC, where magnetic field is zero, is approximately given by

(A) between A and B at a distance of 3.2 cm from B

(B) between B and C at a distance of 3.2 cm from B (C) between A and B at a distance of 1.3 cm from B (D) between B and C at a distance of 1.3 cm from B 11. A straight conductor carries a current. Assume that all free electrons in the conductor move with the same

drift velocity . A and B are two observers on a straight line XY parallel to the conductor. A is stationary, B

moves along XY with a velocity in the direction of the free electrons.

A) A and B observe the same magnetic field

B) A observes a magnetic field, B does not

C) A and B observe magnetic fields of the same magnitude but opposite directions.

D) A and B do not observe any electric field


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12. In the loops shown, all curved sections are either semicircles or quarter circles. All the loops carry the

same current. The magnetic fields at the centres have magnitudes B1, B2, B3 and B4.

A) B4 is maximum B) B3 is minimum C) B4 > B1 > B2 > B3 D) B1 > B4 > B3 > B2

13. An infinite current carrying wire passes through point O

and in perpendicular to the plane containing a current carrying loop ABCD as shown in the figure. Choose the correct option(s).

(A) Net force on the loop is zero (B) Net torque on the loop is zero (C)As seen from O, the loop rotates clockwise (D) As seen from O, the loop rotates anticlockwise

14. Two infinite plates carry j ampere of

current out of the page per unit width of the plate as shown. BP and BQ represent magnitude of magnetic field at points P and Q respectively.

A) BP = 0 B) Bp = 0j C) BQ = 0 D) BQ = 0j


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SECTION 3 (Maximum Marks: 18) This section contains TWO paragraphs.

Based on each paragraph, there are TWO questions.


For each question, darken the bubble corresponding to the correct option in the ORS.

Paragraph–1 Magnetic field exists in the region as shown in figure. In the upper region

uniform magnetic field is 1 0ˆB B k and in lower region uniform magnetic field

is 2 0ˆ2B B k . A charge particle having mass m and positive charge q

moving parallel to x-axis enter in the magnetic field at point A, and comes out

at point C with speed 1v . Given 0 0

0 0

3 3,

2 4

mv mvd D

qB qB

15. The value of 1v is

(A) 0v (B) 0 / 2v (C) 02v (D) 0 / 3v

16. Radius of circular path in lower region is

(A) / 2d (B) d (C) 2d (D) 3d

Paragraph–2 A long cylindrical conductor of radius a has two cylindrical cavities of

diameter a through its entire length, as shown in figure. A current I is

directed out of the page and is uniform through a cross section of the conductor.

17. The magnitude and direction of the magnetic field in terms of

0,I,r and a at point 1P is ____________.

(A) 2 2

0

2 2

I 2r a

r 4r a

directed towards left (B)

2 2

0

2 2

I 2r a

r 4r a

directed towards right

(C) 2 2

0

2 2

I 4r a

r 2r a

directed towards left (D)

2 2

0

2 2

I 4r a

r 2r a

directed towards right


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18. The magnitude and direction of the magnetic field in terms of 0,I,r and a at point

2P is ____________.

(A) 2 2

0

2 2

I 2r aB

r 4r a

directed toward the top of the page

(B) 2 2

0

2 2

I 2r aB

r 4r a

directed toward the bottom of the page

(C) 2 2

0

2 2

I 4r aB

r 2r a

directed toward the top of the page

(D) 2 2

0

2 2

I 4r aB

r 2r a

directed toward the bottom of the page

PART II: CHEMISTRY SECTION 1 (Maximum Marks: 28)




19. The minimum concentration of an electrolyte which is able to cause coagulation of a sol is termed as its (A) emulsification value (B) saponification value (C) flocculation value (D) gold number. 20. Which of the following is a hydrophilic colloidal sol ? (A) Barium sulphate solution (B) Arsenius sulphide solution (C) Starch sol (D) Silver iodide sol. 21. The colloidal sols are purified by (A) peptization (B) coagulation (C) dialysis (D) flocculation 22. If the disperse phase and the dispersion medium both are liquid, the colloidal solution is classified as (A) emulsion (B) foam (C) gel (D) supercooled liquid 23. The emulsifying agent in milk is (A) lactic acid (B) casein (C) lactose (D) fat


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24. A butter is (A) a gel (B) an emulsion (C) a sol (D) none of these

25. Which of the following statements is correct in the context of sodium stearate, 3 2 16CH CH COO Na

?

(A) It is a major component of many bar soaps. (B) The R–group is the nonpolar tail and is hydrophobic (C) The –COO group is the polar–ionic head nad is hydrophilic. (D) All of these





26. Which of the following statement(s) is/are correct ? (A) Adsorption is a non-spontaneous process (B) Surface energy decreases during the process of adsorption (C) Adsorption takes place with decrease of entropy (D) Physical adsorption is exothermic process whereas chemisorption is endothermic 27. Point out the false statement (A) Brownian motion and Tyndall effect are shown by colloidal systems (B) The colloidal solution of a liquid in liquid is called emulsion (C) Hardy–Schulze law is related with coagulation of a sol (D) Higher is the gold number, greater will be the protective power of a lyophilic colloid 28. Which of the following is arranged in order of decreasing coagulating power ? (A) NaCl > BaCl2 > AlCl3 (B) BaCl2 > AlCl3 > NaCl (C) AlCl3 > BaCl2 > NaCl (D) BaCl2 > NaCl > AlCl3


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29. On adding AgNO3 solution in KI solution, a negatively charged colloidal sol is formed when the contents are

(A) 100 mL of 0.1 M AgNO3 + 100 mL of 0.1 M KI (B) 100 mL of 0.1 M AgNO3 + 100 mL of 0.2 M KI (C) 100 mL of 0.2 M AgNO3 + 100 mL of 0.1 M KI (D) 100 mL of 0.1 M AgNO3 + 100 mL of 0.25 M KI 30. Which of the following properties of lyophilic sols are more than that of lyophobic sols ? (A) surface tension compared to medium (B) viscosity compared to meidum (C) stability (D) solubility in a given solvent 31. Select the correct statement(s) about macromolecular colloids (A) Multimolecular or macromolecular colloids consist of aggregate of atoms or small molecules with

diameter less than 1 nm (B) Molecules are hold together by van dar Waal’s forces (C) Most lyophilic sols belong to this class (D) Most lyophobic sols belong to this class 32. Select the correct statement(s).

(A) The cleansing action of soap is due to affinity of soap anions as stearate 17 35C H COO

(B) Soap are known as emulsifyng agents

(C) 17 35C H R part of soap has affinity for grease, oil or dirt and is tail of the anion

(D) COO– part of soap has affinity for water and is head of the anion





Paragraph–1 Ferric hydroxide sol is formed by adding FeCl3 to hot distilled water.

3 2 2 3 2FeCl 6H O Fe O .3H O 6HCl

33. Advantage of boiling during process is that (A) HCl formed is removed along with water vapour from the system (B) FeOCl is removed (C) Fe2O3 is removed (D) FeCl3 is removed 34. Sol is stabilised by (A) HCl (B) FeOCl (C) FeCl3 (D) All of these


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Paragraph–2 There are certain colloids which behave as normal strong electrolytes at low concentrations, but exhibit collidal properties at higher concentrations due to formation of aggregated particles. 35. Aggregated particles are called (A) emulsions (B) micelles (C) aerosols (D) aquosols 36. Select correct statement(s) about CMC. (A) It is the lowest concentration at which formatio of aggreagted particle starts (B) For soaps, CMC is 10

–4 to 10

–3 mol L

–1

(C) Both (a) and (b) (D) None of the above

PART III: MATHEMATICS SECTION 1 (Maximum Marks: 28)




37.

2

3 4 2

x 1dx

x 2x 2x 1

is equal to

(A)

4 2

2

2x 2x 1c

x x 1

(B)

4 2

3

2x 2x 1c

x

(C) 4 2

2

2x 2x 1c

x

(D)

4 2

2

2x 2x 1c

2x

38. 1 1x 3 sin Inx cos Inx dx equals

(A) 3 / 2

x 3 c3

(B) 0 (C) does not exist (D) none of these


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39.

2

3 2cosxdx

2 3cosx

is equal to

(A) sinx

c2 3cosx

(B)

2cosxc

2 3sinx

(C)

2cosxc

2 3cosx

(D)

2sinxc

2 3sinx

40. If

5

a

7 a6

x xdx In c

x 1x x

, then a + is

(A) = 2 (B) > 2 (C) < 2 (D) = 1

41. If n n

n nn

x xf x lim

x x

, x > 1, then

2

2

x f x In x 1 xdx

1 x

is

(A) 2In x 1 x x c (B) 2 2 21x In x 1 x x c

2

(C) 2 2xIn x 1 x In x 1 x c (D) none of these

42. The value of the integral 3 5

2 4

cos x cos xdx

sin x sin x

is

(A) 1sinx 6tan sinx c (B) 1

sinx 2 sinx c

(C) 1 1sinx 2 sinx 6tan sinx c (D)

1 1sinx 2 sinx 5tan sinx c

43. If

2 2

1f x sinxcosxdx Inf x c

2 b a

, then f(x) is equal to

(A) 2 2 2 2

1

a sin x b cos x (B)

2 2 2 2

1

a sin x b cos x

(C) 2 2 2 2

1

a cos x b sin x (D) none of these


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44. If x x

2x

ex x

4e 6edx Ax Blog 9e 4 C

9e 4e

(A) A = 3/2 (B) B = 35/36 (C) C is indefinite (D) 19

A B36

45. Let

1/ 2

3

x 2dx gof x c

31 x

, then

(A) f x x (B) 3/ 2f x x (C) 2/3f x x (D) 1g x sin x

46. If cosec2xdx f g x c , then

(A) range of g(x) = (-,) (B) domain of f(x) = (-,) – {0}

(C) g’(x) = sec2x (D) f’(x) = 1/x for all x (0, )

47. If x tan 1/n In 1/n

nf x lim e

and

113

f xdx g x c

sin xcosx , then

(A) 3

g4 2

(B) g(x) is continuous for all x

(C) 15

g4 8

(D) g(x) is non differentiable at infinitely many points


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48. If 1 1 2 1 2cos x cos 1 x dx Ax f x sin x 2 1 x c x [-1, 0), then

(A) f(x) = x (B) f(x) = -2x (C) A4

(D) A

2

49. The value of

2

x

20

t tdt

1 t

is equal to

(A) 14 x tan x , if x < 0 (B) 0, if x > 0

(C) 2In 1 x , if x > 0 (D) none of these

50. If the primitive of sin(In x) is f(x) {sin g(x) – cos h(x) } + c (c being the constant of integration), then

(A) x 2limf x 1

(B)

x 1

g xlim 1

h x (C) 3g e 3 (D) 5h e 5





Paragraph–1

y = f(x) is a polynomial function passing through point (0, 1) and which increases in the intervals (1, 2) and

(3, ) and decreases in the intervals (-, 1) and (2, 3) 51. If f(1) = -8 then the value of f(2) is (A) -3 (B) -6 (C) -20 (D) -7 52. If f(1) = -8, then the range of f(x) is

(A) [3, ) (B) [-8, ) (C) [-7, ) (D) (-, 6]


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Paragraph–2

If the integrand is a rational function of x and fractional power of a linear fractional function of the form

ax b

cx d

i.e.,

m/n r / sax b ax b

f x, ,...., dxcx d cx d

.

In this form substitute pax bt

cx d

, where p is the LCM of the denominators of fractional powers of

ax b

cx d

53. The value of

1/ 2 1/ 3

dx

1 x 1 x is

(A) 1/ 2 1/3 1/ 6 1/ 62 3 6 6In 1 C

(B) 1/ 2 1/3 1/ 6 1/ 62 3 6 6In 1 C

(C) 1/ 2 1/3 1/ 6 1/ 62 3 6 6In 1 C

(D) 1/ 2 1/3 1/ 6 1/ 62 3 6 6In 1 C

54. The value of 1/ 2 2/ 3

1/ 3

1 x xdx

1 x

is

(A) 4 / 3 7 / 6 5 / 6 1/ 2 1/ 6 1 1/ 63 6 6x x x x 2x 6x 6tan x C

4 7 5

(B) 4 / 3 7 / 6 5 / 6 1/ 2 1/ 6 1 1/ 63 6 6x x x x 2x 6x 6tan x C

4 7 5

(C) 4 / 3 7 / 6 5 / 6 1/ 2 1/ 6 1 1/ 63 6 6x x x x 2x 6x 6tan x C

4 7 5

(D) 4 / 3 7 / 6 5 / 6 1/ 2 1/ 6 1 1/ 63 6 6x x x x 2x 6x 6tan x C

4 7 5


RET–8 (CHAMP)


FIITJEE RET – 8

(2018 – 2020)(2ND

YEAR_CHAMPIONS)

IIT-2017 (P2) DATE: 19.08.2019

ANSWERS

PHYSICS

1. C 2. D 3. C 4. D

5. A 6. B 7. B 8. B,C

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

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

17. A 18. A

CHEMISTRY

19. C 20. C 21. C 22. A or C

23. B 24. A 25. D 26. B, C

27. D 28. C 29. B, D 30. B, C, D

31. Bonus 32. Bonus 33. A 34. D

35. B 36. C

MATHEMATICS

37. D 38. C 39. A 40. B

41. D 42. C 43. A or C 44. B, C, D

45. B, D 46. Bonus 47. Bonus 48. B, D

49. A, B 50. A, B, C, D 51. D 52. B

53. A 54. D

FIITJEE RET – 8

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