(2016 2018)(2ND YEAR CHAMPIONS) - FIITJEE … (2ND YEAR...RET–12 FIITJEE (Hyderabad Classes) Limited., 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad–500 063. Phone: 040-66777000-03

RET–12

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

FIITJEE RET – 12

(2016 – 2018)(2ND

YEAR_CHAMPIONS)

IIT-2015 (P1) DATE: 20.11.2017

Time: 3 hours Maximum Marks: 264

INSTRUCTIONS:

A. General

1. This booklet is your Question Paper containing 60 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:

7. The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part consists of two sections.

8. Section I contains 8 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).

9. Section II contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.

10. Section III contains 2 Match the following type questions and you will have to match entries in Column I with the entries in Column II

D. Marking Scheme

11. For each question in Section I, you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. No negative marks will be awarded for incorrect answers in this section.

12. For each question in Section II, you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. –2 marks will be awarded for incorrect answers in this section.

13. For each question in Section III, you will be awarded 2 marks for each entry in Column I; if you darken ALL the bubble(s) corresponding to the correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. –1 marks will be awarded for incorrect answers in this section.

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–I

PART I: PHYSICS SECTION 1 (Maximum Marks: 32)

This section contains EIGHT questions.

The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive.

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

Marking scheme: +4 If the bubble corresponding to the answer is darkened. 0 In all other cases.

1 An observer whose least distance of distinct vision is '4m', views his own face in a convex mirror of radius

of curvature '3m'. The maximum magnification that can be produced is 1/n. Find n. 2 Two rays are incident on a spherical mirror of radius of R = 5 cm parallel to its optical axis at the distance

h1 = 0.5 cm and h2 = 3 cm. If the distance between the points at which these rays intersect the optical axis

after being reflected at the mirror is x cm, then 8 x is: 3 A thief is running away in a car with velocity of 20 m/s. A police jeep is following him, which is sighted by

thief in his rear view mirror which is a convex mirror of focal length 10 m. He observes that the image of jeep is moving towards him with a velocity of 1 cm/s. The magnification of the mirror for the jeep at that time is 1/10. If actual speed of jeep is 3x m/s, the value of x is:

4 A luminous point P is inside a circle. A ray enters from P and after two reflections by the circle, return to P.

If is the angle of incidence, the distance of P from the centre of the circle is 10 cm and the distance of

the centre from the point where the ray in its course crosses the diameter through P is 6 cm, then calculate

cot .

5 An opaque sphere of radius R = 2m lies on a horizontal plane. On the perpendicular through the point of

contact there is a point source of light a distance R above the sphere. The area of the shadow on the plane

is 4k. Find k.

6. An object is placed in front of a concave mirror at a distance of 50 cm . A plane mirror is introduced

covering the lower half of the convex mirror. If the distance between plane mirror and object is 30 cm, there

is no parallax between image formed by the two mirrors if radius of curvature of mirror is 100 / n. The value

of n is

Space for rough work

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7. When an object is placed at a distance of 25 cm from a concave mirror, the magnification is 1m . The object

is moved 15 cm father away from the mirror, the magnification becomes 2m . If focal length of the mirror is

20cm, then 1 2m /m is

8. A thin rod of length (f/3) is placed along the principle axis of a concave mirror of focal length ‘f’ such that its

image which is real and elongated, just touches the rod. If the linear magnification is m then 4m equals to

____

SECTION 2 (Maximum Marks: 40) This section contains TEN questions.

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

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

Marking scheme: +4 If only the bubble(s) corresponding to all the correct option(s) is (are) darkened. 0 If none of the bubbles is darkened. –2 In all other cases

9. In fig XY is the principal axis of a mirror which forms an

image I of the object O. Referring to the information

given in the figure, it can be concluded that the mirror is

(A) concave and kept to the right of I

(B) concave and kept to the left of I

(C) convex and kept to the right of O

(D) convex and kept to the left of O

O

h1

h2 > h1

X Y

I

10. A plane mirror, reflecting a ray of incident light, is rotated through an angle about an axis through the

point of incidence in the plane of the mirror perpendicular to the plane of incidence, then

(A) the reflected ray does not rotate

(B) the reflected ray rotates through an angle

(C) the reflected by rotates through an angle 2

(D) the incident ray is fixed


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11. Out of the following, which statements are correct ?

(A) Two plane mirrors are inclined to each other at angle of 060 . If a ray of light incident to each other at

an angle parallel to the second mirror, it is reflected from the second mirror parallel to the first mirror.

(B) A bird flying high up in the air does not cast a shadow on the ground because layers of atmosphere are

dense

(C) If a ray reflected successively from two plane mirrors inclined at a certain angle undergoes a deviation

of 0300 , then the number of images observable is 11

(D) A clock indicates a time of 3:25. On seeing it in a plane mirror, the times appears as 8:35

12. For a given object and plane mirror, image may move when

(A) object is moving

(B) mirror is moving

(C) relative gap between mirror and object is changing

(D) relative gap between mirror and object is not changing

13. A point source of light, S, is placed midway between two converging mirrors having equal focal length f, as

shown in the figure. Find the value(s) of d for which only one image is formed.

(A) f (B) 2f (C) 3f (D) 4f

14. An object AB is placed parallel and close to the optical axis between

focus F and center of curvature C of a converging mirror of focal

length f as shown in figure then.

(A) Image of A will be closer than that of B from the mirror

(B) Image of AB will be parallel to the optical axis

(C) Image of AB will be a straight line inclined to the optical axis

(D) Image of AB will not be a straight line

A B

C F

15. Mark the correct statement(s) w.r.t a concave spherical mirror

(A) For real extended object, it can form a diminished virtual image

(B) For real extended object, it can form a magnified virtual image

(C) For virtual extended object, it can form a diminished real image

(D) For virtual extended object, it can form a magnified real image


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16. A real object is moving toward a fixed spherical mirror. The image

(A) must move away from the mirror

(B) may move away from the mirror

(C) may move toward the mirror if the mirror is concave

(D) must move toward the mirror if the mirror is convex

17. A plane mirror M is arranged parallel to a wall W at a distance

from it. The light produced by a point source S kept on the wall is

reflected by the mirror and produced a patch of light on the wall.

The mirror moves with velocity v towards the wall.

Which of the following statement (s) is /are correct ?

(A) The patch of light will move with speed v on the wall

(B) The patch of light will not move on the wall

(C) As the mirror comes closer, the patch of light will become

larger and shift away from the wall with speed larger than v

(D) The size of the patch of light on the wall remains the same

s

v

M

18. Which of the following statements are correct ?

(A) A ray of light is incident on a plane mirror and gets reflected. If the mirror is rotated through an angle

, then the reflected ray gets deviated through angle 2

(B) A ray of light gets reflected successively from two mirrors which are mutually inclined. Angular

deviation suffered by the ray does not depend upon angle of incidence on first mirror.

(C) A plane mirror cannot form real image of a real object

(D) if an object approaches toward a plane mirror with velocity v, then the image approaches the object

with velocity 2v.


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SECTION 3 (Maximum Marks: 16) This section contains TWO questions.

Each question contains two columns, Column I and Column II

Column I has four entries (A), (B), (C) and (D)

Column II has five entries (P), (Q), (R), (S) and (T)

Match the entries in Column I with the entries in Column II

One or more entries in Column I may match with one or more entries in Column II.

The ORS contains a 4 5 matrix whose layout will be similar to the one shown below: (A) (P) (Q) (R) (S) (T) (B) (P) (Q) (R) (S) (T) (C) (P) (Q) (R) (S) (T) (D) (P) (Q) (R) (S) (T)

For each entry in Column I, darken the bubbles of all the matching entries. For example, if entry (A) in Column I matches with entries (Q), (R) and (T), then darken these three bubbles in the ORS. Similarly, for entries (V), (C) and (D).

Marking entry in Column I. +2 If only the bubble(s) corresponding to all the correct match (s) is (are) darkened. 0 If none of the bubbles is darkened. –1 In all other cases.

19. Four particles are moving with different velocities in front of a

stationary plane mirror (lying in y–z plane) . At t= 0, velocity of A is

Aˆv i , velocity of B is

Bˆ ˆv i 3j , velocity of C is

Cˆ ˆv 5i 6j ,

velocity of D is D

ˆ ˆv 3i j . Accele –ration of particle is A is A

ˆ â 2i j

and acceleration of particle C is C

â 2tj . The particles B and D move

with uniform velocity (Assume no collision to take place till t= 2 seconds). All quantities in S. I units. Relative velocity of image of

object A with respect to object A is denoted by A,Av . Velocities of

images relative to corresponding object are given in column I and their values are given column II at t =2 second. Match column I with corresponding values in column II.

A

B

C

D

y

x

Column – I

Column – II

(A) A.AV (p) ˆ2i

(B) B'.BV (q) ˆ6i

(C) C',CV (r) ˆ ˆ12i 4j

(D) D',DV (s) ˆ10i


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20. An object O is kept perpendicular to the principal axis of a spherical mirror. Each situation (a,b,c and d) gives object coordinates u in centimeter with sign, the type of mirror, and then the distance (centimeters with sign) between the focal point and the pole of the mirror. On the right side information, regarding the image is given

Correctly, match the situation on the left side with the image described on the right side.

Situation u Mirror Image

A –18 Concave, 12 p. Real, erect, enlarged

B –12 Concave, 18 q. Virtual, erect, diminished

C –8 Convex, 10 r. Real, inverted, enlarged

D –10 Convex, 8 s. Virtual, erect, enlarged

PART II: CHEMISTRY SECTION 1 (Maximum Marks: 32)





21. A solution contains 0.8133 g of K2SO4 in 500 mL. If osmotic pressure is found to be 0.69 atm at 27C. Calculate the value of van’t Hoff factor.

22. The vapour pressure of a mixture of two volatile liquids is expressed as Pm = 6 + 1.5 xB, where xB mole

fraction of ‘B’ is mixture. The vapour pressure of ‘A’ at the same temperature is 23. ‘n’ moles of a non–electrolyte are added to ‘N’ moles of solvent. The addition causes a lowering in vapour

pressure of solvent by 20%. The ratio of moles of solvent and its solute is (assume that, large dilute solution)

24. 4g of substance ‘A’, dissolved in 100g H2O depressed freezing point of water by 0.1C, while 4g of another

substance ‘B’ depressed freezing point of same amount of H2O by 0.2C. molecular weight of A is ‘x’ times that of ‘B”. The value of ‘x’ is


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25. Liquid A and B form an Ideal solution. Mole fraction of B in the vapour state is 0.75 and vapour pressures

of pure A and B are 80 and 60 Torr respectively. Calculate the ratio of mole fraction of B to A in liquid state. 26. The elevation in boiling point of one molal solution of AxBy is 8.4. The salt is 80% dissociated in water, then

x + y is (Kb of solvent is 2K molal–1

) 27. When 20 g of naphthoic acid (C11H8O2) is dissolved in 50 g of benzene

(Kf = 1.72 K kg mol–1), a freezing point depression of 2K is observed.

The Van’t Hoff factor (i) is 1

x where x is ……………

28. The osmotic pressure of urea solution at 10°C is 200 mm, becomes 105.3 mm when it is diluted and

temperature raised to 25°C. The ratio of original concentration to new concentration would be :





29. 75.2g of C6H5OH is dissolved in 1Kg of solvent of Kf = 14 Km

–1. If depression in freezing point is 7K, then

% of phenol that dimerises is (A) 75% (B) 25% (C) 60% (D) 40% 30. A binary liquid (AB) shows positive deviation from Raoult’s law when

(A) 0 liqA A Ap p X and 0 liq

B B Bp p X (B) Intermolecular forces : A–A, B–B > A–B

(C) mixV 0 (D) mixH 0

31. Just sufficient 2 4 3Al SO (s) is added to a 0.1 M solution of BaCl2 such that all the BaSO4 is precipitated

completely. Volume of solution is maintained constant. Then (A) freezing point of the original solution is raised (B) boiling point of the original solution is raised (C) vapour pressure of the original solution is raised (D) osmotic pressure of the original solution is raised


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32. A graph is plotted with temperature of a solution containing benzene and toluene as a function of mole

fraction. Choose the correct options.

bvapour

liquidc

d

aB.Pt.

toluene

mol fraction

benzene

(A) a b represents evaporation (B) b c represents condensation

(C) c d represents evaporation (D) c d represents condensation 33. Which of the following statements is/are correct about azeotropic mixture? (A) Azeotropic mixtures are non-ideal solution (B) The components of azeotropic mixture cannot be separated by fractional distillation (C) Azeotropes obey Rauult’s law (D) Solution with positive deviation from Raoult’s law, forms minimum boiling azeotrope 34. For a 20% wt/wt aqueous solution of X(molecular weight = 100) having density (1.2 gm/ml) (A) Molality of X is 2.5m (B) Molarity of X is 2.4M (C) Mole fraction of X is 0.8 (D) Mole fraction of H2O is 0.2 35. Identify the correct statement. (A) 1 M NaCl has higher freezing point than 1 M glucose solution. (B) 1 M NaCl solution has almost same boiling point as 1 M KCl solution, assuming 100% ionisation. (C) Apparent molecular weight of NaCl will be less than 58.5 in water because it undergoes dissociation. (D) i = 1 when acetic acid is dissolved in benzene. 36. Which of the following liquid pairs do not shows positive deviation form raoults law? (A) Acetone-chloroform (B) Benzene – methanol (C) water – nitric acid (D) water – hydrochloric acid 37. 1.0g of a monobasic acid HA in 100g water lowers the freezing point by 0.155 K. If 0.75g, of same acid

requires 15 mL of N/5 NaOH solution for complete neutralization then %, degree of ionization of acid is (K f of H2O = 1.86 K kg mol

–1) :

(A) 20% (B) 25% (C) 40% (D) 50%


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38. Consider following solutions :

0.1 m C6H5 3NH Cl ; 0.1m KCl; 0.1 m Glucose ; 0.1 m Na2C2O4. 10 H2O

(A) the solution with highest boiling point is 0.1 m Na2C2O4. 10H2O (B) the solution with highest freezing point is 0.1 m glucose

(C) 0.1 m 6 5 3C H NH Cl and 0.1 m NaCl will have the same osmotic pressure

(D) 0.1 m glucose solution will have the lowest osmotic pressure










39.

Column – I Column – II

(A) Benzene + Toluene (p) Non – ideal solution

(B) Ethanol + Water (q) Ideal solution

(C) Benzene + Chloroform (r) Hmix > 0

(D) CCl4 + CHCl3 (s) Hmixing = 0


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40.

Column – I Column – II

(A) 0.1 M Ca3(PO4)2 (p) Solution with highest boiling point

(B) 0.1 M NaCl (q) Solution with Van’t Hoff factor greater than one

(C) 0.1 M glucose (r) Solution with lowest osmotic pressure

(D) 0.1 M CaCl2 (s) Solution with lowest freezing point

PART III: MATHEMATICS SECTION 1 (Maximum Marks: 32)





41. Let be the complex number 2 2

cos isin3 3

. Then the number of distinct complex numbers z satisfying

2

2

2

z 1

z 1

1 z

= 0 is equal to

42. If z is any complex numbers satisfying |z – 3 – 2i| 2, then the minimum value of |2z – 6 + 5i| is

43. Let = ei/3

, and a, b, c, x, y, z be non-zero complex numbers such that a + b + c = x; a + b + c2 = y; a +

b2 + c = z, then the value of

2 2 2

2 2 2

x y z

a b c

is

44. For any integer k, let k = k k

cos isin7 7

, where i = 1 , value of the expression

12

k 1 kk 1

3

4k 1 4k 2k 1

is


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45. The number of complex numbers z such that |z – 1| = |z + 1| = |z – i| is 46. If z1 and z2 are two non-zero complex numbers such that |z1 + z2| = |z1| + |z2|, then arg z1 – arg z2 is equal

to

47. If ( 1) is a cube root of unit and (1 + 2)n = (1 +

4)n, then the least positive value of n is

48. If z1, z2 and z3 are complex numbers such that |z1| = |z2| = |z3| = 1 2 2

1 1 11

z z z

, then

|z1 + z2 + z3| is equal to





49. If z1 = a + ib and z2 = c + id are complex numbers such that |z1| = |z2| = 1 and 1 2Re z z = 0, then the pair of

complex numbers 1 = a + ic and 2 = b + id satisfies

(A) |1| = 1 (B) |2| = 1 (C) 1 2Re 0 (D) 1 2 0

50. Let z1 and z2 be complex numbers such that z1 z2 and |z1| = |z2|. If z1 has positive real part and z2 has

negative imaginary part, then

1 2

1 2

z z

z z

may be

(A) zero (B) real and positive (C) real and negative (D) purely imaginary 51. Let z1 and z2 be two distinct complex numbers and let z = (1 – t)z1 + iz2 for some real number t with 0 < t <

1. If arg (w) denotes the principal argument of a nonzero complex number w, then (A) |z – z1| + |z – z2| = |z1 – z2| (B) (z – z1) = (z – z2)

(C) 1 1 1

2 1 2 1

z z z z

z z z z

= 0 (D) arg (z – z1) = arg (z2 – z1)


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52. Let , be real and z be a complex number. If z2 + z + = 0 has two distinct roots on the line Re (z) = 1,

then it is necessary that

(A) (1, ) (B) (0, 1) (C) (–1, 0) (D) || = 1

53. If ( 1) is a cube root of unity, and (1 + )7 = A + B. Then (A, B) equals

(A) (–1, 1) (B) (0, 1) (C) (1, 1) (D) (1, 0)

54. If z is a complex number of unit modulus and argument , then 1 z

arg1 z

equals

(A) – (B) 2

(C) (D) –

55. If z is a complex number such that |z| 2, then the minimum value of 1

z2

(A) is equal to 5

2 (B) lies in the interval (1, 2)

(C) is strictly greater than 5

2 (D) is strictly greater than

3

2 but less than

5

2

56. Let = 1 3

i2 2

. Then the value of the determinant 2 2

2 4

1 1 1

1 1

1

is

(A) 3 (B) 3 ( – 1) (C) 32 (D) 3 (1 – )

57. Let z = cos + i sin . Then the value of 15

2m 1

m 1

Im z

at = 2 is

(A) 1

sin2 (B)

1

3sin2 (C)

1

2sin2 (D)

1

4sin2

58. a, b, c are integers, not all simultaneously equal, and is cube root of unit ( 1), then minimum value of

|a + b + c2| is

(A) 0 (B) 1 (C) 3

2 (D)

1

2


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59. Match the statements given in Column I with the values given in Column II

Column I Column II

(A) If ˆ ˆ ˆ ˆ â j 3k,b j 3k and c 2 3k form a triangle, then

the internal angle of the triangle between a and b is

p.

6

(B) If

b2 2

a

f(x) 3x dx a b , then the value of f6

is q. 2

3

(C) The value of

5 /

e 7 / 6

sec x dxlog 3

is

r.

3

(D) The maximum value of

1Arg

1 z

for |z| = 1, z 1 is

given by

s.

t.

2


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60. Match the statements / expressions given in Column I with the values given in Column II

Column I Column II

(A) In R2, if the magnitude of the projection vertex of the vector

ˆ ˆ ˆ î j on 3i j is 3 and if = 2 3 , then possible

value(s) of || is (are)

p. 1

(B) Let a and b be real numbers such that the function f(x) = 2

2

3ax 2, x 1

bx a , x 1

is differentiable for all x R. Then

possible value(s) of a is (are)

q. 2

(C) Let 1 be a complex cube root of unity, If (3 – 3 + 22)4n + 3

+ (2 + 3 – 32)4n + 3

+ (–3 + 2 + 32)4n + 3

= 0, then possible value(s) of n is (are)

r. 3

(D) Let the harmonic mean of two positive real numbers a and b be 4. If q is a positive real number such that a, 5, q, b is an arithmetic progression, then the value(s) of |q – a| is (are)

s. 4

t. 5


RET–12


FIITJEE RET – 12

(2016 – 2018)(2ND

YEAR_CHAMPIONS)

IIT-2015 (P1) DATE: 20.11.2017

ANSWERS

PHYSICS

1. 3 2. 5 3. 7 4. 2 5. 3 6. 4 7. 4 8. 6 9. B 10. C,D 11. A,C,D 12. A,B,C,D

13. BONUS 14. A,D 15. B,C,D 16. B,C,D 17. B,D 18. A,B,C,D 19. A–s,B–p,C–s,D–q

20. A–r,B–s,C–q,D–q

CHEMISTRY

21. 3 22. 6 23. 5 24. 2

25. 4 26. 5 27. 2 28. 2

29. A 30. A, B, C, D 31. A, C 32. A, B, C

33. A, B, D 34. A, B 35. B, C 36. A, C, D

37. BONUS 38. BONUS

39. A q, s ; B p, r ; C p ; D p,r

40. A p, q, s ; B q ; C r ; D q

MATHEMATICS

41. 1 42. 5 43. BONUS 44. 4

45. 1 46. 0 47. 3 48. 1

49. ABC 50. AD 51. BONUS 52. A

53. C 54. C 55. B 56. B

57. D 58. B 59. A BONUS; B p; C BONUS; D t

60. A p,q ; B p,q ; C p,q,s,t ; D q,t

Documents

(2016 2018)(2ND YEAR CHAMPIONS) - FIITJEE … (2ND YEAR...RET–12 FIITJEE (Hyderabad Classes) Limited., 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad–500 063. Phone: 040-66777000-03