FIITJEE RET – 6

RET–6

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

FIITJEE RET – 6

(2018 – 2020)(2ND

YEAR_REGULAR)

IIT-2014 (P1)_SET–A DATE: 13.08.2019

Time: 3 hours Maximum Marks: 180

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

9. Section II contains 10 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).

D. Marking Scheme

10. For each question in Section I, you will be awarded 3 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.

11. For each question in Section II, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer ONLY. In all other cases zero (0) marks will be awarded. No negative 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.:

RET–6


PAPER–I

PART I: PHYSICS SECTION – I: (One or more than one options are correct)

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

1. A thin flexible wire of length L is connected to two

adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of circle. The tension in the wire is

(A) IBL (B) IBL

(C) IBL

2 (D)

IBL

4

2. A conducting fluid of mass density m and

electrical resistivity e is kept in an insulating

vessels of dimensions b h . The vessel is

placed on a horizontal floor where a uniform horizontal magnetic field of induction B is

established perpendicular to the face h as shown in the figure. How much potential difference V must be applied on the liquid between the side faces designated by

dimensions b h so that the fluid pressure at the

bottom of the vessel vanishes ? The acceleration of free fall is g.

(A) m egVB

(B) m egV

B

(C) m egVB

(D) can not be determined

Space for rough work

RET–6


3. As shown in the figure, four identical loops are placed in a uniform magnetic field B. The loops carry

equal current i. n̂ denotes the normal to the plane of each loop. Potential energies in descending order are

I II III IV

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

4. A hard insulated conducting wire is bent into

shape of a five – pointed star like planar structure and carries current I. On the left

and on the right side of the line 1 2A A ,

uniform magnetic fields each of induction B exists in direction perpendicularly into and perpendicularly out of the plane of the star respectively. If length of a side of a unit cell of the grid shown is , find force of interaction between the current and the magnetic field.

(A) 16IB towards the right (B)16IB towards the left

(C) 8IB towards the left (D) 8IB towards the right


RET–6


5. On a frictionless horizontal tabletop is held at rest a rigid square loop of side length carrying an electric current. A uniform magnetic field pointing upwards to the left of the dashed line as shown in the figure is switched on and then the loop is released.

Considering different length of the side segments x and y (x<y) shown in the figure, which of the following conclusion can you make ?

(A) If x2

and y ,2

the loop starts rotating anticlockwise

(B) If x2

and y ,2


(C) If x2

and y ,2


(D) If x2

and y ,2

more information is required to decide which way the loop stats rotating.

6. A charged particle is fired at an angle (neither 0 nor 180) to a uniform magnetic field directed along the x–axis. During its motion along a helical path, the particle will

(A) never move parallel to the x–axis

(B) move parallel to the x–axis once during every rotation for all values of

(C) move parallel to the x–axis at least once during every rotation if = 45 (D) never move perpendicular to the x–direction 7. Four particles are projected from a point with equal speeds in an

inward magnetic field. The paths of the particles are shown. Then: (A) the particle 2 is neutral (B) the particles 1 and 4 are positive (C) the particle 3 is negative (D) the specific charge of the particle 1 is more than that of particle 3

and specific charge of particle 3 is greater than that of the particle 2.


RET–6


8. If in a region, a uniform magnetic field and a uniform electric field, both exist, a charged particle moving in this region:

(A) Cannot trace a circular path (B) May trace a circular path. (C) May trace a straight line path (D) Cannot move in the region with constant velocity 9. Suppose a uniform electric field and a uniform magnetic field exist along mutually perpendicular direction in

a gravity free space. If a charged particle is released from rest, at a point in the space: (A) particle can not remain in static equilibrium (B) first particle will move along a curved path but after some time its velocity will become constant (C) particle will come to rest at regular interval of time (D) acceleration of the particle will never become equal to zero

10. A proton is fired from origin with velocity 0 0ˆ ˆv v j v k in a uniform magnetic field 0

ˆB B j . IN the

subsequent motion of the proton; choose INCORRECT statements: (A) its z co-ordinate can never be negative (B) its x co-ordinate can never be positive (C) its x and z co-ordinates cannot be zero at the same time after it is fired

(D) its y co-ordinate will be proportional to its time of motion

SECTION – II: (Integer value type)

This section contains 10 questions. The answer to each of the questions is a single digit integer, ranging from 0

to 9 (both inclusive).

11. Consider a wireframe shown in figure. Equal currents I flow

through all the three branches of the wire frame. The frame is a combination of two semicircles CAD and CED of radius a. It is placed in uniform magnetic filed B acting perpendicular to the plane of frame. The magnitude of magnetic force acting on the frame is nBIa, then n is?


RET–6


12. An -particle and a proton having same kinetic energy enters in uniform magnetic field perpendicularly.

Let X be the ratio of their magnitude of acceleration and Y the ratio of their time periods respectively. Then value of 2XY is _____

13. A beam of protons with a velocity 54 10 m/ s enters a uniform magnetic field of 0.3 tesla at an angle 060

to the magnetic field. If the radius of the helical path taken by the proton beam is given by 33n 10 m ,

then n is

14. A uniform magnetic field 0ˆB B j exists in space. A particle of mass m and charge ‘+q’ is projected towards

negative x-axis with speed v from a point (d, 0, 0). The maximum value of v for which the particle does not

hit the y-z plane is2Bqd

km, where k is a constant. Find the value of k.

15. A charge 4 C enters in a region of uniform magnetic field with a velocity ˆ ˆ4i 7j m/ s experiences a force

ˆ ˆ5i Cj N. Find the value of 7C

5.

16. A rod AB of mass m and length is placed

on two smooth rails P and Q in a uniform magnetic induction B as shown in fig. The rails are connected to a current source supplying a constant current I. If the speed attained by rod AB when it leaves off the other end of rails of length L. is given by

0K BI LV

2m then 0K is


RET–6


17. A rectangular loop of wire ABCD is oriented

with the left corner at the origin, one edge along X – axis and the other edge along Y –axis as shown in the fig. A magnetic field exist in space in direction perpendicular to the XY plane as shown and has a magnitude that is given as B = y where is a

constant. If the total magnetic force on the loop if it carries current I is given by

20F K ia . Then 0K is

18. Shows a long straight current carrying wire

with a current 1I and a thin strip of width b

and length placed parallel to it with a

current 2I as shown in figure. If the magnetic

force of interaction between current 1 2I and I

is given by 0 1 22

1

I I rn N

N b b

then 1 2N N

is _____

19. A square cardboard of side and mass m is

suspended from a horizontal axis XY as shown in figure. A single wire is wound along the periphery of board and carrying a clockwise current I. At t= 0, a vertical downward magnetic field of induction B is switched on. If the minimum magnitude of B so that the board will be able to rotate upto

horizontal level is 0N mg

2I then 0N is


RET–6


20. An electron moves through a uniform magnetic field given by x xˆ ˆB B i 3B j T. At a particular instant, the

electron has the velocity ˆ ˆv 2.0i 4.0j m/ s and magnetic force acting on it is 19 ˆ6.4 10 N k . Find xB

PART II: CHEMISTRY SECTION – I: (One or more than one options are correct)


21. A set of five amines are given (I – V)

NH

I

NHNo2

II

NCH3 CH3

NO2

III

NH CH3

IV Examine the following and identify the correct statements. (A) Between I & II, the stronger base is I. (B) The weakest base among those listed is II and the strongest is IV. (C) III is a weaker base than 4–nitroaniline. (D) II is a weaker base because of more electron withdrawing and base weakening effect. 22. Four statements relating to nitrogenous compounds are given below. Choose the correct statements.

(A) Allyl isocyanide contains nine –bonds and three –bonds (B) Methyl isocyanide on reduction with LiAlH4 gives ethylamine. (C) m–Dinitrobenzene on reduction with NH4HS gives m–nitro aniline. (D) Acetaloxime on reaction with P2O5 gives acetonitrile.


RET–6


23. 2 20

Br /H O2

O CPh NH A

. Then A is

(A)

NH2

BrBr

Br

(B)

NH2

Br

(C)

NH2

Br

(D) Both b & c

24. alc.KOH

3 2A CHCl R NC 3KCl 3H O . ‘A’ is

(A)

NH2

(B)

CH2 NH2

(C) CH3 C

CH3

NH2

CH3

(D) CH3 N

H

CH3

25. NHhydrolysis NaOH3

Br2A B C D E

H OKolbes 2

Synthesis excessn butane I H

‘E’ undergoes Gabriel pthalimide synthesis. (A) I = CH3–CH2–CN (B) D = CH3–CH2–CONH2

(C) H = CH3–CH2–CN (D) C is an alcohol


RET–6


26. NH P ONaNO KMnOSn HCl 3 2 52 4A B C D E

CHClLIAlH 343 2 2alc.NaOH

F G CH CH CH NC

(A) C = CH3–CH2–CHO (B) ‘E’ undergoes Hoffmann rearrangement (C) F = CH3–CH2–CN (D) D = CH3–CH2–COOH 27. Correct reactions among the following are

(A)

N2

+ Cl Cl

CuCl

HCl

(B)

N2

+ Cl Br

Cu

HBr

(C)

N2

+ Cl

H2O

(D)

N2

+ Cl

HO N NPhenol

28.

CO NH2

NaOBrA

CF3COOOHB

Correct statement are (A) ‘A’ doesn’t give friedal craft’s alkylation (B) ‘A’ Undergoes friedal craft’s acylation (C) ‘A’ undergoes friedal craft’s alkylation very easily (D) ‘B’ on reduction gives A


RET–6


29.

R-XAgCN

A

NaCN

B Correct statements regarding A & B is (A) both are functional isomers (B) at high ‘T’ they are interconvertable (C) on hydrolysis both gives same product (D) on LAH both gives same product 30.

NH2

CH3COClA

(i) Br2/Cs2

(ii) H2O/H+

Major product. Then major product is

(A)

NH2

Br

(B)

NH2

Br

(C) Both a & b (D)

NH2

Br

Br


RET–6


SECTION – II: (Integer value type) This section contains 10 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9 (both inclusive).

31. How many of the following can be prepared by gabrial pthalimide synthesis

CH3NH2, CH3–CH2–NH2, Ph–NH2, PH–NH–Ph, N–3 butyl amine, CH3–NH–CH3, N, N, N Trimethyl amine. 32.

COOH

N3HA

HNO2 H+

H2OCB

B has how many bonds.

33.

N2Cl

Ph-OHproduct

Total no. of ‘’ bonds present in product is/are

34. How many primary amines are possible for the formula4 11C H N?

35. Consider the following sequence of reactions :

CONH2

P4O10A

MeMgBr, H3O+

BCa(OH)2, I2

C

D

compound containing 5 membered ring(s) The number of five membered ring(s) in the compound (D).is


RET–6


36. During the conversion of an amide to amine by using Hoffmann degradation number of base molecules used

37. Deamination (or) diazotization of n–butyl amine with NaNO2 / HCl given Isomeric butene. 38. Which of the following compound is more basic

1

NH2

2

NH2

3

OH

4

OH

5

CO NH2

39. How many of the below listed compounds on treatment with HNO2 would go for ring expansion?

CH2 NH2

,

NH2,

NH2

,

CH2 NH2,

NCH3CH3

,

CH2NH2

OH

H2C NH2

NH

CO NH2

, ,

,


RET–6


40.

NH

O

O

N K+

O

O

N R

O

O

RX/DMF Ethanolreflux

KOHRNH2

Out of the given amines, how many cannot be prepare by this method

1) CH3CH2NH2 2) CH3NHCH3 3) 2 2 CH CH NH 4)

NH2

5)

NH2

6)

CH2NH2

7)

CONH2

8)

NHCH3

PART III: MATHEMATICS SECTION – I: (One or more than one options are correct)


41. The shortest distance between the parabola y

2 = 4x and y

2 = 2x – 6 is

(A) 2 (B) 5 (C) 3 (D) none of these

42. The equation of the directrix of the parabola with vertex at the origin and having the axis along the x-axis

and a common tangent of slope 2 with the circle x2 + y

2 = 5 is/are

(A) x = 10 (B) x = 20 (C) x = –10 (D) x = –20


RET–6


43. Parabola y

2 = 4x and the circle having it’s centre at (6, 5) intersect at right angle. Possible point of

intersection of these curve can be

(A) (9, 6) (B) 2, 8 (C) (4, 4) (D) 3,2 3

44. The locus of the midpoint of the focal distance of a variable point moving on the parabola y

2 = 4ax is

parabola whose (A) latus rectum is half the latus rectum of the original parabola

(B) vertex is a

,02

(C) directrix is y-axis

(D) focus has coordinates (a, 0)

45. Tangent is drawn at any point (x1, y1) other than the vertex on the parabola y

2 = 4ax. If tangents are drawn

from any point on this tangent to the circle x2 + y

2 = a

2 such that all the chords of contact pass through a

fixed point (x2, y2) then

(A) x1, a, x2 are in GP (B) 1y

2, a, y2 are in GP (C) 1 1

2 2

y x4, ,

y x are in GP (D) x1x2 + y1y2 = a

2

46. Let PQ be a chord of the parabola y

2 = 4x. A circle drawn with PQ as a diameter passes through the vertex

V of the parabola. If area of PVQ = 20 sq. unit, then coordinates of P are (A) (–16, –8) (B) (–16, 8) (C) (16, –8) (D) (16, 8) 47. The normal y = mx – 2am – am

3 to the parabola y

2 = 4ax subtends a right angle at the vertex if

(A) m = 1 (B) m = 2 (C) m = – 2 (D) m = 1

2

48. AB is a double ordinate of the parabola y2 = 4ax. Tangents drawn to the parabola at A and B meet the y-

axis at A1 and B1, respectively. If the area of trapezium AA1B1B is equal to 12a2, then the angle subtended

by A1B1 at the focus of the parabola is equal to (A) 2 tan

–1(3) (B) tan

–1 (3) (C) 2 tan

–1 (2) (D) tan

–1 (2)


RET–6


49. Three normals drawn from the point (7, 14) to the parabola x

2 – 8x – 16y = 0. The coordinates of the feet of

the normals are (A) (0, 0) (B) (5, 3) (C) (–4, 3) (D) (16, 8)

50. If y = 2x – 3 is a tangent to the parabola y2 =

14a x

3

, then a is equal to

(A) 0 (B) –1 (C) 14

3 (D)

14

3

SECTION – II: (Integer value type) This section contains 10 questions. The answer to each of the questions is a single digit integer, ranging from 0


51. The point (a, 2a) is an interior point of the region bounded by the parabola y

2 = 16x and the double

ordinate through the focus. Then, the number of integral value of a is 52. Latus rectum of the parabola which has axis parallel to y-axis and which passes through points (0, 2), (–1,

0) and (1, 6) is

53. If on a given base BC [B(0, 0) and C(2, 0)], a triangle described such that the sum of the tangents of the

base angles is 4, then the equation of the locus of the opposite vertex A is a parabola whose directrix is y = k. The value of 8k – 9 is

54. If the circle (x – 6)

2 + y

2 = r

2 and the parabola y

2 = 4x have maximum number of common chords, then the

least integral value of r is


RET–6


55. PN is an ordinate of the parabola y2 = 4ax. A straight line is drawn through the middle point M of PN

parallel to the axis meeting the parabola at Q. NQ meets the tangent at the vertex A, at a point T, then

AT9

NP

=

56. The straight line x + y = k, touches the parabola y = x – x

2, if k is

57. If P(t

2, 2t), t [0, 2], is an arbitrary point on the parabola y

2 = 4x, Q is the foot of perpendicular from focus

S on the tangent at P, then the maximum area of PQS is

58. Through the vertex A of the parabola 2 4y ax two chords AP and AQ are drawn, and the circles on AP

and AQ as diameters intersect in R. Prove that, if , , and be the angles made with the axis by the

tangents at P and Q and by AR, then cos cot 2 tan is

59. The equation of the line touching both the parabolas y

2 = 4x and x

2 = –32y is ax + by + c = 0. Then the

value of a + b + c is 60 Consider the locus of centre of the circle which touches the circle x

2 + y

2 = 4 and the line x = 4. The

distance of the vertex of the locus from the origin is


RET–6


FIITJEE RET – 6

(2018 – 2020)(2ND

YEAR_REGULAR)

IIT-2014 (P1)_SET–A DATE: 13.08.2019

ANSWERS

PHYSICS

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

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

9. A,C,D 10. A,B,C 11. 6 12. 1

13. Bonus 14. 2 15. Bonus 16. 4

17. 1 18. Bonus 19. 1 20. 2

CHEMISTRY

21. A, B, D 22. A, C, D 23. A 24. A, B, C

25. Bonus 26. ABCD or BCD 27. A, B, D 28. A, D

29. A, B 30. B 31. 2 32. 5 or 6

33. 7 34. 4 or 5 35. 2 36. 4

37. Bonus 38. 2 39. 3 40. 5

MATHEMATICS

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

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

49. A, B, D 50. A, C 51 3 52. 1

53. 8 54. 5 55. 6 56. 1

57. 5 58. 0 59. 3 60. 3

RET–6


FIITJEE RET – 6

(2018 – 2020)(2ND

YEAR_REGULAR)

IIT-2014 (P1)_SET–B DATE: 13.08.2019

Time: 3 hours Maximum Marks: 180

INSTRUCTIONS:

A. General

1. This booklet is your Question Paper containing 60 questions.

6. 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.

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

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

9. 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:

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

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

14. Section II contains 10 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).

D. Marking Scheme

15. For each question in Section I, you will be awarded 3 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.

16. For each question in Section II, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer ONLY. In all other cases zero (0) marks will be awarded. No negative 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.:

RET–6


PAPER–I

PART I: PHYSICS SECTION – I: (One or more than one options are correct)


1. A charged particle is fired at an angle (neither 0 nor 180) to a uniform magnetic field directed along the x–axis. During its motion along a helical path, the particle will

(A) never move parallel to the x–axis

(B) move parallel to the x–axis once during every rotation for all values of

(C) move parallel to the x–axis at least once during every rotation if = 45 (D) never move perpendicular to the x–direction 2. Four particles are projected from a point with equal speeds in an

inward magnetic field. The paths of the particles are shown. Then: (A) the particle 2 is neutral (B) the particles 1 and 4 are positive (C) the particle 3 is negative (D) the specific charge of the particle 1 is more than that of particle 3

and specific charge of particle 3 is greater than that of the particle 2. 3. If in a region, a uniform magnetic field and a uniform electric field, both exist, a charged particle moving in

this region: (A) Cannot trace a circular path (B) May trace a circular path. (C) May trace a straight line path (D) Cannot move in the region with constant velocity 4. Suppose a uniform electric field and a uniform magnetic field exist along mutually perpendicular direction in

a gravity free space. If a charged particle is released from rest, at a point in the space: (A) particle can not remain in static equilibrium (B) first particle will move along a curved path but after some time its velocity will become constant (C) particle will come to rest at regular interval of time (D) acceleration of the particle will never become equal to zero

5. A proton is fired from origin with velocity 0 0ˆ ˆv v j v k in a uniform magnetic field 0

ˆB B j . IN the

subsequent motion of the proton; choose INCORRECT statements: (A) its z co-ordinate can never be negative (B) its x co-ordinate can never be positive (C) its x and z co-ordinates cannot be zero at the same time after it is fired

(D) its y co-ordinate will be proportional to its time of motion


RET–6


6. A thin flexible wire of length L is connected to two

adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of circle. The tension in the wire is

(A) IBL (B) IBL

(C) IBL

2 (D)

IBL

4

7. A conducting fluid of mass density m and

electrical resistivity e is kept in an insulating

vessels of dimensions b h . The vessel is

placed on a horizontal floor where a uniform horizontal magnetic field of induction B is

established perpendicular to the face h as shown in the figure. How much potential difference V must be applied on the liquid between the side faces designated by

dimensions b h so that the fluid pressure at the

bottom of the vessel vanishes ? The acceleration of free fall is g.

(A) m egVB

(B) m egV

B

(C) m egVB

(D) can not be determined


RET–6


8. As shown in the figure, four identical loops are placed in a uniform magnetic field B. The loops carry

equal current i. n̂ denotes the normal to the plane of each loop. Potential energies in descending order are

I II III IV

(A) I, II, III, IV (B) IV, II, III, I (C) I, III, II, IV (D) IV, III, II, I 9. A hard insulated conducting wire is bent into

shape of a five – pointed star like planar structure and carries current I. On the left

and on the right side of the line 1 2A A ,

uniform magnetic fields each of induction B exists in direction perpendicularly into and perpendicularly out of the plane of the star respectively. If length of a side of a unit cell of the grid shown is , find force of interaction between the current and the magnetic field.

(A) 16IB towards the right (B)16IB towards the left

(C) 8IB towards the left (D) 8IB towards the right


RET–6


10. On a frictionless horizontal tabletop is held at rest a rigid square loop of side length carrying an electric current. A uniform magnetic field pointing upwards to the left of the dashed line as shown in the figure is switched on and then the loop is released.

Considering different length of the side segments x and y (x<y) shown in the figure, which of the following conclusion can you make ?

(A) If x2

and y ,2


(B) If x2

and y ,2


(C) If x2

and y ,2


(D) If x2

and y ,2

more information is required to decide which way the loop stats rotating.

SECTION – II: (Integer value type)

This section contains 10 questions. The answer to each of the questions is a single digit integer, ranging from 0


11. A rod AB of mass m and length is placed

on two smooth rails P and Q in a uniform magnetic induction B as shown in fig. The rails are connected to a current source supplying a constant current I. If the speed attained by rod AB when it leaves off the other end of rails of length L. is given by

0K BI LV

2m then 0K is


RET–6


12. A rectangular loop of wire ABCD is oriented

with the left corner at the origin, one edge along X – axis and the other edge along Y –axis as shown in the fig. A magnetic field exist in space in direction perpendicular to the XY plane as shown and has a magnitude that is given as B = y where is a

constant. If the total magnetic force on the loop if it carries current I is given by

20F K ia . Then 0K is

13. Shows a long straight current carrying wire

with a current 1I and a thin strip of width b

and length placed parallel to it with a

current 2I as shown in figure. If the magnetic

force of interaction between current 1 2I and I

is given by 0 1 22

1

I I rn N

N b b

then 1 2N N

is _____

14. A square cardboard of side and mass m is

suspended from a horizontal axis XY as shown in figure. A single wire is wound along the periphery of board and carrying a clockwise current I. At t= 0, a vertical downward magnetic field of induction B is switched on. If the minimum magnitude of B so that the board will be able to rotate upto

horizontal level is 0N mg

2I then 0N is


RET–6


15. An electron moves through a uniform magnetic field given by x xˆ ˆB B i 3B j T. At a particular instant, the

electron has the velocity ˆ ˆv 2.0i 4.0j m/ s and magnetic force acting on it is 19 ˆ6.4 10 N k . Find xB

16. Consider a wireframe shown in figure. Equal currents I flow

through all the three branches of the wire frame. The frame is a combination of two semicircles CAD and CED of radius a. It is placed in uniform magnetic filed B acting perpendicular to the plane of frame. The magnitude of magnetic force acting on the frame is nBIa, then n is?

17. An -particle and a proton having same kinetic energy enters in uniform magnetic field perpendicularly.

Let X be the ratio of their magnitude of acceleration and Y the ratio of their time periods respectively. Then value of 2XY is _____

18. A beam of protons with a velocity 54 10 m/ s enters a uniform magnetic field of 0.3 tesla at an angle 060

to the magnetic field. If the radius of the helical path taken by the proton beam is given by 33n 10 m ,

then n is

19. A uniform magnetic field 0ˆB B j exists in space. A particle of mass m and charge ‘+q’ is projected towards

negative x-axis with speed v from a point (d, 0, 0). The maximum value of v for which the particle does not

hit the y-z plane is2Bqd

km, where k is a constant. Find the value of k.

20. A charge 4 C enters in a region of uniform magnetic field with a velocity ˆ ˆ4i 7j m/ s experiences a force

ˆ ˆ5i Cj N. Find the value of 7C

5.


RET–6


PART II: CHEMISTRY SECTION – I: (One or more than one options are correct)


21. NH P ONaNO KMnOSn HCl 3 2 52 4A B C D E

CHClLIAlH 343 2 2alc.NaOH

F G CH CH CH NC

(A) C = CH3–CH2–CHO (B) ‘E’ undergoes Hoffmann rearrangement (C) F = CH3–CH2–CN (D) D = CH3–CH2–COOH 22. Correct reactions among the following are

(A)

N2

+ Cl Cl

CuCl

HCl

(B)

N2

+ Cl Br

Cu

HBr

(C)

N2

+ Cl

H2O

(D)

N2

+ Cl

HO N NPhenol


RET–6


23.

CO NH2

NaOBrA

CF3COOOHB

Correct statement are (A) ‘A’ doesn’t give friedal craft’s alkylation (B) ‘A’ Undergoes friedal craft’s acylation (C) ‘A’ undergoes friedal craft’s alkylation very easily (D) ‘B’ on reduction gives A 24.

R-XAgCN

A

NaCN

B Correct statements regarding A & B is (A) both are functional isomers (B) at high ‘T’ they are interconvertable (C) on hydrolysis both gives same product (D) on LAH both gives same product


RET–6


25.

NH2

CH3COClA

(i) Br2/Cs2

(ii) H2O/H+

Major product. Then major product is

(A)

NH2

Br

(B)

NH2

Br

(C) Both a & b (D)

NH2

Br

Br 26. A set of five amines are given (I – V)

NH

I

NHNo2

II

NCH3 CH3

NO2

III

NH CH3

IV Examine the following and identify the correct statements. (A) Between I & II, the stronger base is I. (B) The weakest base among those listed is II and the strongest is IV. (C) III is a weaker base than 4–nitroaniline. (D) II is a weaker base because of more electron withdrawing and base weakening effect.


RET–6


27. Four statements relating to nitrogenous compounds are given below. Choose the correct statements.

(A) Allyl isocyanide contains nine –bonds and three –bonds (B) Methyl isocyanide on reduction with LiAlH4 gives ethylamine. (C) m–Dinitrobenzene on reduction with NH4HS gives m–nitro aniline. (D) Acetaloxime on reaction with P2O5 gives acetonitrile.

28. 2 20

Br /H O2

O CPh NH A

. Then A is

(A)

NH2

BrBr

Br

(B)

NH2

Br

(C)

NH2

Br

(D) Both b & c

29. alc.KOH

3 2A CHCl R NC 3KCl 3H O . ‘A’ is

(A)

NH2

(B)

CH2 NH2

(C) CH3 C

CH3

NH2

CH3

(D) CH3 N

H

CH3


RET–6


30. NHhydrolysis NaOH3

Br2A B C D E

H OKolbes 2

Synthesis excessn butane I H

‘E’ undergoes Gabriel pthalimide synthesis. (A) I = CH3–CH2–CN (B) D = CH3–CH2–CONH2

(C) H = CH3–CH2–CN (D) C is an alcohol



31. During the conversion of an amide to amine by using Hoffmann degradation number of base molecules

used 32. Deamination (or) diazotization of n–butyl amine with NaNO2 / HCl given Isomeric butene. 33. Which of the following compound is more basic

1

NH2

2

NH2

3

OH

4

OH

5

CO NH2


RET–6


34. How many of the below listed compounds on treatment with HNO2 would go for ring expansion?

CH2 NH2

,

NH2,

NH2

,

CH2 NH2,

NCH3CH3

,

CH2NH2

OH

H2C NH2

NH

CO NH2

, ,

,

35.

NH

O

O

N K+

O

O

N R

O

O

RX/DMF Ethanolreflux

KOHRNH2

Out of the given amines, how many cannot be prepare by this method

1) CH3CH2NH2 2) CH3NHCH3 3) 2 2 CH CH NH 4)

NH2

5)

NH2

6)

CH2NH2

7)

CONH2

8)

NHCH3


RET–6


36. How many of the following can be prepared by gabrial pthalimide synthesis

CH3NH2, CH3–CH2–NH2, Ph–NH2, PH–NH–Ph, N–3 butyl amine, CH3–NH–CH3, N, N, N Trimethyl amine. 37.

COOH

N3HA

HNO2 H+

H2OCB

B has how many bonds.

38.

N2Cl

Ph-OHproduct

Total no. of ‘’ bonds present in product is/are

39. How many primary amines are possible for the formula4 11C H N?

40. Consider the following sequence of reactions :

CONH2

P4O10A

MeMgBr, H3O+

BCa(OH)2, I2

C

D

compound containing 5 membered ring(s) The number of five membered ring(s) in the compound (D).is


RET–6


PART III: MATHEMATICS SECTION – I: (One or more than one options are correct)


41. Let PQ be a chord of the parabola y

2 = 4x. A circle drawn with PQ as a diameter passes through the vertex

V of the parabola. If area of PVQ = 20 sq. unit, then coordinates of P are (A) (–16, –8) (B) (–16, 8) (C) (16, –8) (D) (16, 8) 42. The normal y = mx – 2am – am

3 to the parabola y

2 = 4ax subtends a right angle at the vertex if

(A) m = 1 (B) m = 2 (C) m = – 2 (D) m = 1

2

43. AB is a double ordinate of the parabola y

2 = 4ax. Tangents drawn to the parabola at A and B meet the y-

axis at A1 and B1, respectively. If the area of trapezium AA1B1B is equal to 12a2, then the angle subtended

by A1B1 at the focus of the parabola is equal to (A) 2 tan

–1(3) (B) tan

–1 (3) (C) 2 tan

–1 (2) (D) tan

–1 (2)

44. Three normals drawn from the point (7, 14) to the parabola x

2 – 8x – 16y = 0. The coordinates of the feet of

the normals are (A) (0, 0) (B) (5, 3) (C) (–4, 3) (D) (16, 8)

45. If y = 2x – 3 is a tangent to the parabola y2 =

14a x

3

, then a is equal to

(A) 0 (B) –1 (C) 14

3 (D)

14

3


RET–6


46. The shortest distance between the parabola y2 = 4x and y

2 = 2x – 6 is

(A) 2 (B) 5 (C) 3 (D) none of these

47. The equation of the directrix of the parabola with vertex at the origin and having the axis along the x-axis

and a common tangent of slope 2 with the circle x2 + y

2 = 5 is/are

(A) x = 10 (B) x = 20 (C) x = –10 (D) x = –20 48. Parabola y

2 = 4x and the circle having it’s centre at (6, 5) intersect at right angle. Possible point of

intersection of these curve can be

(A) (9, 6) (B) 2, 8 (C) (4, 4) (D) 3,2 3

49. The locus of the midpoint of the focal distance of a variable point moving on the parabola y

2 = 4ax is

parabola whose (A) latus rectum is half the latus rectum of the original parabola

(B) vertex is a

,02

(C) directrix is y-axis

(D) focus has coordinates (a, 0)

50. Tangent is drawn at any point (x1, y1) other than the vertex on the parabola y

2 = 4ax. If tangents are drawn

from any point on this tangent to the circle x2 + y

2 = a

2 such that all the chords of contact pass through a

fixed point (x2, y2) then

(A) x1, a, x2 are in GP (B) 1y

2, a, y2 are in GP (C) 1 1

2 2

y x4, ,

y x are in GP (D) x1x2 + y1y2 = a

2



51. The straight line x + y = k, touches the parabola y = x – x

2, if k is

52. If P(t

2, 2t), t [0, 2], is an arbitrary point on the parabola y

2 = 4x, Q is the foot of perpendicular from focus

S on the tangent at P, then the maximum area of PQS is


RET–6


53. Through the vertex A of the parabola 2 4y ax two chords AP and AQ are drawn, and the circles on AP

and AQ as diameters intersect in R. Prove that, if , , and be the angles made with the axis by the

tangents at P and Q and by AR, then cos cot 2 tan is

54. The equation of the line touching both the parabolas y

2 = 4x and x

2 = –32y is ax + by + c = 0. Then the

value of a + b + c is 55 Consider the locus of centre of the circle which touches the circle x

2 + y

2 = 4 and the line x = 4. The

distance of the vertex of the locus from the origin is 56. The point (a, 2a) is an interior point of the region bounded by the parabola y

2 = 16x and the double

ordinate through the focus. Then, the number of integral value of a is 57. Latus rectum of the parabola which has axis parallel to y-axis and which passes through points (0, 2), (–1,

0) and (1, 6) is

58. If on a given base BC [B(0, 0) and C(2, 0)], a triangle described such that the sum of the tangents of the

base angles is 4, then the equation of the locus of the opposite vertex A is a parabola whose directrix is y = k. The value of 8k – 9 is

59. If the circle (x – 6)

2 + y

2 = r

2 and the parabola y

2 = 4x have maximum number of common chords, then the

least integral value of r is

60. PN is an ordinate of the parabola y

2 = 4ax. A straight line is drawn through the middle point M of PN

parallel to the axis meeting the parabola at Q. NQ meets the tangent at the vertex A, at a point T, then

AT9

NP

=


RET–6


FIITJEE RET – 6

(2018 – 2020)(2ND

YEAR_REGULAR)

IIT-2014 (P1)_SET–B DATE: 13.08.2019

ANSWERS

PHYSICS

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

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

9. B 10. A,B,D 11. 4 12. 1

13. Bonus 14. 1 15. 2 16. 6

17. 1 18. Bonus 19. 2 20. Bonus

CHEMISTRY

21. ABCD or BCD 22. A, B, D 23. A, D 24. A, B

25. B 26. A, B, D 27. A, C, D 28. A

29. A, B, C 30. Bonus 31. 4 32. Bonus

33. 2 34. 3 35. 5 36. 2

37. 5 or 6 38. 7 39. 4 or 5 40. 2

MATHEMATICS

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

45. A, C 46. B 47. A, C 48. A, C

49. A, B, C, D 50. B, C, D 51. 1 52. 5

53. 0 54. 3 55. 3 56. 3

57. 1 58. 8 59. 5 60. 6

FIITJEE RET – 6

Documents

Transcript of FIITJEE RET – 6