(2019 2021)(1ST YEAR REGULAR) - fiitjeehyderabad.com (1ST YEAR)_2015...FIITJEE RET – 1 (2019 –...

RET–1

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

FIITJEE RET – 1

(2019 – 2021)(1ST

YEAR_REGULAR)

IIT-2015 (P1)_SET–A DATE: 24.06.2019

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. Force is ˆ ˆ ˆ(6i j 2k)N displacement is ( ˆ ˆ î 2j 6k )m and work done is 6J , where value of = 6n is,

then n = ?

2. You are given vectors ˆ Â 5i 6.5j and ˆ ˆB 10i 7j . A third vector C lies in the x-y plane. Vector C is

perpendicular to vector A and the scalar product of C with B is 15. From this information, if the X-

component of C is (39/2x), then x is? 3. On a horizontal flat ground, a person is standing at a point A. At this point, he installs a 5 m long pole

vertically. Now, he moves 5 m towards east and then 2 m towards north and reaches at a point B. There he installs another 3 m long vertical pole. A bird flies from the top of the first pole to the top of the second

pole. If the magnitude of the displacement of the bird is 25 n then n?

4. A vector Q

which has a magnitude of 8 is added to the vector P

which lies along x-axis. The resultant of

two vectors lies along y-axis and has magnitude twice that of P. The magnitude of P

is 8

n, n= ?

5. Angle between the vectors ˆ î j and ˆ ˆj k is 2

n

, then n is?

6. If a and b are two units vectors such that a +2 b and 5 a -4 b are perpendicular to each other, then the

angle between a and b is2

n

, then n is?

7. The components of a vector along x and y-directions are A cos θ and A sin θ respectively. If the co-

ordinate system is rotated by 600 then the components are found to be equal to 3 and 4. Then the value of

A is?

8. The projection of a vector ˆ ˆ ˆr 3i j 2k on the Y–Z plane has magnitude given by 20

n. The value of n is

Space for rough work

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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. Which of the following is independent of the choice of co-ordinate system

(A) RQP

(B) iRQP xxx )̂(

(C) P Q R (D) Angle between P and Q

10. For Two vectors kjbiP ˆ2ˆˆ2 and kjiQ ˆˆˆ

(A) P parallel to Q if b =2 (B) P parallel to Q if b =-4

(C) P perpendicular to Q if b =-4 (D) P perpendicular to Q if b =2

11. A car travels 6 km towards north at an angle of 045 to

the east and then travels distance of 4 km towards north

at angle of 0135 to the east as shown in fig. Shortest

distance between initial and final points is.

(A) 32km (B) 1 32m (C) 52m (D) 52km


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12. A cube is placed so that one corner is at the origin and

three edges are along the x–,y–, and z–axes of a coordinate system fig.

The angle between the edge along the z–axis (line ab) and the diagonal from the origin to the opposite corner (line ad) is

(A) 1 1cos

3

(B) 1 1cos

5

(C) 1 1cos

3

(D) None

13. If ˆ ˆ Â 2i j k and ˆ ˆ ˆB i j k are two vectors, then the unit vector

(A) Perpendicular to A is ˆ ˆj k

2

(B) Parallel to A is ˆ ˆ ˆ2i j k

6

(C) Perpendicular to B is ˆ ˆj k

2

(D) Parallel to A is ˆ ˆ î j k

3

14. Given ˆ ˆ â 2i 3j 10k and ˆ ˆ ˆb 5i 2j 7k ,the unit vector which is perpendicular to both a and b is

(A) ˆ ˆ î 36 j 11k

1418

(B)

ˆ ˆ î 36 j 11k

1218

(C)

ˆ ˆ î 36 j 11k

1418

(D) none of the above


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15. If P and Q are two non-collinear vectors, then choose correct option(s):

(A) P Q vector is parallel to the direction of the cross product P Q

(B) P Q vector is perpendicular to the direction of the cross product P Q

(C) If P can be expressed as ˆ âi bj and Q as ˆ ˆci dj , where a,b,c and d are non-zero integers, and

ˆP Q cj is possible (c is a non-zero integer)

(D) If P can be expressed as ˆ âi bj and Q as ˆ ˆci dj , where a,b,c and d are non-zero integers, and

ˆP Q cj is not possible (c is a non-zero integer)

16. Four forces acting on a particle keep it at rest. Then: (A) the forces must be coplanar. (B) The forces cannot be coplanar. (C) The forces may or may not be coplanar. (D) If three of these forces are coplanar, so must be the fourth.

17. If ,P Q R ,Q R P and ,R P Q then

(A) ,P Q and ,R are coplanar (B)angle between ,P and Q may be less than 90º

(C) ( ) P Q R cannot be equal to zero (D) ,P Q and ,R are mutually perpendicular

18. Which of these is a unit vector

(A) 1 1ˆ î j3 3

(B) 1 1 1ˆ ˆ î j k3 3 3

(C) 1 1 1ˆ ˆ î j k2 2 2

(D) 1 1ˆ î j2 2


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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. Match the physical quantities given in Column I with dimensions expressed in terms of mass (M), length

(L), time (T), and charge (Q) given in Column II and write the correct answer against the matched quantity in a tabular from in your answer book.

Column – I Column – II

(A) Angular momentum (p) 2 2ML T

(B) Latent heat (q) 2 1ML T

(C) Torque (r) 3 1 2ML T Q

(D) Capacitance (s) 1 2 2 2M L T Q

(t) 2 2L T


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20. Match the following :

ˆ ˆ ˆ ˆ ˆ ˆA 3i 12j 4k, B 2i j 2k


(A) Projection of B on A (p) 26

3

(B) Projection of A on B (q) 2

(C) Component of B perpendicular A (r) ˆ ˆ ˆ25i 82j 16k

9

(D) Component of A perpendicular B (s) ˆ ˆ ˆ40i 22j 36k

13

(t) None of these

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





21. The radius of the nucleus (in fermi) whose mass number is equal to 27.

22. The ratio of energies of two radiations one with = 1250 0

A and other with = 5000 0

A .

23. The frequency of radiation of wavelength 600 nm is 14 1x 10 s . Then x is

24. Maximum of photons of light of = 4000 0

A . Which provide 2J energy is equal to 18x 10 . Then x is

25. Energy required to stop the ejection of electrons from Cu-plate 0.27 eV. Calculate the work function (in eV)

When radiation of 235nm strikes the plate.


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26. The difference between the energy gap of the “ground state & 2nd

excited state” and the “ground state & 1st

excited state” is equal to: 27. If in Bohr’s model for an unielectronic species, the time period of revolution is represented as Tn,Z where n

represents the shell number and Z represents the atomic number, then if the value of T2,1:T1,2 is represented as x : 1 then what is the value of x/4

28. The work function () of some metals is listed below. The number of metals which will show photoelectric effect when light of 300 nm wavelength falls on the metal is:

Metal Li Na K Mg Cu Ag Fe Pt W

in eV 2.4 2.3 2.2 3.7 4.8 4.3 4.7 6.3 4.75





29. 3115P has

(A) 31 nucleons (B) 15 protons (C) 16 neutrons (D) 1 Isotopic number

30. An isotone of 7632Ge is

(A) 7732Ge (B) 77

33 As (C) 7734Se (D) 78

34Se

31. Which of the following statement is/are correct. (A) In hydrogen atom, energy of first excited state is –3.4 eV. Then, KE of same orbit of hydrogen atom is

+ 3.4 ev. (B) The work function for a metal is 4 eV. To emit a photo electron of zero velocity from the surface of the

metal, the wavelength of incident light should be 3100 A.

(C) The energy of electron at distance from nucleus is zero. (D) As ‘n’ value increases in hydrogen atom, the velocity of electron increases.


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32. Which of the following quantities is quantized (A) Energy of an electron (B) Orbit Angular Momentum (C) Radius of a n

th orbit (D) Velocity of an electron in a n

th orbit

33. Which of the following statements is/are true? (A) The ratio of the radii of the first three Bohr orbits in H-atom is in the ratio 1:8:27 (B) The ratio of Total Energy, Kinetic Energy & Potential Energy for an electron in any orbit of H-atom is

1:1:2 (C) If the frequency of the green light is 6 x 10

14 Hz, then it’s wavelength is 500 nm

(D) The neutron was discovered much later than the Bohr’s model 34. The electron in a H-atom might absorb which of the following values of energy for excitation? (A) 13.6 eV (B) 10.2 eV (C) 12.5 eV (D) 13.05 eV 35. For an alpha particle moving towards the gold nucleus, at the distance of closest approach (A) The potential energy becomes zero (B) The kinetic energy becomes zero (C) The total energy of alpha particle becomes zero (D) The total energy is greater than zero 36. The magnitude of photo electric current is not dependent on (A) frequency of incident photon (B) intensity of electromagnetic radiation (C) energy of incident photon (D) wavelength of incident photon 37. As an electron jumps from 4

th orbit to the 2

nd orbit in Be

3+ ion, its

(A) K.E. increases (B) speed increases (C) Frequency of revolution increases (D) angular momentum increases 38. Which of the following statement(s) is/are correct ? (A) The ratio of the radii of the first three Bohr orbits of hydrogen atom is 1 : 8 : 7.

(B) The ratio of magnitude of total energy : kinetic energy : potential energy for electron in any orbit of hydrogen atom is 1 : 1 : 2.

(C) The frequency of a green light is 6 x 104 Hz, then its wavelength is 500 nm.

(D) The ratio of de–Broglie wavelength of a H–atom. He–atom and CH4 – molecule moving with equal kinetic energy is 4 : 2 : 1.


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39.


(A) energy per molecule (p) h

(B) wave number (q) C/

(C) frequency (r) 1/

(D) energy of one quantum (s) h/Na

40.


(A) Rutherford (p) discovery of charge on electron

(B) Thomson (q) discovery of e/m of electron

(C) Millikan (r) discovery of nucleus

(D) Faraday (s) cathode ray tube experiment


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





41. The vertices of a triangle are (0, 3), (–3, 0) and (3, 0). The sum of the coordinates of the orthocenter is 42. Two vertices of a triangle are (3, –2) and (–2, 3) and its orthocenter is (–6, 1). If its third vertex is (a, b),

then a + b = 43. A point ‘A’ divides the join of P(–5, 1) and Q(3, 5) in the ratio k : 1. Then the integral value of k for which

the area of ABC, where B is (1, 5) and C is (7, –2), is equal to 2 units in magnitude is 44. The distance between the circumcentre and the orthocenter of the triangle whose vertices are (0, 0), (6, 8)

and (–4, 3) is L. Then the value of 2

5L is

45. If the area of the triangle formed by the points (2a, b), (a + b, 2b + a) and (2b, 2a) is 2 sq. units, then the

area of the triangle whose vertices are (a + b, a – b), (3b – a, b + 3a) and (3a – b, 3b – a) will be 46. In a triangle OAB, E is the mid point of OB and D is a point on AB such that AD : DB = 2 : 1. If OD and AE

intersects at P, if this ratio is a : b then a + b is

47. If G is the centroid of triangle ABC, then 2 2 2

2 2 2

AB BC CA

AG BG CG

48. If the points (–2, –5), (2, –2) and (8, a) are collinear, then the value of a is A/2 then A is


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49. A line segment is divided so that the lesser part is to the greater part is equal to the greater part is to the

whole. If R is the ratio of the lesser part to the greater part, then

(A) 2R R 1 0 (B) 2 1R R 2

(C)

2 1 1R R RR

1R R 2

(D) 2 1R R 1R R 2

50. The area of triangle ABC is 20cm

2. The coordinates of vertex A are (–5, 0) and those of B are

(3, 0). The vertex C lies on the line x – y = 2. The coordinates of C are (A) (5, 3) (B) (–3, –5) (C) (–5, –7) (D) (7, 5) 51. The ends of a diagonals of a square are (2, –3) and (–1, 1). Another vertex of the square can be

(A) 3 5

,2 2

(B) 5 1

,2 2

(C) 1 5

,2 2

(D) none of these

52. The orthocenter of the triangle with vertices 3 1 1 1

2, , ,2 2 2

and 1

2,2

is

(A) 3 3 3

,2 6

(B) 1

2,2

(C)

5 3 2,

4 4

(D) 1 1

,2 2

53. A, B, C are respectively the points (1, 2), (4, 2), (4, 5). If T1, T2 are the points of trisection of the line

segment AC and S1, S2 are the points of trisection of the line segment BC, the area of the quadrilateral T1 S1 S2 T2 is

(A) 1 (B) 3

2 (C) 2 (D)

5

2


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54. If (–6, –4), (3, 5), (–2, 1) are the vertices of a parallelogram, then remaining vertex can be (A) (0, –1) (B) (–1, 0) (C) (–11, –8) (D) (7, 10) 55. The points A (–4, –1), B (–2, –4), C (4, 0) and D (2, 3) are the vertices of a (A) parallelogram (B) rectangle (C) rhombus (D) square 56. Two consecutive vertices of a rectangle of area 10 unit

2 are (1, 3) and (–2, –1). Other two vertices are

(A) 3 21 18 1

, , ,5 5 5 5

(B) 3 21 11 2

, , ,5 5 5 5

(C) 2 11 13 9

, , ,5 5 5 5

(D) 13 9 18 1

, , ,5 5 5 5

57. ABC is an isosceles triangle. If the co-ordinates of the base are B (1, 3) and C (–2, 7). The co–ordinates

of vertex A can be

(A) (1, 6) (B) 1

, 52

(C) 5

, 66

(D) 1

7,8

58. If A (a, a), B (–a, –a) are two vertices of an equilateral triangle, then its third vertex is

(A) a 3 a 3

,2 2

(B) a 3,a 3 (C) a 3, a 3 (D) a 3, a 3











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59. Consider the triangle whose vertices are (0, 0), (5, 12) and (16, 12). Match the following

Column I Column II

(A) Centroid of the triangle p. 21 8

,2 3

(B) Circumcentre of the triangle q. (7, 9)

(C) Incentre of the triangle r. (0, 56/3)

(D) Orthocentre of the triangle s. (7, 8)

60. Match the following

Column I Column II

Collinear points Conditions

(A) (a, b + c), (b, c + a), (c, a + b) p. If ad + bc = 2cd

(B) (a, b), (c, d), (a + c, b – d) q. If 1 1

1a b

(C) (a, 0), (0, b), (1, 1) r. If a = 1/2 , –4/3

(D) (a, 2–2a), (–a + 1, 2a), (–4 –a, 6 –a) s. Always


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FIITJEE RET – 1

(2019 – 2021)(1ST

YEAR_REGULAR)

IIT-2015 (P1)_SET–A DATE: 24.06.2019

ANSWERS

PHYSICS

1. 1 2. 6 3. 8 4. 5

5. 6 6. 6 7. 5 8. 4

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

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

17. C,D 18. B,D 19. A-q;B-t;C-p;D-s

20. A-q;B-p;C-t;D-r

CHEMISTRY

21. 4 22. 4 23. 5 24. 4

25. 5 26. Bonus 27. 8 28. 4

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

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

37. A, B, C 38. B, D

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

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

MATHEMATICS

41. 3 42. 5 43. 7 44. 5 45. 8 46. 5 47. 3 48. 5 49. A, B, C, D 50. B, D 51. A, B 52. B 53. B 54. B, C, D 55. A, B 56. A, C 57. C, D 58. B, C

59. A s, B p, C q, D r

60. A s, B p, C q, D r

RET–1


FIITJEE RET – 1

(2019 – 2021)(1ST

YEAR_REGULAR)

IIT-2015 (P1)_SET–B DATE: 24.06.2019

Time: 3 hours Maximum Marks: 264

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:

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

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

16. 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.

17. 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

18. 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.

19. 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.

20. 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.:

RET–1


PAPER–I

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





1. Angle between the vectors ˆ î j and ˆ ˆj k is 2

n

, then n is?

2. If a and b are two units vectors such that a +2 b and 5 a -4 b are perpendicular to each other, then the

angle between a and b is2

n

, then n is?

3. The components of a vector along x and y-directions are A cos θ and A sin θ respectively. If the co-

ordinate system is rotated by 600 then the components are found to be equal to 3 and 4. Then the value of

A is?

4. The projection of a vector ˆ ˆ ˆr 3i j 2k on the Y–Z plane has magnitude given by 20

n. The value of n is

5. Force is ˆ ˆ ˆ(6i j 2k)N displacement is ( ˆ ˆ î 2j 6k )m and work done is 6J , where value of = 6n is,

then n = ?

6. You are given vectors ˆ Â 5i 6.5j and ˆ ˆB 10i 7j . A third vector C lies in the x-y plane. Vector C is

perpendicular to vector A and the scalar product of C with B is 15. From this information, if the X-

component of C is (39/2x), then x is? 7. On a horizontal flat ground, a person is standing at a point A. At this point, he installs a 5 m long pole

vertically. Now, he moves 5 m towards east and then 2 m towards north and reaches at a point B. There he installs another 3 m long vertical pole. A bird flies from the top of the first pole to the top of the second

pole. If the magnitude of the displacement of the bird is 25 n then n?

8. A vector Q

which has a magnitude of 8 is added to the vector P

which lies along x-axis. The resultant of

two vectors lies along y-axis and has magnitude twice that of P. The magnitude of P

is 8

n, n= ?


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9. Given ˆ ˆ â 2i 3j 10k and ˆ ˆ ˆb 5i 2j 7k ,the unit vector which is perpendicular to both a and b is

(A) ˆ ˆ î 36 j 11k

1418

(B)

ˆ ˆ î 36 j 11k

1218

(C)

ˆ ˆ î 36 j 11k

1418

(D) none of the above

10. If P and Q are two non-collinear vectors, then choose correct option(s):

(A) P Q vector is parallel to the direction of the cross product P Q

(B) P Q vector is perpendicular to the direction of the cross product P Q

(C) If P can be expressed as ˆ âi bj and Q as ˆ ˆci dj , where a,b,c and d are non-zero integers, and

ˆP Q cj is possible (c is a non-zero integer)

(D) If P can be expressed as ˆ âi bj and Q as ˆ ˆci dj , where a,b,c and d are non-zero integers, and

ˆP Q cj is not possible (c is a non-zero integer)

11. Four forces acting on a particle keep it at rest. Then: (A) the forces must be coplanar. (B) The forces cannot be coplanar. (C) The forces may or may not be coplanar. (D) If three of these forces are coplanar, so must be the fourth.

12. If ,P Q R ,Q R P and ,R P Q then

(A) ,P Q and ,R are coplanar (B)angle between ,P and Q may be less than 90º

(C) ( ) P Q R cannot be equal to zero (D) ,P Q and ,R are mutually perpendicular


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13. Which of these is a unit vector

(A) 1 1ˆ î j3 3

(B) 1 1 1ˆ ˆ î j k3 3 3

(C) 1 1 1ˆ ˆ î j k2 2 2

(D) 1 1ˆ î j2 2

14. Which of the following is independent of the choice of co-ordinate system

(A) RQP

(B) iRQP xxx )̂(

(C) P Q R (D) Angle between P and Q

15. For Two vectors kjbiP ˆ2ˆˆ2 and kjiQ ˆˆˆ

(A) P parallel to Q if b =2 (B) P parallel to Q if b =-4

(C) P perpendicular to Q if b =-4 (D) P perpendicular to Q if b =2

16. A car travels 6 km towards north at an angle of 045 to

the east and then travels distance of 4 km towards north

at angle of 0135 to the east as shown in fig. Shortest

distance between initial and final points is.

(A) 32km (B) 1 32m (C) 52m (D) 52km

17. A cube is placed so that one corner is at the origin and

three edges are along the x–,y–, and z–axes of a coordinate system fig.

The angle between the edge along the z–axis (line ab) and the diagonal from the origin to the opposite corner (line ad) is

(A) 1 1cos

3

(B) 1 1cos

5

(C) 1 1cos

3

(D) None


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18. If ˆ ˆ ˆA 2i j k and ˆ ˆ ˆB i j k are two vectors, then the unit vector

(A) Perpendicular to A is ˆ ˆj k

2

(B) Parallel to A is ˆ ˆ ˆ2i j k

6

(C) Perpendicular to B is ˆ ˆj k

2

(D) Parallel to A is ˆ ˆ ˆi j k

3











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19. Match the following :

ˆ ˆ ˆ ˆ ˆ ˆA 3i 12j 4k, B 2i j 2k


(A) Projection of B on A (p) 26

3

(B) Projection of A on B (q) 2

(C) Component of B perpendicular A (r) ˆ ˆ ˆ25i 82j 16k

9

(D) Component of A perpendicular B (s) ˆ ˆ ˆ40i 22j 36k

13

(t) None of these

20. Match the physical quantities given in Column I with dimensions expressed in terms of mass (M), length

(L), time (T), and charge (Q) given in Column II and write the correct answer against the matched quantity in a tabular from in your answer book.


(A) Angular momentum (p) 2 2ML T

(B) Latent heat (q) 2 1ML T

(C) Torque (r) 3 1 2ML T Q

(D) Capacitance (s) 1 2 2 2M L T Q

(t) 2 2L T


RET–1


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





21. Energy required to stop the ejection of electrons from Cu-plate 0.27 eV. Calculate the work function (in eV)

When radiation of 235nm strikes the plate.

22. The difference between the energy gap of the “ground state & 2

nd excited state” and the “ground state & 1

st

excited state” is equal to: 23. If in Bohr’s model for an unielectronic species, the time period of revolution is represented as Tn,Z where n

represents the shell number and Z represents the atomic number, then if the value of T2,1:T1,2 is represented as x : 1 then what is the value of x/4

24. The work function () of some metals is listed below. The number of metals which will show photoelectric effect when light of 300 nm wavelength falls on the metal is:

Metal Li Na K Mg Cu Ag Fe Pt W

in eV 2.4 2.3 2.2 3.7 4.8 4.3 4.7 6.3 4.75

25. The radius of the nucleus (in fermi) whose mass number is equal to 27.

26. The ratio of energies of two radiations one with = 1250 0

A and other with = 5000 0

A .

27. The frequency of radiation of wavelength 600 nm is 14 1x 10 s . Then x is

28. Maximum of photons of light of = 4000 0

A . Which provide 2J energy is equal to 18x 10 . Then x is


RET–1






29. The electron in a H-atom might absorb which of the following values of energy for excitation? (A) 13.6 eV (B) 10.2 eV (C) 12.5 eV (D) 13.05 eV 30. For an alpha particle moving towards the gold nucleus, at the distance of closest approach (A) The potential energy becomes zero (B) The kinetic energy becomes zero (C) The total energy of alpha particle becomes zero (D) The total energy is greater than zero 31. The magnitude of photo electric current is not dependent on (A) frequency of incident photon (B) intensity of electromagnetic radiation (C) energy of incident photon (D) wavelength of incident photon 32. As an electron jumps from 4

th orbit to the 2

nd orbit in Be

3+ ion, its

(A) K.E. increases (B) speed increases (C) Frequency of revolution increases (D) angular momentum increases 33. Which of the following statement(s) is/are correct ? (A) The ratio of the radii of the first three Bohr orbits of hydrogen atom is 1 : 8 : 7.

(B) The ratio of magnitude of total energy : kinetic energy : potential energy for electron in any orbit of hydrogen atom is 1 : 1 : 2.

(C) The frequency of a green light is 6 x 104 Hz, then its wavelength is 500 nm.

(D) The ratio of de–Broglie wavelength of a H–atom. He–atom and CH4 – molecule moving with equal kinetic energy is 4 : 2 : 1.

34. 3115P has

(A) 31 nucleons (B) 15 protons (C) 16 neutrons (D) 1 Isotopic number


RET–1


35. An isotone of 7632Ge is

(A) 7732Ge (B) 77

33 As (C) 7734Se (D) 78

34Se

36. Which of the following statement is/are correct. (A) In hydrogen atom, energy of first excited state is –3.4 eV. Then, KE of same orbit of hydrogen atom is

+ 3.4 ev. (B) The work function for a metal is 4 eV. To emit a photo electron of zero velocity from the surface of the

metal, the wavelength of incident light should be 3100 A.

(C) The energy of electron at distance from nucleus is zero. (D) As ‘n’ value increases in hydrogen atom, the velocity of electron increases. 37. Which of the following quantities is quantized (A) Energy of an electron (B) Orbit Angular Momentum (C) Radius of a n

th orbit (D) Velocity of an electron in a n

th orbit

38. Which of the following statements is/are true? (A) The ratio of the radii of the first three Bohr orbits in H-atom is in the ratio 1:8:27 (B) The ratio of Total Energy, Kinetic Energy & Potential Energy for an electron in any orbit of H-atom is

1:1:2 (C) If the frequency of the green light is 6 x 10

14 Hz, then it’s wavelength is 500 nm

(D) The neutron was discovered much later than the Bohr’s model











RET–1


39.


(A) Rutherford (p) discovery of charge on electron

(B) Thomson (q) discovery of e/m of electron

(C) Millikan (r) discovery of nucleus

(D) Faraday (s) cathode ray tube experiment

40.


(A) energy per molecule (p) h

(B) wave number (q) C/

(C) frequency (r) 1/

(D) energy of one quantum (s) h/Na

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





41. If the area of the triangle formed by the points (2a, b), (a + b, 2b + a) and (2b, 2a) is 2 sq. units, then the

area of the triangle whose vertices are (a + b, a – b), (3b – a, b + 3a) and (3a – b, 3b – a) will be 42. In a triangle OAB, E is the mid point of OB and D is a point on AB such that AD : DB = 2 : 1. If OD and AE

intersects at P, if this ratio is a : b then a + b is


RET–1


43. If G is the centroid of triangle ABC, then 2 2 2

2 2 2

AB BC CA

AG BG CG

44. If the points (–2, –5), (2, –2) and (8, a) are collinear, then the value of a is A/2 then A is 45. The vertices of a triangle are (0, 3), (–3, 0) and (3, 0). The sum of the coordinates of the orthocenter is 46. Two vertices of a triangle are (3, –2) and (–2, 3) and its orthocenter is (–6, 1). If its third vertex is (a, b),

then a + b = 47. A point ‘A’ divides the join of P(–5, 1) and Q(3, 5) in the ratio k : 1. Then the integral value of k for which

the area of ABC, where B is (1, 5) and C is (7, –2), is equal to 2 units in magnitude is 48. The distance between the circumcentre and the orthocenter of the triangle whose vertices are (0, 0), (6, 8)

and (–4, 3) is L. Then the value of 2

5L is

SECTION 2 (Maximum Marks: 40)

This section contains TEN questions.




49. If (–6, –4), (3, 5), (–2, 1) are the vertices of a parallelogram, then remaining vertex can be (A) (0, –1) (B) (–1, 0) (C) (–11, –8) (D) (7, 10) 50. The points A (–4, –1), B (–2, –4), C (4, 0) and D (2, 3) are the vertices of a (A) parallelogram (B) rectangle (C) rhombus (D) square


RET–1


51. Two consecutive vertices of a rectangle of area 10 unit2 are (1, 3) and (–2, –1). Other two vertices are

(A) 3 21 18 1

, , ,5 5 5 5

(B) 3 21 11 2

, , ,5 5 5 5

(C) 2 11 13 9

, , ,5 5 5 5

(D) 13 9 18 1

, , ,5 5 5 5

52. ABC is an isosceles triangle. If the co-ordinates of the base are B (1, 3) and C (–2, 7). The co–ordinates

of vertex A can be

(A) (1, 6) (B) 1

, 52

(C) 5

, 66

(D) 1

7,8

53. If A (a, a), B (–a, –a) are two vertices of an equilateral triangle, then its third vertex is

(A) a 3 a 3

,2 2

(B) a 3,a 3 (C) a 3, a 3 (D) a 3, a 3

54. A line segment is divided so that the lesser part is to the greater part is equal to the greater part is to the

whole. If R is the ratio of the lesser part to the greater part, then

(A) 2R R 1 0 (B) 2 1R R 2

(C)

2 1 1R R RR

1R R 2

(D) 2 1R R 1R R 2

55. The area of triangle ABC is 20cm

2. The coordinates of vertex A are (–5, 0) and those of B are

(3, 0). The vertex C lies on the line x – y = 2. The coordinates of C are (A) (5, 3) (B) (–3, –5) (C) (–5, –7) (D) (7, 5) 56. The ends of a diagonals of a square are (2, –3) and (–1, 1). Another vertex of the square can be

(A) 3 5

,2 2

(B) 5 1

,2 2

(C) 1 5

,2 2

(D) none of these


RET–1


57. The orthocenter of the triangle with vertices 3 1 1 1

2, , ,2 2 2

and 1

2,2

is

(A) 3 3 3

,2 6

(B) 1

2,2

(C)

5 3 2,

4 4

(D) 1 1

,2 2

58. A, B, C are respectively the points (1, 2), (4, 2), (4, 5). If T1, T2 are the points of trisection of the line

segment AC and S1, S2 are the points of trisection of the line segment BC, the area of the quadrilateral T1 S1 S2 T2 is

(A) 1 (B) 3

2 (C) 2 (D)

5

2











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59. Match the following

Column I Column II

Collinear points Conditions

(A) (a, b + c), (b, c + a), (c, a + b) p. If ad + bc = 2cd

(B) (a, b), (c, d), (a + c, b – d) q. If 1 1

1a b

(C) (a, 0), (0, b), (1, 1) r. If a = 1/2 , –4/3

(D) (a, 2–2a), (–a + 1, 2a), (–4 –a, 6 –a) s. Always

60. Consider the triangle whose vertices are (0, 0), (5, 12) and (16, 12). Match the following

Column I Column II

(A) Centroid of the triangle p. 21 8

,2 3

(B) Circumcentre of the triangle q. (7, 9)

(C) Incentre of the triangle r. (0, 56/3)

(D) Orthocentre of the triangle s. (7, 8)


RET–1


FIITJEE RET – 1

(2019 – 2021)(1ST

YEAR_REGULAR)

IIT-2015 (P1)_SET–B DATE: 24.06.2019

ANSWERS

PHYSICS

1. 6 2. 6 3. 5 4. 4

5. 1 6. 6 7. 8 8. 5

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

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

17. A 18. A,B,C

19. A-q;B-p;C-t;D-r

20. A-q;B-t;C-p;D-s

CHEMISTRY

21. 5 22. Bonus 23. 8 24. 4

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

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

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

37. A, B, C, D 38. C, D

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

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

MATHEMATICS

41. 8 42. 5 43. 3 44. 5

45. 3 46. 5 47. 7 48. 5

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

53. B, C 54. A, B, C, D 55. B, D 56. A, B

57. B 58. B

59. A s, B p, C q, D r

60. A s, B p, C q, D r

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