JEE (Advanced) P-I

8/12/2019 JEE (Advanced) P-I

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1 Head Office: 5/5, Amer Complex, Opp. PNB, M.P. Nagar, Zone-II, Bhopal (M.P.) Ph. 0755-4074100 Web: www.heritageiita.com

MM : 240 JEE (Advanced) 2014 Time : 3 Hr.Topics covered :

Chemistry : Some Basic Concepts of Chemistry, Structure of Atom, Classification of Elements and

Periodicity in Properties, Chemical Bonding and Molecular Structure

Mathematics : Elementary Trigonometric Functions, Transformation Formulae, Trigonometric Equations,

Properties of Triangle, Sets, Relations and Functions (XI class syllabus)

Physics : Mathematical Tools (Graphs and Vectors), Units and Measurement, Kinematics

Instructions :

(i) The question paper consists of 3 parts (Chemistry, Mathematics and Physics). Each part has 6 sections.

(ii) Section I contains 6 multiple choice questions which have only one correct answer. Each question carries

+3 marks each for correct answer and1 mark for each wrong answer.

(iii) Section II contains 4 multiple choice questions which have one or more answers are correct. Each question

carries +4 marks each for correct answer. There are no negative marks in this section.

(iv) Section III contains 2 questions. Each question contains STATEMENT-1 (Assertion) and STATEMENT-2

(Reason).

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOTa correct explanation for Statement-1

(C) Statement-1 is True, Statement-2 is False

(D) Statement-1 is False, Statement-2 is True

Each question carries +3 marks each for correct answer and1 mark for each wrong answer.

(v) Section IV: This section contains one paragraph. Based upon this paragraph, 3 multiple choice questions have

to be answered. Each question has only one correct answer and carries +4 marks for correct answer and

1 mark for wrong answer.

(vi) Section V contains 2 questions. For each question, one choice of column-I matches with one or more than one

choice of column-II. For each question, you will be awarded 2 marks for each row in which you have darkened

the bubble(s) corresponding to the correct answer. Thus, each question in this section carries a maximum of

8 marks. There are no negative marks in this section.

(vii) Section VI: This section contains 3 questions. The answers to each of the questions is a single digit integer,

ranging from 0 to 9 without being given any option. Each question has only one correct answer and carries

+4 marks for correct answer. There are no negative marks in this section.

(viii) Rough work must not be done on the answer sheet and do not use white-fluid or any other rubbing material

on Answer Sheet.

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PART - I : CHEMISTRYSECTION - I

Single Correct Answer Type

This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, outof which ONLY ONE is correct.

1. When 100 ml of 0.1 M AgNO3is treated with 0.166 gm of KI, how much of AgI will be precipitated?

(A) 1.25 g (B) 0.578 g

(C) 0.235 g (D) 6.25 g

2. If velocity of electron moving in 2nd orbit of Bohr in He+is x, find the velocity of electron moving in 3rdorbit ofBohr in Li2+

(A) x (B) x/2

(C) 2x (D)2

3

x

3. In which of the following case bond strength has been increased?

(A) 2 2N N (B) 2 2O O

(C) 2 2O O

(D) CO CO4. Which is not true about ice?

(A) It has a cage like structure (B) It has less density than water

(C) Each O atom is surrounded by 4 H-atoms (D) Each O atom has 4-bonds around it

5. What is the bond order and magnetic behaviour of O2?

(A) 1.5 and paramagnetic (B) 1.5 and diamagnetic

(C) 2.5 and paramagnetic (D) 2 and paramagnetic

6. What is the separation energy for He+when the electron is present in its 1st excited state?

(A) 13.6 4 eV (B) 13.6 eV

(C) 3.4 eV (D) 1.5 eV

SECTION - II

Multip le Correct Answer Type

This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, outof which ONE OR MORE is/are correct.

7. Atomic number of an element is equal to

(A) Atomic weight divided by two (B) Electrical charge of the nucleus

(C) Number of protons in the atom (D) Weight of the nucleus

8. Magnitude of K.E. in an orbit is equal to

(A) Half of the potential energy (B) The total energy in the orbit

(C) Twice of the potential energy (D) Half of the total energy

9. Boric acid (H3BO3) is

(A) Tribasic (B) Dibasic

(C) Monobasic (D) Aprotic

10. The pairs having dissimilar geometry is/are

(A) BF3, NH3 (B) H2O, C2H2

(C) SO2, CO2 (D) NH3, PH3


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SECTION-V

Matrix-Match Type

This section contains 2 questions. Each question contains statements given in two columns which have to be matched.The statements in Column Iare labelled A, B, C and D, while the statements in Column IIare labelled p, q, r, s andt. Any given statement in Column Ican have correct matching with One OR More statement(s) in Column II. Theappropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the followingexample. If the correct matches are A-p, s and t; B-q and r; C-p and q; and D-s and t; then the correct darkening of

bubbles will look like the following.

A

B

C

D

p

p

p

p

q

q

q

q

r

r

r

r

s

s

s

s

p q r s

t

t

t

t

t

16. Match the following

Column I Column II(A) Fullerene (p) Lanthanoid

(B) Promethium (q) Actinide

(C) Lawrencium (r) Allotrope

(D) CO (s) Radioactive

(t) Neutral oxide


Column I Column II

Compounds Structure of compounds(A) (CH3)3B (p) Square planar

(B) NH4Cl (q) Trigonal bipyramidal

(C) [ICl4] (r) Tetrahedral

(D) PCl5 (s) Trigonal

(t) Square pyramidal

SECTION-VI

Integer Answer Type

This section contains 3 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. Theappropriate bubbles below the respective question numbers in the ORS have to be darkened. For example, if the correctanswers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of bubbles willlook like the following :

0

X

Y

Z 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9


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18. During reduction of KMnO4in acidic medium, the change in oxidation state for Mn is

19. The number of H-bonds per molecule of H2O is

20. How many of the following possess non-zero dipole moment?

Cl

,

Cl

,

Cl

OH

,

OH

OH

Cl

Cl

PART - II : MATHEMATICS

SECTION - I


This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer,out of which ONLY ONEis correct.

21. The general solution of the equation 3tan( 15) = tan(+ 15) is given by

(A) = n, n Z (B) ,4

n n Z

(C) ,8

n n Z

(D) ,3

n n Z

22. Let 0,2

and a= (sin)cosec, b= (sin)sin, c= (cosec)sin, d= (cosec)cosec. Then

(A) d> c> a> b (B) b> a> c> d

(C) d> c> b> a (D) d> a> b> c

23. The value of cosec 15 sec15 is

(A) 1 (B) 2

(C) 2 2 (D) 2 2

24. The domain of the function f(x) = log2(log1/2(log3(x))) is

(A) (1, 3) (B) [1, 3]

(C) (, 1)(3, ) (D) (3, )

25. The value of (b c) cot ( )cot ( )cot2 2 2

A B Cc a a b is equal to

(A) 0 (B) 1(C) abc (D) a+ b + c

26. STATEMENT-1: If f(x) = 2 lnxand g(x) = lnx2, then fand gare same functions.

STATEMENT-2: (1 + tan(262 )). (1 + tan( 217)) = 2.

STATEMENT-3: In a triangleABC, if4

sin5

A and11

sin12

B then angle Cis acute angle.

(A) F T F (B) T F F

(C) F T T (D) T F T


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SECTION - II

Multiple Correct Answer Type

This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer,out of which ONE OR MORE is/are correct.

27. Consider the equation sin2

sin3

x x

. If the equation has real solution(s), then

(A) The number of integral values of is 3

(B) The sum of integral values of is zero

(C) If is 3 , then 2 ,3

x n n Z

(D) If is 2, then 2 ,3

x n n Z

28. LetA0A1A2 An1be a regular polygon on nsides. Let be the distance of its centre from vertex A0, be the length of perpendicular from centre of the polygon to the side A0A1and a be the distance between A0andA1. The area of the polygon is

(A)

2

2sin2

nn

(B) 2 tannn

(C)2

cot4

na

n

(D) 2 tannn

29. Consider the function f(x) =2

2

1

3 2

x

x x

(A) The domain of fis R {2} (B) The domain of fis R {1, 2}

(C) The range of fis R {2, 1} (D) The range of fis R {1}

30. LetA= {a, b, c} and B= (p, q). Then

(A) The number of elements in cartesian productAB is 6(B) The number of non-empty subsets ofABis 63

(C) The number relations fromAto Bis 64

(D) The number of relations from BtoAis 64

SECTION - III

Reasoning Type

The section contains 2 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, outof which ONLY ONE is correct.

31. STATEMENT-1 : The general solution of the equationtan 6 tan 4

11 tan6 tan4

x x

x x

is given by ,2 8

nx n Z

.

and

STATEMENT-2 : The general solution of tanx= 1 is given by x= ,4

n

n Z.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1




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Column I Column II

(A) Let 2( ) 9 9 9f x x . The interval (p)7

, 111

lying in the domain of f, is

(B) Let1 2 | |

( ) sec 3

x

f x

. The interval (q) (5, 10)

lying in the domain of fis

(C)2

2

2

3

x xy

x x

. The value of ycan be (r) (10, 5)

(D)29

( )( 1)( 5)( 3)

xf x

x x x

The interval lying (s) (1, 1)

in the domain of fis

(t) [1, 3]

37. Match the followingColumn I Column II

(A) In a triangleA,BC, angle Cis double of the (p)12

sum of other two angles. If sin(C 2B) =

sin(C+ 2A) =1

2, then an angle of the

triangleABCcan be

(B) The value of xsatisfying the equation (q)4

cosecx+ cotx= 2 sinxcan be

(C) The fundamental period of the function (r)3

f(x) = sin2x sin4xis

(D) The value of xsatisfying (s)2

sin4x+ cos4x= sinx cosx is

(t)2

3

SECTION-VI

Integer Answer Type

This section contains 3 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. Theappropriate bubbles below the respective question numbers in the ORS have to be darkened. For example, if the correctanswers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of bubbles willlook like the following :

0

X

Y

Z 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9


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38. Let the maximum and minimum values of the function f() = 5sin+ 3cos 26

be Mand m. The value

of M+ mis____

39. In a tr iangle AB C, if the side AC is double that of the side AB , then the ratio

tan : tan : 2.2 2

B C B C

The value of is____

40. Let |sin| + |cos| = |sin|. The number of values of is [ , ] satisfying the given equation is____

PART - III : PHYSICS

SECTION - I


This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, outof which ONLY ONE is correct.

41. The dimensions ofa

bin the equation

2a tP

bx

where P is pressure, xis distance and tis time are

(A) [M2LT3] (B) [MT2]

(C) [ML3T1] (D) [LT3]

42. The horizontal range of a projectile is 4 3 times its maximum height. The angle of projection is

(A) 30 (B) 45

(C) 60 (D) 90

43. Which of the following graph shows decreasing slope?

(A)x

y

(B)x

y

(C) x

y

(D) x

y

44. A particle moves in xyplane. The position vector of particle at any time tis 2 {(2 ) (2 ) }mr t i t j

. The ratio

of change of at time t= 2 seconds (where is the angle which its velocity vector makes with positivex-axis) is

(A)2

rad/s17

(B)1

rad/s14

(C)4

rad/s7

(D)6

rad/s5


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45. A particle is moving inxyplane such that2

xy and v

x= 4 2t. The displacement versus time graph of the particle

would be

(A)

s

t

(B)

s

t

(C)

s

t(D)

s

t

46. A particle is moving in x-yplane. At certain instant of time, the components of its velocity and acceleration are asfollows v

x= 3 m/s, v

y= 4 m/s, a

x= 2 m/s2, a

y= 1 m/s2. The rate of change of speed at this moment is

(A) 210 m/s (B) 4 m/s2

(C) 25 m/s (D) 2 m/s2

SECTION - IIMultip le Correct Answer Type

This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out

of which ONE OR MORE is/are correct.

47. A particle is projected with a speed uat an angle with the horizontal acquires a velocity vwhen it is atan angle with the horizontal. Then

(A)cos

uv

(B) v= ucos

(C)cos

cos

uv

(D)cos

cos

uv

48. The motion of a body is given by 6 3dv

vdt

where vis the velocity (in m/s) at time t(in second). The body

is at rest at t= 0. Then

(A) The velocity of the body when its acceleration is zero is 2 m/s

(B) The initial acceleration of the body is 6 m/s2

(C) The velocity of body when the acceleration is half the initial value is 1 m/s

(D) The body has a uniform acceleration

49. Water is flowing in a river of width 36 m with a speed of 2 m/s. A person in a boat at a point Pon the bankof the river wants to cross the river by the shortest path to reach a point Qdirectly opposite on the other bank.If he can row his boat with a speed of 4 m/s in still water, he rows his boat at an angle of

(A) 30 upstream with the line PQ (B) 30 downstream with the line PQ

(C) tan1(0.5) upstream with the line PQ (D) tan1(2) downstream with the line PQ

50. If Ris the range of a projectile on a horizontal plane and hits maximum height for a given angle of projection,the maximum horizontal range with the same velocity of projection is

(A) 2 h (B)2

8

R

h

(C)2

28

hR

R (D)

2

28

Rh

h


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SECTION - III

Reasoning Type

This section contains 2 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, outof which ONLY ONE is correct.

51. STATEMENT-1 : In a uniform circular motion, the angle between acceleration vector and velocity vector is always2

.

and

STATEMENT-2 : In uniform circular motion, speed is constant.





52. The following figure shows path of two projectiles

R

2R

1 2

STATEMENT-1 : Both projectiles have same time of flight.

and

STATEMENT-2 : The second projectile has speed double that of first projectile.





SECTION-IV

Paragraph Type

This section contain 1 paragraph. Based upon this paragraph, 3 multiple choice questions have to be answered. Eachquestion has 4 choices (A), (B), (C) and (D) for i ts answer, out of which ONLY ONE is correct.

Paragraph for Question Nos. 53 to 55

The vertical displacement yof a projectile varies with the horizontal displacement xas

2y ax bx where aand bare constants

53. The trajectory of projectile is a

(A) Straight line (B) Circle

(C) Parabola (D) Hyperbola

54. The horizontal range of the projectile is

(A) a (B) b

(C)a

b(D)

a

b

55. The maximum height attained by the projectile is

(A)a

b(B)

2a

b

(C)2

a

b(D)

2

4

a

b


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SECTION-V

Matrix-Match Type

This section contains 2 questions. Each question contains statements given in two columns which have to be matched.

The statements in Column Iare labelled A, B, C and D, while the statements in Column IIare labelled p, q, r, s

and t.Any given statement in Column Ican have correct matching with One OR More statement(s) in Column II. The

appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following

example. If the correct matches are A-p, s and t; B-q and r; C-p and q; and D-s and t; then the correct darkening of

bubbles will look like the following.

A

B

C

D

p

p

p

p

q

q

q

q

r

r

r

r

s

s

s

s

p q r s

t

t

t

t

t

56. A ball is projected from ground. Take x-axis along horizontal and y-axis along verticle such that motion takesplace in x-yplane. Match the column

Column I Column II

(A)

t

(p) vyversus time graph

(B)

t

(q) xversus time graph

(C)

t

(r) yversus time graph

(D)

t

(s) Speed versus time graph

(t) Kinetic energy versus time graph


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57. A particle is moving along x-axis under a force such that its position-time graph is as shown

t

x

1

2

3

4

5 6

Column I Column II

(A) Particle is moving along positive x-direction (p) Between 5 and 6

with increasing speed

(B) Particle is moving along positive x-direction (q) Between 4 and 5

with decreasing speed

(C) Particle moves in negative x-direction with (r) Between 1 and 2

increasing speed

(D) Particle moves in negative x-direction with (s) Between 2 and 3

decreasing speed

(t) Between 3 and 4

SECTION-VI

Integer Answer Type

This section contains 3 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The

appropriate bubbles below the respective question numbers in the ORS have to be darkened. For example, if the correct

answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of bubbles will

look like the following :

0

X

Y

Z 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

58. A projectile attains maximum height of 1 m and 4 m for same range Rwithout changing the speed of projection.Find Rin metre.

59. Let1

a

and2

a

are two non-collinear unit vectors such that1 2

| | 3,a a

then the value of1 2 1 2

( ) (2 )a a a a

is1

x. Find x.

60. Heat is evolved in a resistance on passing current upto definite time. Measurements for current, time andresistances suffer error of 1%, 2%, 2%. The maximum % error in heat evolved will be x%. Find x.


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CHEMISTRY

1. (C)

2. (A)

3. (D)

4. (D)

5. (A)

6. (B)

7. (B, C)

8. (A, B)

9. (C, D)

10. (A, B, C)

11. (A)

12. (B)

13. (A)

14. (D)

15. (C)

16. A (r)

B (p, s)

C (q, s)

D (t)

17. A (s)

B (r)

C (p)

D (q)

18. (5)

19. (4)

20. (3)

MATHEMATICS

21. (B)

22. (C)

23. (D)

24. (A)

25. (A)

26. (C)

27. (A, B, C)

28. (A, B, C)

29. (B, C)30. (A, B, C, D)

31. (D)

32. (A)

33. (C)

34. (B)

35. (C)

36. A (p, s, t)

B (q, r)

C (p)

D (p, s)

37. A (p, q, t)

B (r)

C (s)

D (q)

38. (4)

39. (6)

40. (2)

PHYSICS

41. (B)

42. (A)

43. (A)

44. (A)

45. (C)

46. (D)

47. (D)

48. (A, B, C)

49. (A)

50. (D)

51. (C)

52. (C)

53. (C)

54. (D)

55. (C)

56. A (p)B (r)

C (q)

D (s, t)

57. A (r)

B (s, t)

C (q)

D (p)

58. (8)59. (2)

60. (6)

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