Jee (Advanced) P-III

8/12/2019 Jee (Advanced) P-III

http://slidepdf.com/reader/full/jee-advanced-p-iii 1/16

– 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 : Hydrogen, s-Block Elements, Some p-Block Elements (B, C), Organic Chemistry-(Some Basic

Principles and Techniques)

Mathematics : Probability (part-1) based on Permutation and Combination, Sequence and Series, Exponential

and Logarithmic Series, Straight lines, Circle.

Physics : Rigid Body Rotation, Gravitation, Properties of Bulk Matter

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 and –1 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 NOT a 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 and –1 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.

HA

Code-A3




PART - I : CHEMISTRY

SECTION - 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. Which of the following liberates oxygen gas on heating?

(A) BaSO4 (B) LiNO3

(C) NaOH (D) Both (A) & (B)

2. Which of the following structure of C3 –4 is least stable?

(A) C — C C — — — –3 –1

(B) C C

C –2

–1 –1

(C) C C C –2 –2

(D) All are equal

3. The silicate anion in the mineral kinoite is a chain of three SiO4, tetrahedra, that share corners with adjacent

tetrahedra. The charge on silicate anion is

(A) – 6 (B) – 4

(C) – 8 (D) – 2

4. Which of the following is most stable species?

(A) (B) C CH

(C) (D)

5. Which of the following molecule have (2 R, 3 Z) configuration?

(A) CH

CH3

CH

CH3C

H OH

(B) CCH3

HC

H

CH3C

HO H

(C) CCH3

HC

H

CH3C

H OH

(D) CH

CH3

CH

CH3C

HO H

6. Among the following the most acidic phenol is

(A)

OH

F

(B)

OH

CH3

(C)

OH

CN

(D)

OH

NH2




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, out

of which ONE OR MORE is/are correct.

7. In which of the following first species is less stable than second?

(A) ,

CH2

(B) ,

CH2

+

+

(C) ,

CH2

–

–

(D) ,

8. In which of the following the enol form is dominant over keto form?

(A)ON

H

(B)

O

O

(C)

O

O

(D)

O

9. The element(s), which is/are disproportionate with aq. NaOH, are

(A) P4

(B) Red P

(C) Cl2

(D) F2

10. Na2S

2O

3 is converted to Na

2S

4O

6 when it is treated with

(A) FeCl3

(B) AgNO3

(C) CuSO4

(D) I2

SECTION - III

Reasoning Type

The section contains 2 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out

of which ONLY ONE is correct.

11. STATEMENT-1 : All B atoms in borax are sp3 hybridised.

and

STATEMENT-2 : There is no B – B bond in borax.








12. STATEMENT-1 : Boron does not react with HCl.

and

STATEMENT-2 : Boron reacts with H2SO

4 to give H

3BO

3 and SO

2.





SECTION-IV

Paragraph Type

This section contain 1 paragraph. Based upon this paragraph 3 multiple choice questions have to be answered. Each

question has 4 choices (A), (B), (C) and (D) for i ts answer, out of which ONLY ONE is correct.

Paragraph for Question Nos. 13 to 15

Lithium ion has very high charge density therefore it gives mainly its oxide. Sodium ion has low charge density, it gives

mainly peroxide K, Rb and Cs ions give superoxide with O2 gas.

22

1 OO2 22

2 2O O 2O

13. O –2 ion is maximum polarised by

(A) Li+ (B) Na+

(C) Rb+ (D) K+

14. In hydrolysis, the alkali oxides, peroxides and superoxides act as

(A) Bronsted acid (B) Bronsted base

(C) Lewis acid (D) Lewis base

15. Which compound will liberate O2 gas with cold H2O?

(A) Na2O

2(B) KO

2

(C) Na2O (D) Cs

2O

2

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 I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and

t. Any given statement in Column I can 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




16. Match the following

Column I Column II

(A)

OH

NH2

1

2(p) 1st carbon

(B)

NO2

1

2 CHO

3

4(q) 2nd carbon

(C)

NO2

1

2

OH

3

4

(r) 3rd carbon

(D)

NH2

1

2

OH

3

4

(s) 4th carbon

(t) Reactant is more reactive than phenol towards SE

reaction


Column I Column II

(A) Diamond (p) sp3 hybridised carbon

(B) Fullerene (q) sp

2

hybridised carbon(C) -graphite (r) Good conduction of electricity

(D) -graphite (s) ABAB … type layer structure

(t) ABC ABC … type layer structure

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

18. The number of millilitres of ‘5.6 V’ H2O

2(aq.) solution that can be completely oxidised by using 1 mL 1 M KMnO

4

in acidic medium is

19. The moles of NaClO3 formed when 6 mole of Cl

2 gas is passed through conc. and hot NaOH is

20. The total number of types of monochloroderivatives formed by methylcyclohexane is (x + 2). The value of x is




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 ONE is correct.

21. A four digit number (x1 x

2 x

3 x

4) is selected at random. The probability that selected number be such that

x1 > x

2 > x

3 > x

4 is

(A)14

25(B)

5

108

(C)7

300(D)

7

100

22. If sum of n terms of an A.P. is n2 + 3n, then sum of square of each term of that A.P. is

(A)24

(2 9 13)3

nn n (B)

22(2 9 13)

3

nn n

(C)22

( 9 )3

nn n (D) 3 2

3 12n n 23. A line through the point A(– 2, 0) which makes an angle of 30° with the positive direction of x-axis is rotated

about A in anticlockwise direction through an angle 15°. Then equation of line in the new position is

(A) (2 3)( 2)y x (B) y = – x – 2

(C) (2 3)( 2)y x (D) y = x + 2

24. A circle of radius 2 lies in the first quadrant and touches both co-ordinate axes. The equation of circle with

centre at (10, 8) and touching above circle externally is

(A) x2 + y2 – 20x – 16y – 50 = 0 (B) x2 + y2 – 20x – 16y – 200 = 0

(C) x2 + y2 – 20x – 16y – 36 = 0 (D) x2 + y2 – 20x – 16y + 100 = 0

25. Tangents drawn from the point P(8, 6) to the circle x2 + y2 – 2x – 2y – 2 = 0 touch the circle at the points A and B.

The equation of circumcircle of the triangle PAB is

(A) x2 + y2 – 9x – 7y + 14 = 0 (B) x2 + y2 + 9x + 7y – 14 = 0

(C) x2 + y2 – 9x + 7y + 14 = 0 (D) x2 + y2 + 9x – 7y + 14 = 0

26. STATEMENT-1 : From point (0, 0) two tangents can be drawn to circle x2 + y2 – 6x – 8y + 16 = 0.

STATEMENT-2 : If a1, a

2, a

3,............,a

n are in A.P. then its reciprocal are in H.P.

STATEMENT-3 : Image of circle x2 + y2 – 6x + 8 = 0 with respect to line y = x is x2 + y2 – 6y + 8 = 0.

Identify the correct combination of true (T) and false (F) of the given three statements.

(A) TFT (B) TTT

(C) F F F (D) TFF

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. Equation of tangents drawn from (6, 0) to circle x2 + y2 – 10x – 10y + 49 = 0 are

(A) x – y = 6 (B) 12x – 5y = 72

(C) 12x + 5y = 72 (D) x = 6




28. Let L1 be a straight line passing through the origin and L

2 be the straight line x + y = 4. If the intercepts made

by the circle x2 + y2 – 4x – 6y – 3 = 0 on L1 and L

2 are equal and if m

1, m

2 be slopes of possible equation

of L1 then

(A) 1 224

7m m (B) 1 2

12

7m m

(C) 1 217

7m m (D) 1 2

11

7m m

29. If x + y = 15, x, y > 0 then

(A) Maximum value of xy2 is 500 (B) Maximum value of xy2 is (7.5)3

(C) Maximum value of x2y3 is 62 93 (D) Maximum value of x2y3 is 510

30. The point (1, 4) is inside the circle S whose equation is of the form x2 + y2 – 6x – 10y + k = 0. Then possible

values of k if the circle neither touches the axes nor cuts them is/are

(A) 27 (B) 26

(C) 28 (D) 30

SECTION - III

Reasoning Type

The section contains 2 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out


31. STATEMENT-1 : Tangent to the circle x2 + y2 = 25 at (3, 4) is parallel to the line 3x + 4y – 11 = 0.

and

STATEMENT-2 : If two lines are parallel then their slopes are equal.





32. Consider the circle x2 + y2 = 100.

STATEMENT-1 : From (10, 10), two mutually perpendicular tangents can be drawn to given circle.and

STATEMENT-2 : The locus of the point from which two mutually perpendicular tangents can be drawn to given

circle is x2 + y2 = 200.





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.


Consider all possible arrangements of letters of word ‘ORANGE’ and a word is selected at random.

33. The probability that in selected word, vowels are in alphabetical order, is

(A)1

3(B)

1

2

(C)1

6(D)

1

36




34. The probability that first and last letter of selected word are vowels, is

(A)1

5(B)

2

5

(C)1

10(D)

1

3

35. The probability that first letter of selected word is vowel and last letter of selected word is consonant, is

(A) 15

(B) 215

(C)1

15(D)

3

10

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 I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, sand t. Any given statement in Column I can 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


Column I Column II

(A) Equation of the base of an equilateral triangle (p) 1 sq-unit

is x + y = 2 and vertex opposite to it is

(2, – 1). Then area of triangle is

(B) Area of triangle formed by joining the origin (q) 2 sq-unit

to the point of intersection of the line

5 2 3 5x y and circle x2 + y2 = 10 is

greater than or equal to

(C) Area of triangle formed by the line (r) 5 sq-unit

xy + 2x + 2y + 4 = 0 and x + y + 2 = 0 is

less than or equal to

(D) Area of triangle formed by 2x2 – 5xy + 3y2 = 0 (s)1

2 3 sq-unit

and y = 2 is less than or equal to

(t) 3 2 sq-unit





Column I Column II

(A) Let a, b, c be positive real numbers different (p) Are in A.P.

from 1. If loga200, 2log

b10, 2log

c5 + log

c4

are in H.P., then a, b, c

(B) Let a, b, c be different positive real numbers (q) Are in G.P.

such that a > b > c. If 2log(a – c),

log(a2 – c2), log(a2 + 2b2 + c2) are in A.P.,

then a, b, c

(C) If a, b, c are in A.P. and a2, b2, c2 are in (r) Are in H.P.

H.P., then a3

, b3

, c3

(D) If a, b, c are in A.P., b, c, d are in G.P., (s) Are in A.G.P.

c, d, e are in H.P., then a, c, e

(t) Satisfy 3b = 2a + c

SECTION-VI

Integer Answer Type


appropriate 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 will


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

38. A third order diagonal matrix is formed using the digits 1, 2, 3, 4, 5, 6 without repetition (along principal

diagonal). The probability that the sum of the diagonal elements of a matrix thus formed is 9, is p then1

p

([] represents greatest integer function) is _______.

39. A straight line with negative slope and passing through (2, 2) cuts x-axis at P and y-axis at Q then absolute

minimum value of OP + OQ is _______.

40. C1 : x2 + y2 = r 2, C

2 : x2 + y2 – 4x – 4y – 1 = 0. The largest integral value of r for which C

1 and C

2 have

exactly two common tangents is _______.




PART - III : PHYSICS

SECTION - I




41. Moment of inertia of an non-uniform annular disc about an axis shown. Mass per unit area of disc varies with

distance r as = 0r ; where is a positive constant.

(A)5 50

5b a

(B)5 50

2

5b a

a

b

x x

(C)4 40

2b a

(D)3 30

5 b a

42. A projectile is fired from ground with speed u at an angle with horizontal. If L

represents angular momentum

of the projectile about point of projection, then the plot ofdL

dt

versus time (t) is represented by

(A)

dL

dt

2 sinu g

u sin g

t

(B)

dL

dt

t

(C)

dL

dt

u sin

g

t

(D)

dL

dt

t

43. The gravitational potential in a region is given by

V = N

50kg

x y

Magnitude of gravitational force on a particle of mass 2 kg placed at origin is

(A) Zero (B) 100 2 N

(C) 50 N (D) 100 N




44. A solid uniform disc of mass m and radius R is pivoted about a horizontal axis through its center. A small

body of mass m is attached to the rim of the disc at point A and system is released from rest. What is the

velocity of the m when it reaches point B?

30°

A

B

R

m

(A) ˆ ˆgR i j (B)ˆ

ˆ3

igR j

(C)ˆ2 ˆ

3 3

jgR i

(D) ˆ ˆ2

3

gRi j

45. A balloon is tied inside a cubical chamber containing air as shown. If the chamber now accelerates towards right then

Air a

(A) Balloon moves backward (B) Balloon moves forward

(C) No change in position of balloon (D) Depends on the gas inside the balloon

46. A solid sphere of radius R is kept inside a cylindrical tank having a piston of negligible mass at its top. If a

mass M is placed on the piston so that the liquid compresses, fractional change in the radius of sphere(B = bulk moduls of sphere, A = area of piston)

R

(A) No change (B) Mg AB

(C)3

Mg

AB(D)

2

Mg

AB

SECTION - II

Multip le Correct Answer Type


of which ONE OR MORE is/are correct.




47. A disc of radius r rolls on a horizontal ground with linear acceleration a and angular acceleration

Q

P

R

ar

r

(A) Acceleration of point P is 22 2a R r (B) Acceleration of point P is a + r

(C) Acceleration of point Q is 2 22a r R (D) Acceleration at point Q is a + R + 2r

48. A cubical block of density (c) is floating on a liquid of density

l.

l

PB

= Pressure at the bottom of vessel

l = length of the cubical block inside liquid

FB

= Force of buoyancy on cubical block

Fn

= Net force by the liquid on the block

If the container is made to move with some acceleration in upward direction

(A) PB increases (B) PB remains same

(C) l increases (D) l remains same and FB increases

49. Two wires of same mass A and B are made of same material. Diameter of wire B is twice of diameter of wire

A then

(A) Strain in both the wires is same

(B) Strain in wire A is 4 times strain in B

(C) Extension of wire A is 16 times extension of B

(D) Both the wires will have same extension

50. Choose the incorrect statement(s) from the following

(A) Total energy and total angular momentum of solar system is constant(B) A rocket must necessarily have escape velocity from the very beginning of its motion to escape from earth

(C) A satellite can be in a stable orbit in a plane not passing through the earths center

(D) Velocity of escape for a particle resting on earth is equal to velocity of escape for a particle orbiting around

earth

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 : Radius of gyration of a body does not depend on the distribution of mass about the axis of

rotation.

and

STATEMENT-2 : Radius of gyration is the distance from axis where we can assume the total mass of the body

to be concentrated for it to have same moment of inertia.





52. STATEMENT-1 : Net torque on the rotating planet around the sun is zero.

and

STATEMENT-2 : Angular momentum of sun + planet system is conserved.





SECTION-IV

Paragraph Type

This section contain 1 paragraph. Based upon this paragraph, 3 multiple choice questions have to be answered. Each

question has 4 choices (A), (B), (C) and (D) for i ts answer, out of which ONLY ONE is correct.


It is observed that for a substantial range of stresses, the stress-strain relation is linear, and the specimen recovers to

its original dimensions when load is removed. The qualitative variation of stress versus strain is as shown below

Stress Fracture point

Strain

ABC

D

53. In the above curve forces exerted by material are conservative upto

(A) A (B) B

(C) C (D) D

Two types of rubber are found to have the stress-strain curves as shown.

Stress

Strain

B

A




54. Which one of the two would be preferable for absorbing vibrations of heavy machines?

(A) A (B) B

(C) Either A or B (D) None of these

55. Which one would be favourable for car tyre?

(A) A (B) B

(C) Either A or B (D) Neither A nor B

SECTION-VMatrix-Match Type

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

The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s

and t. Any given statement in Column I can 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 wooden block is tied from the bottom of a container containing a liquid as shown

l

w

= density of liquid

= density of wood

Now, with following changes mentioned in column I match their effects on tension T in the string in

column II.

Column I Column II

(A) w increased (p) T increases

(B) l increased (q) T decreases

(C) Accelerated upwards (r) Buoyant force decreases

(D) Accelerated downwards (s) Buoyant force increases

(t) Pressure at bottom increases

57. Given rigid bodies of equal masses and radii and are simultaneously released from rest. Match the column Iwith column II

Column I Column II

(A) Time to reach bottom is maximum (p) Hollow sphere

(B) Angular acceleration is maximum (q) Ring

(C) Rotational kinetic energy when (r) Solid sphere

reach bottom is maximum

(D) Total kinetic energy is maximum (s) Hollow cylinder

(t) Disc




SECTION-VI

Integer Answer Type


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


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 solid sphere of radius r hits a cushion with a pure rolling motion and rebounds, with a pure rolling motion.

If the ratio of the height h of the cushion to the radius of solid sphere is2

;n

n

where n is an integer, then

find the value of n. (Assume that the force exerted on the ball by the cushion is horizontal during the impact).

59. What is the shearing stress in –4

2

N10

m

between horizontal layers of water, If velocity of river water is

36 km/h and distance between bottom and top surface of water is 10 m. Viscosity of water is 10 –3 poiseuille.

60. A mass m (450 g) is kept on a cubical block of volume (125 n3 cm3). When mass m is removed l decreases

by 2 cm. Find the value of n. (water

= 1 g/cm3)

l

m

Water



CHEMISTRY

1. (D)

2. (B)

3. (C)

4. (C)

5. (B)

6. (C)

7. (C, D)

8. (A, B, D)

9. (A, C)

10. (A, C, D)

11. (D)

12. (B)

13. (A)

14. (B)

15. (B)

16. A (q, t)

B (r)

C (s)

D (q, t)

17. A (p)

B (q, r)

C (q, s)

D (q, t)

18. (5)

19. (2)

20. (9)

ANSWERS

MATHEMATICS

21. (C)

22. (B)

23. (D)

24. (D)

25. (A)

26. (A)

27. (C, D)

28. (A, C)

29. (A, C)

30. (A, B, C)

31. (C)

32. (A)

33. (C)

34. (A)

35. (D)

36. A (s)

B (p, q, r)

C (q, r)

D (p, q, r)

37. A (q)

B (q)

C (p, q, r, s, t)

D (q)

38. (6)

39. (8)

40. (5)

PHYSICS

41. (A)

42. (B)

43. (B)

44. (B)

45. (B)

46. (C)

47. (A, C)

48. (A, D)

49. (B, C)

50. (B, C, D)

51. (D)

52. (B)

53. (B)

54. (B)

55. (A)

56. A (q)

B (p, s, t)

C (p, s, t)

D (q, r)

57. A (q, s)

B (r)

C (q, s)

D (q, s)

58. (5)

59. (1)

60. (3)

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Jee (Advanced) P-III