jpt 2 classroom jee adv 26-05-2013 p 1 c 0 english

8/13/2019 JPT 2 Classroom JEE Adv 26-05-2013 P 1 C 0 English

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Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

Date : 26-05-2013 Duration : 3 Hours Max. Marks : 222

PAPER 1

CODE

0

JEE PREPARATORY TEST-2 (JPT-2) (JEE ADVANCED)

INSTRUCTIONSA. General :

1. This Question Paper contains 60 questions.

2. The question paper CODE is printed on the right hand top corner on this sheet of this booklet.

3. No additional sheets will be provided for rough work.

4. Blank paper, clipboard, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets

in any form are notallowed.

5. The answer sheet, a machine-gradable Objective Response Sheet (ORS), is provided separately.

6. Do not Tamper / mutilate the ORSor this booklet.

7. Do not break the seals of the question-paper booklet before instructed to do so by the invigilators.

8. Write your Name, Roll No. and Signin the space provide on the back page of this booklet.

B. Filling the bottom-half of the ORS :

Use only Black ball point pen only for filling the ORS. Do not use Gel / Ink / Felt pen as it might smudge the ORS.

9. Write your Roll no. in the boxes given at the top left corner of your ORS with black ball point pen. Also, darken

the corresponding bubbles with Black ball point pen only. Also fill your roll no on the back side of your ORS

in the space provided (if the ORS is both side printed).

10. Fill your Paper Code as mentioned on the Test Paper and darken the corresponding bubble with Black ball

point pen.

11. If student does not fill his/her roll no. and paper code correctly and properly, then his/her marks will not be

displayed and 5 marks will be deducted (paper wise) from the total.

12. Since it is not possible to erase and correct pen filled bubble, you are advised to be extremely careful while

darken the bubble corresponding to your answer.

13. Neither try to erase / rub / scratch the option nor make the Cross (X) mark on the option once filled. Do not

scribble, smudge, cut, tear, or wrinkle the ORS. Do not put any stray marks or whitener anywhere on the

ORS.

14. If there is any discrepancy between the written data and the bubbled data in your ORS, the bubbled data will

be taken as final.

C. Question paper format and Marking scheme :

15. The question paper consists of 3 parts (Physics, Chemistry & Mathematics). Each part consists ofFourSections.

16. For each question in SectionI, you will be awarded 3 marks if you darken the bubble(s) corresponding to

the correct choice for the answer and zero mark if no bubbled is darkened. In case of bubbling of incorrect

answer, minus one (1) markwill be awarded.

17. For each question in SectionII, you will be awarded 4 marks if you darken the bubble corresponding to the

correct answer and zero marks if no bubble is darkened. There is no negative marking for incorrect

answer in this section.

18. For each question in SectionIII, you will be awarded 2 marks for each row in which you have darkened the

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

8 marks. In case of bubbling of incorrect answer, minus one (1) markwill be awarded for each row.

19. For each question in SectionIV, you will be awarded 4 marks if you darken the bubble corresponding to

the correct answer and zero marks if no bubble is darkened. There is no negative marking for incorrect

answer in this section.

DONOTBREAKTHESEA

LSWITHOUTBEING

INSTRUCTEDTODOSOB

YTHEINVIGILATOR

TARGET : JEE (ADVANCED) 2013 COURSE CODE : JP, JF, JR, JCC


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PHYSICS

Space for Rough Work

PART- I - PHYSICS

SECTION - I

Straight Objective Type

This section contains 10 multiple choice questions. Each question has choices (A), (B), (C) and (D),

out of which ONLY ONEis correct.

1. In a spherical container of radius R, liquid of density ! and surface tension T is

filled upto half volume of container. Consider ABC as imaginary half circular plane

which divides the liquid into equal parts, then force applied by the left part liquid on

the right part liquid will be A

B

C(A)

23 0

P RgR RT

2

" #$! % & $' (

) *(B)

3 2

0gR P R TR! % $ %

(C)

23 0

P RgR 2TR

2

" #$! % &' (

) *(D)

23 0

P R2gR 2TR

3 2

$!% &

2. A parallel beam of diameter d is incident on air-glass interface as

shown in figure. The diameter of refracted light beam is :

( d 3mm+ , 45, + - and glass

air

n 3

n 2+ )

(A) 12 mm (B) 14 mm

(C) 6 mm (D) 4.5 mm

3. A vehicle is moving on a circular path of radius R with speed gR . A simple pendulum of length ! hangs

from the ceiling of the vehicle. The time period of small oscillations of the pendulum is [ where R..! ]

(A)g

2$ ! (B)2g

2$ ! (C) 2g

2$ ! (D) None of these


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PHYSICS


4. A particle is dropped from certain height above ground level. At same time a person starts motion in horizontal

plane with speed 10m/s. When speed of particle become same as of person, then the radius of curvatuire of

path taken by particle with respect to person (at same instant) is :

(A) 10 2m (B) 20 2m (C)10

m2

(D) 10m

5. Two blocks are kept as shown in figure. The coefficient of friction between two blocks is 12

while ground is

smooth. The maximum possible kinetic energy of two block system without having relative motion between

them is :

2kg

2kg

K=10N/m

Smooth

(A) 5J (B) 10J (C) 15J (D) 20J

6. Two small balls A and B made of same material, A is solid but B is hollow.

these are connected by an ideal spring and this system is kept over a

smooth plank such that centre of mass of two balls coincide with mid point

of plank. Initially spring is compressed by ceratin amount and plank is in

horizontal position. Now we release system then

L/2 L/2

A B

(A) Plank will rotate clock wise

(B) Plank will rotate anti clock wise

(C) Plank will not rotate

(D) It will depend upon string constant.


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PHYSICS


7. A small solid sphere of radius R made of a material of bulk modulus B is

surrounded by an incompressible liquid in a cylindrical container. A mass

less piston of area A floats on the surface of the liquid. The magnitude of

fractional change in the radius of the spheredR

R

" #' () *

when a mass M is

placed slowly on the piston to compress the liquid is:

M

(A)Mg

3AB(B)

Mg

AB

(C)3Mg

AB(D) None of these

8. On a smooth surface there are five identical equally spaced balls A,B,C,D and E present with initial velocities

10m/s, 5m/s, 2m/s,3m/s,3m/s respectively, Collision between any two ball assumed to be elasitc. Then

after all possible collision which pair of balls will have same speed as of initial

(A) A & D (B) B & C (C) B & D (D) A & C

9. In a container water is filled upto certain height with hole at its

bottom. A bird is coming towards free surface of liquid with velocity

/ 0bV 12i 10j+ &"

# #m/s and fish is rising up wards with velocity

/ 0fishV 3j m/ s+"

# . The speed of bird as seen by fish under normal

incidence condition at the moment when water level in container

is 20m from its bottom is : (given hole area = 1cm2; surface are of

liquid = 20cm2)

Bird y

X

Fish

(A) 20m/s (B) 40m/s

(C) 10m/s (D) 12m/s


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PHYSICS


10. Initially wedge was at rest and spring is in natural length. Now a solid sphere of

same mass that of wedge is attached to the spring and is released as shown in

figure. (assume sphere is in pure Rolling). The maximum extension in spring is : K=3mg

= 37

Smooth

(A)2

meter5

(B)3

meter5

(C) 4 meter6

(D) 2meter

SECTION - II

Multiple Correct Answers Type

This section contains 5 multiple correct answer(s) type questions. Each question has 4 choices (A),

(B), (C) and (D), out of which ONE OR MORE is/are correct.

11. A positive charge particle with velocity v xi y j+ %" # # moves in a magnetic field B yi x j+ %

"# # . The magnitude of

magnetic force acting on the particle is F. Which one of the following statements are correct.

(A) No force will act on particle if x = y

(B) / 02 2F x y1 & if x > y(C) The force will act along positive Z-axis if x > y

(D) The force will act along positive Z-axis if y > x

12. A diatomic gas is filled inside a conducting cylinder. Now we push the

piston slowly to make volume of gas half of initial. Pick correct statements

(A) Pressure of gas Increases because there is more average change in

linear momentum of molecule in each collision

(B) Pressure force on side wall of container increased

(C) Pressure force on piston is increased

(D) More molecules collide with piston per unit time


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PHYSICS


13. In a photoelectric effect experiment a photon of energy 13ev is incident on a metal of work function = 0.9ev

due to which a photo electron is emitted from metal. Energy of this photo electron is sufficient to excite a

H atom from its ground state then

(A) Kinetic energy of emitted photo electron may be 12.1ev

(B) Kinetic energy of emitted photo electron may be 10.2ev

(C) In subsequent emission spectrum of H-atom either 1 or 2 or 3 spectral lines will be present.

(D) Maximum possible stopping potential is 12.1 volt.

14. In the figure there are four arcs carrying positive and negative charges.All

of them have same charge density 2 . Pick incorrect statement (s)

3R

R

y

x(A) The net dipole moment for the given charge distribution is / 0 24 5 R .2(B) The resultant electric filed at the center is zero.

(C) If a uniform E"

is switched on perpendicular to the plane then charge

distribution starts rotating about X-axis.

(D) Potential at the centre of the given charge distribution is non-zero.

15. Given solid sphere is in pure rolling on a rough surface. Pick correct

statement(s) : (Take $= 22/7)

A

O

(A) There are two points in sphere having velocity in vertical direction

(B) There is no point in sphere having velocity in vertical direction

(C) Ratio of distance travelled by A and O is14

11in one complete round

(D) Ratio of distance travelled by A and O is 1 in one complete round

SECTION - III

Matrix - Match TypeThis section contains 1 question. Each question contains statements given in

two columns which have to be matched. Statements in Column are labelledas A,B,C and D whereas statements in Column are labelled as p,q,r and s.

The answers to these questions have to be appropriately bubbled as illustrated

in the following example.

If the correct matches are A-p , A-r , B-p , B-s , C-r , C-s and D-q ,

p q r s

p q r s

p q r s

p q r s

A

B

C

D

p q r s

then the correctly bubbled matrix wil l look like the following :



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PHYSICS


16. A non conducting piston divides an adiabatic container into two equal parts. Such that piston is in equlibrium

and temperature on both side is also same as T0. Now Istchamber is heated such that piston moves very

slowly until volumes of IIndchamber is reduced to

th1

4of the initial. In both chambers same monatomic gas

is filled such that the number of moles are same. (24/3= 2.5)

I II

Column - I Column II

(A)

st

0

Heat supplied to l chamber

nRT(p) 27

(B)

st

0

W.D. by gas of l chamber

nRT(q)

5

2

(C)

nd

0

Final temp.of II chamber

T (r)9

4

(D)

st

0

Final temp.of I chamber

T(s)

35

2

SECTION - IV

Integer Answer Type

This section contains 4 questions. The answer to each of the questions is a

single digit integer, ranging from 0 to 9. The appropriate bubble below therespective question number in the ORS have to be darkened.


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PHYSICS


17. When two unknown resistors are connected in series with a battery, 225W power is delivered to the combination

with a total current 5A. For the same total current 50W is delivered when the resistors are connected in

parallel. Find the ratio of two resistances.

18. Two identical wires are stretched by same tension of 100 N and each emits a note of frequency

200 cycles/sec. The tension in one wire is increased by 1N. calculate the number of beats heard per second

when the wires are plucked simultaneously.

19. Elctromagnetic radiation falls on a metallic body whose work function is 2ev. For a particular radiation of

frequency 3 , the maximum kinetic energy of the photoelctron is found to be 4ev. Find the maximum kinetic

energy (in ev) of photoelectron for the radiation of5

3

3.

20. In the figure shown there is no slipping any where as mass of plank and each sphere is m. The ratio of

acceleration of C.M. of bigger and smaller sphere will be

2RR


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CHEMISTRY

P1JPT2260513C0-8

PART- II - CHEMISTRY

Atomic masses : [H = 1, D = 2, Li = 7, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg = 24, Al = 27, Si = 28,

P = 31, S = 32, Cl = 35.5, K = 39, Ca = 40, Cr = 52, Mn = 55, Fe = 56, Cu = 63.5, Zn = 65, As = 75,

Br = 80, Ag = 108, I = 127, Ba = 137, Hg = 200, Pb = 207]

SECTION - I


This section contains 10 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out ofwhichONLY ONE is correct.

21. The compressibilty factor of N2at 330K & 800 atm is 1.90 and at 570K & 200 atm is 1.10. A certain mass of

N2

occupies a volume of 1dm3at 330K and 800 atm. Calculate the volume of N2gas at 570K and 200 atm.

(A) 1 L (B) 2 L (C) 3 L (D) 4 L

22. Fe2O

3(s) may be converted to Fe by the reaction, ! "2 3 2Fe O 3H g# ! " ! "22Fe s 3H O g# ; for which

pK 8$ at temperature 720C. What % of H2remains unreacted after the reaction has come to equilibrium.

(A) 22%% (B) 34%% (C) 66%% (D) 78%%

23. The ratio of magnetic moments of Fe(III) & Co(III) is

(A) 5 : 7 (B) 35 : 24 (C) 7: 3 (D) 24 : 15

24. Calculate the work done (in J) when 4.5 g of H2O

2reacts against a pressure of 1 atm at 25C ?

2H2O

2($ ) &O2(g) + 2H2O ($ )

(A) 21.63 10' ( (B)24.5 10( (C) 23.2 10( (D)

26.1 10' (

25. If 1 2 3 4w ,w ,w ,w for an ideal gas are magnitude of work done in isothermal, adiabatic, isobaric, isochoric

reversible expansion processes. (assume expansion to be from same initial points to same final volumewherever applicable) The correct order will be

(A)1 2 3 4

w w w w) ) ) (B) 3 2 1 4w w w w) ) )

(C)3 2 4 1

w w w w) ) ) (D) 3 1 2 4w w w w) ) )



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CHEMISTRY

P1JPT2260513C0-9


26. The density of O2is maximum at

(A) STP (B) 273 K and 2 atm (C) 546K and 1 atm (D) 546 K and 2 atm

27. Select the correct statements out of I, II and III for zero order reactionI : Quantity of the product formed is directly proportional to timeII : Larger the initial concentration of the reactant, greater the half-life periodIII : If 50% reaction takes place in 100 minutes, 75% reaction take place in 150 minutes.

(A) I only (B) I and II only (C) II and III only (D) I, II and III

28. Identify the final product F

OH

2/*** *&H Ni

High temp ACu/+

***& B 2/ #

** **&NH OH H C H

#

***& D 2/ #

*** *&H O H

EPolymerisation

**** *& F

(A) Bakelite (B) Nylon-6 (C) Polyester (D) Natural rubber

29. Which species is not formed in reaction of aniline by using conc.2 4

H SO &3

HNO ?

(A)

NH3

NO2

(B)

NH2

NO2

(C)

NH2

NO2

(D)

NH2

SO3H

30. Total number of diazonoium salt used in formation of final product when excess of it is treated withhydroquinone (benzene-1,4-diol) in slightly basic medium.(A) 1 (B) 2 (C) 3 (D) 4


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CHEMISTRY

P1JPT2260513C0-10


SECTION - II

Multiple Correct Answer Type

This section contains 5 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of

whichONE OR MORE is/are correct.

31. Which of the following statements are incorrect ?

(A) In 2 6B H (s) there are four 2c-2ebonds

(B) In ! "3 3SiH P,,

there is back bonding

(C) (CH3)

3and ! "3 3SiH N

, ,

are pyramidal

(D) 2 6Al Cl (s) has banana bonding

32. Select the correct statements about the electrolysis(A) Electric current is used to drive a non spontaneous reaction

(B) G+ is positive for chemical process during electrolysis

(C) cations and anions move towards the anode and cathode respectively(D) over voltage is generally associated with anode in the electrolysis of NaCl (aq)

33. Which of the following statements are incorrect(A) 0.1 M KCl solution will have same osmotic pressure as 0.1 M glucose solution(B) 0.1 M KCl solution will have same boiling point as 0.1 M urea solution(C) 0.1 M glucose & 0.1M urea solution are isotonic(D) 0.1 M MgCl

2solution will have less RLVP(Relative lowering in V.P.) then 0.1 M NaCl.


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CHEMISTRY

P1JPT2260513C0-11


34. Correct statement about A,B and C is/are

4-****$LiA H C

NH2

O

* * *&

+

2 5P O A

Br2/KOH

B

(A) A can be hydrolysed in basic medium(B) B can form alcohol on treatment with aqueous NaNO

2/ HCl

(C) C produces foul smell on treatment with chloroform in presence of base(D) Compound A, B and C have same number of C.

35. Which method is/are correct for preparation of Pinacolone ?

(A)

HO

OH

H#***&

O

(B)

OH

Cl

3AgNO****&

O

(C)

OH

NH2

2/NaNO HCl **** *&

O

(D)

HO

H

2 4.Conc H SO*****&

O


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CHEMISTRY

P1JPT2260513C0-12


SECTION - III

Matrix - Match TypeThis section contains 1 question. Each question contains statements given in

two columns which have to be matched. Statements in Column are labelled

as A,B,C and D whereas statements in Column are labelled as p,q,r and s.

The answers to these questions have to be appropriately bubbled as illustrated

in the following example.If the correct matches are A-p , A-r , B-p , B-s , C-r , C-s and D-q ,

p q r s

p q r s

p q r sp q r s

A

B

CD

p q r s

then the correctly bubbled matrix will look like the following :

36. Column - I Column II

(A) Increasing order of ionisation energy (p) F O S Se. . .

(B) Increasing order of electron affinity (q) O N F Ne. . .

(C) Increasing order of atomic size (r) Na Mg Al Si. . .

(D) Increasing order of Zeff

. (s) 2O O O O' #. . .

SECTION - IV

Integer Answer Type

This section contains 4 questions. The answer to each of the questions is a

single digit integer, ranging from 0 to 9. The appropriate bubble below the

respective question number in the ORS have to be darkened.


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CHEMISTRY

P1JPT2260513C0-13

37. The total number of lone pairs in chlorate ion is :

38. Total number of nodes for 4s orbital is equal to :

39. The maximum covalency of oxygen in ozone.

40. How many molecules given below are more basic than aniline ?

H2N C NH2

NH

CH3 C NH2

NH

CH3 CH2 NH2 NH3 I II III IV

NH2

CH3

CH3 C NH2

OCH3 S NH2

O

O

V VI VIICH3 N H

CH3

CH3 N CH3

CH3

VIII IX



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MATHEMATICS

PART- III - MATHEMATICS

SECTION - I



whichONLY ONE is correct.

41. If one root of the equation 2ax bx c 0! ! " , a,b,c #R, is cube of other, then2b 2ac

a c

$

!is equal to

(A) ac% (B) bc% (C)2c

a% (D)

2c

b%

42. Locus of point of intersection of the tangents drawn to the parabola 2x 8y" at end points of its variable chord

having difference of abscissa as unity is(A) circle (B) parabola (C) ellipse (D) Hyperbola

43. A variable line is such that its distance from origin always remains 2 units. Minimum value of the length ofintercept made by it between coordinate axis is(A) 2 (B) 4 (C) 8 (D) 16

44. If a function is formed randomly with domain & 'A 4,5,7( and codomain & 'B 1,2,3,4,5,6,7,8( , then find theprobability that it is non-decreasing.

(A)3

8(B)

7

64(C)

113

512(D)

15

64

45. The right angled triangle ABC right angled at A and b 18cm" and c 63cm" . The circle C1is drawn

with centre lying on hypotenuse BC and touching the side AB and CA. Another circle C2is drawn concentric

with C1and passing through A. The area of the circle C

2is

(A) 2144 cm) (B) 2196 cm) (C) 2288 cm) (D) 2392 cm)



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MATHEMATICS


46. The number of triplets * +x,y,z , where x,y,z , -0,2# ) , satisfying the inequality

* +* +* +4 2 21 cos x 2 cot y 4 sin4 z 12cos x! ! ! . is(A) 16 (B) 18 (C) 20 (D) 24

47. If 0,4

)/ 01 # 2 3

4 5is a root of the equation tanx cot x n,! " then * +

n

nlim sin cos

671 ! 1 "

(A) e (B) e (C)3

2e (D) 2e

48. The value of 20 30 20 30 20 300 0 1 1 20 201. C . C 2. C . C .... 21 C . C! ! ! is

(A) * +50 4920 30C 20 C! (B) * +50 4929 29C 20 C!

(C) * +50 4930 29C 20 C! (D) * +50 49

31 29C 20 C!

49. Let a 1, b 2" "!

!

and c 3"!

and c,b,a!

!!

be three non-coplanar vectors. If d 4"!

, then

db c a d c a b d a b c

a b c

8 9 8 9 8 9! !: ; : ; : ;

8 9: ;

! ! ! ! ! !! ! ! ! ! !

!! !

is equal to

(A) 2 (B) 4 (C) 1 (D) None of these

50. The value of 20

dx

1 2sin x

)

!< is

(A) 0 (B)2 3

)(C)

3

)(D) none of these


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MATHEMATICS


SECTION - II

Multiple Correct Answer Type


whichONE OR MORE is/are correct.

51. For the function * +

2 2

2 2

tan x cot x 1f x tan x cot x 1

$ !" ! $ , which of the following statement(s) is/are correct

(A) Global maximum value of f(x) is5

3(B) Global minimum value of f(x) is 1

(C) Global maximum value of f(x) does not exist (D) Global minimum value of f(x) does not exist

52. Let ABCD be a square such that vertices A,B,C,D lie on circles 2 2x y 2x 2y 1 0! $ $ ! " ,

2 2x y 2x 2y 1 0! ! $ ! " , 2 2x y 2x 2y 1 0! ! ! ! " and 2 2x y 2x 2y 1 0! $ ! ! " respectively with centre of

square being origin and sides are parallel to coordinate axes. The length of side of such square can be

(A) 2 2$ (B) 2 2! (C) 3 3$ (D) 3 3!

53. If21

, zz are two non-zero complex numbers such that2

2

2

1

2

21 |3||2||32| zzzz !"$ , then

(A) 01221

"! zzzz (B)1

2

z

z

is purely imaginary

(C)1

2

z

z

is purely real (D) Amp2

1

2 )%"335

0224

/

z

z


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P1JPT2260513C0-17

MATHEMATICS


54. If 2 2 2x 2x y 5x y 5 0$ ! ! $ " and * +y 1 1," then

(A) * +y ' 1 1" (B) * +4

y '' 13

" $ (C) * +22

y '' 13

" $ (D) * +2

y ' 13

"

55. If the global maximum value of f(x) = - x2+ ax a22a 2 for x #[0, 1] be - 5, then acan take the value

(A)4 2 13

3

$ !(B)

4 2 13

3

$ $(C) 1 (D) 3

SECTION - III

Matrix - Match Type

This section contains 1 questions. Each question contains statements

given in two columns which have to be matched. Statements in Column

are labelled as A,B,C and D whereas statements in Column are labelled

as p,q,r and s. The answers to these questions have to be appropriately

bubbled as illustrated in the following example.

If the correct matches are A-p , A-r , B-p , B-s , C-r , C-s and D-q ,

then the correctly bubbled matrix will look like the following :

p q r s

p q r s

p q r s

p q r s

A

B

C

D

p q r s

56. Column I Column II

(A) The ratio of inradius to circumradius of (p) 0

a n sided polygon is6 2

4

!, then value of

n

4is

(B) Length of the portion of the tangent intercepted between (q) 1

coordinate axes to the curve 2 / 3 2 / 3 2 / 3x y 2! "

at any of its point is

(C) Number of integral values of x, satisfying the (r) 2

inequality 2 1 13x 8x 2sin (sin4) cos (cos4)$ $! = $ is

(D) Number of solutions of system of equations (s) 3

2x 3y z 2$ ! " , 4x 6y 2z 4$ ! " and

6x 9y 3z 3$ ! " is


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P1JPT2260513C0-18

MATHEMATICS


SECTION - IV

Integer Answer Type

This section contains 4 questions. The answer to each of the questions isa single digit integer, ranging from 0 to 9. The appropriate bubble below therespective question number in the ORS have to be darkened.

57. A variable line with negative slope is drawn through the fixed point A(3,4). If it cuts the coordinate axes at B

and C, find the minimum value of the area of BCG> , where G is the centroid of the OBC> . (O is origin)

58. If the greatest value of the function * + 4 3 21 2 3

f x x x x 24 3 2

" $ $ ! ; , -x 2,4# $ is M, then find the value of [M];

where [ ] denotes greatest integer function.

59. If a,b,c are in A.P. , b , c, d are in G.P. and c,d,e are in H.P. then find the value of |c| , given that a 32" and

e 2" .

60. If the roots of the equation * + * + * + * +3 2 2 21 x 2 x 2 x 1 0? ! $ ? ! $ ? ! ! ? ! " ; R? # are in a A.P. with non-zerocommon difference and one of the roots is independent of ? , then the sum of all possible values of ? is m.

Find the value of 4m.


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jpt 2 classroom jee adv 26-05-2013 p 1 c 0 english

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