JEE PREPARATORY TEST-1 (JPT-1) (JEE ADVANCED)

PAPER - 2INSTRUCTIONSA. General :

1. This Question Paper contains 63 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 gadgetsin any form are not allowed.

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

6. Do not Tamper / mutilate the ORS or 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 Sign in 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 theORS.

9. Write your Roll no. in the boxes given at the top left corner of your ORS with black ball point pen. Also, darkenthe corresponding bubbles with Black ball point pen only. Also fill your roll no on the back side of your ORSin 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 ballpoint pen.

11. If student does not fill his/her roll no. and paper code correctly and properly, then his/her marks will not bedisplayed 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 whiledarken 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 notscribble, smudge, cut, tear, or wrinkle the ORS. Do not put any stray marks or whitener anywhere on theORS.

14. If there is any discrepancy between the written data and the bubbled data in your ORS, the bubbled data willbe taken as final.

C. Question paper format and Marking scheme :

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

16. For each question in Section�I, you will be awarded 3 marks if you darken the bubble corresponding to thecorrect choice for the answer and zero mark if no bubbled is darkened. In case of bubbling of incorrectanswer, minus one (�1) mark will be awarded.

17. For each question in Section�II, you will be awarded 4 marks if you darken the bubble(s) correspondingto the correct choice(s) for the answer and zero mark if no bubbled is darkened. There is no negativemarking for incorrect answer(s) in this section.

18. For each question in Section�III, you will be awarded 4 marks if you darken the bubble(s) correspondingto the correct choice for the answer and zero mark if no bubbled is darkened. In case of bubbling ofincorrect answer, minus one (�1) mark will be awarded.

19. For each question in Section�IV, you will be awarded 2 marks for each row in which you have darkened thebubble corresponding to the correct answer. Thus, each question in this section carries a maximum of8 marks. There is no negative marking for incorrect answer(s) in this section.

20. For each question in Section�V, you will be awarded 4 marks if you darken the bubble corresponding tothe correct answer and zero marks if no bubble is darkened. There is no negative marking for incorrectanswer in this section.

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

Date : 19-05-2013 Duration : 3 Hours Max. Marks : 240

CODE

0JEE PREPARATORY TEST-1 (JPT-1) (JEE ADVANCED)

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

RESONANCE P2JPT1190513C0-1

PHYSICS

Space for Rough Work

PART- I - PHYSICS

SECTION - IStraight Objective Type

This section contains 8 multiple choice questions. Each question has choices (A), (B), (C) and (D), outof which ONLY ONE is correct.

1. 50 divisions on the vernier scale coincides with 49 divisions on the main scale of a vernier calliper. The leastcount of instrument is, if graduation on the main scale is 2mm.

(A) 1

25mm (B)

150

mm (C) 2

49mm (D)

149

mm

2. The dimensional formula for wavelength is equivalent to :

(A) E LC

B(B)

E

B LC(C)

B LCE

(D) B

E LC

3. A thin uniform spherical shell and a uniform solid cylinder of the same mass and radius are allowed to rolldown a fixed incline without sliping starting from rest. The times taken by them to roll down the same

distance are t1 and t

2 respectively then 1

2

t

t is

(A) 1415

(B) 1514

(C) 3

10(D)

103

4. A ring of radius R rolls without sliding with a constant velocity with respect to ground. The radius of curvature of the path followed by any particle of the ring at the highest point of its path will be(A) R (B) 2R (C) 4R (D) None

5. A right circular cylinder of specific gravity floats in water with its axis vertical, one third volume being abovethe water. If �� be the specific gravity of air then select the correct option.

(A) 3 = 3 + (B) 3 = 2 + (C) 2 = 2 + (D) 3 = 1+ 2


PHYSICS


6. Three identical positive charges each of value Q are arranged at the vertices of an equilateral triangle of sidelength a. The intensity of the electric field at the vertex of a regular tetrahedron of which the triangle is thebase is :

(A) 2

6KQa

(B) 2

2KQa

(C) 2

3KQa

(D) None

7. If the electrostatic potential is given by 2 2 20 x y z where 0 is constant, then the charge density

of the given potential would be :

(A) 0 (B) 0 06 (C) 0 02 (D) 0

0

6

8. The current density J

inside a long, solid cylindrical wire of radius a 12mm is in the direction of the central

axis, and its magnitude varies linearly with radial distance r from the axis according to 0J rJ

a where

5

0 2

10 AJ

4 m

. The magnitude of magnetic field at

ar

2 in T is :

(A) 10 T (B) 4 T (C) 5 T (D) 3 T

SECTION - IIMultiple Correct Answers Type

This section contains 6 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.



PHYSICS


9. For the situation shown in the figure (assume r >> length of dipole) mark out the correct statement.

(A) Force acting on the dipole is zero

(B) Force acting on the dipole is approximately 30

PQ4 r

and is acting upward.

(C) Torque acting on the dipole is 20r4

PQ

in clockwise direction

(D) Torque acting on the dipole is 20r4

PQ

in anti-clockwise direction

10. A current of 4A flows in a coil when connected to a 12V DC source. If the same coil is connected to a 12V,50 rad/sec AC source a current of 2.4A flows in the circuit choose the correct options.(A) The inductance of the coil is 0.08 Henry.

(B) The power developed in the circuit, if a 2500 F capacitor is connected in series with the coil is 17.33W

(C) The inductance of the coil is 0.4 Henry

(D) The power developed in the circuit, if a 2500 F capacitor is connected in series with the coil is 25.28W

11. Which of the following statements is/are correct regarding the electric field produced by changing magneticfield ?(A) It is non-conservative in nature(B) It is non-electrostatic in nature(C) Potential can be defined corresponding to this field(D) The lines of this field are closed curves


PHYSICS


12. A rocket of constant mass starts vertically upwards with speed V0 choose the correct options (R is the

radius of the earth).

(A) Speed V at a height h is given by 2 20

2ghV V

h1

R

(B) The maximum height reached by the rocket fired with a speed of 90% of escape velocity is 2.26R.

(C) The maximum height reached by the rocket fired with a speed of 90% of escape velocity is 4.26R.

(D) Speed V at a height h is given by 2 20

2ghV V

h1

2R

13. An ideal gas can be expanded from an initial state to a certain volume through two different processes

(i) 2PV constant and (ii) 2P KV where K is a positive constant. Based on the given situation, choose the

correct statements.(A) Final temperature in (ii) will be greater than in (i)(B) Final temperature in (ii) will be less than in (i)(C) Total heat given to the gas in case (ii) is greater than in (i)(D) Total heat given to the gas in case (ii) is less than in (i)

14. As a wave propagates(A) The wave intensity remains constant for a plane wave(B) The wave intensity decreases as the inverse of the distance from the source for a spherical wave(C) The wave intensity decreases as the inverse square of the distance from the source for a spherical wave(D) Total powar of the spherical wave over the spherical surface centred at the source remains constant at alltimes.

SECTION - IIIComprehension Type

This section contains 1 paragraph. Based upon each paragraph, 2 multiple choice questions have to beanswered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.


PHYSICS


Paragraph for Question Nos. 15 to 16

Three concentric spherical conducting shells A,B and C of radii R,2R and 4R respectively are shown in figure.A and C are shorted and B is uniformly charged with +Q.

+

+

+

+

++

++

++

++

+

R

4R

2R

A

C

15. The charge on conductor A is :

(A) Q3

(B) Q3

(C) 2Q3

(D) None

16. The potential at A is

(A) 0

Q4 R

(B) 0

Q16 R

(C) 0

Q20 R

(D) None

SECTION - IVMatrix - Match Type

This section contains 1 questions. Each question contains statements given in twocolumns, which have to be matched. The statements in Column-I are labelledA, B, C and D, while the statements in Column-II are labelled p, q, r, s and t. Anygiven statement in Column-I can have correct matching with ONE OR MOREstatement(s) in Column-II. The appropriate bubbles corresponding to the answersto 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 ofbubbles will look like the following :


PHYSICS


17. Column I Column II

(A) Graphical representation of pressure variation in both (p) Maximum kinetic Energy at B end open organ pipe

A B C

(B) Graphical representation of pressure variation in one end (q) Maximum potential Energy at B closed organ pipe

B

(C) Snapshot of string fixed at both ends (r) Maximum particle velocity at B

BA

(D) Snapshot of a string fixed at one end and connected at a (s) Maximum particle acceleration at B smooth massless ring that is constrained to move vertically

B (Extreme position)

(t) Longitudinal wave


PHYSICS


SECTION - VInteger Answer Type

This section contains 4 questions. The answer to each of the questions is a doubledigit integer, ranging from 00 to 99. The appropriate bubble below the respectivequestion number in the ORS have to be darkened.

18. A cyclotron is operated at an oscillator frequency of 80

MHz and has a dee. radius R = 60cm. The magnitude

of magnetic field B (in Tesla) to accelerate deutrons is x

1 0 Tesla. find x ? (mass of deutron 273.34 10 Kg )

19. A wooden stick of length 3L is rotated about an end with constant angular velocity in a uniform magneticfield B perpendicular to the plane of motion. If the upper one third of its length is coated with copper. The

potential difference across the whole length of stick is 2x B L

2

, find x ?

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

3L

L


PHYSICS


20. r and r ' denote angle inside an equilateral prism as usual, in degrees consider that during some time interval

from t 0 to t t , r ' varies with time 2r ' 10 t , During this time r will vary as x � t2 . Find x ?

21. A certain region of a soap bubble reflects red light of vacuum wavelength = 650 nm. The minimumthickness that this region of soap bubble could have is 13 × 10�x m. Find x ? (The index of reraction ofthe soap film is 1.25)


RESONANCE

CHEMISTRY

JPT1PAPER2190513C0-9

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]


This section contains 8 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out ofwhich ONLY ONE is correct.

22. 100ml of a buffer of 1M NH3(aq) and 1M NH

4+(aq) are placed in two half cells separately. A current of

1.5amp is passed through both half cells for 20min, if electrolysis of only water take place. The pH of :(A) Anode half cell will decrease (B) Cathode half cell will decrease(C) Both half cell will decrease (D) Both half cell remain same

23. 100 ml 0.1 M H2O

2 is mixed with 400 ml 0.5 M H

2O

2. The volume of 0.1 M KMnO

4 (acidic) required to react

with H2O

2 mixture is :

(A) 840 ml (B) 420 ml (C) 630 ml (D) None of these

24. How many moles of atoms are present on the surface of 2cm long iron rod assuming cubic shape havingFCC unit cell edge length 0.556nm.(A) 2.57 x 10-8 (B) 6.23 x 10-7 (C) 4 x 106 (D) 2.24 x 10-2

25. Identify the correct relation between rate constant (k), activation energy (Ea), temperature T (K)

(A) a2

1 1 2

Ek 1 1log

k 2.303R T T

(B)

21

a

1

2

T1

T1

R

E

k

klog

(C)

21

a

1

2

T1

T1

R

E

k

klog (D)

21

a

1

2

T1

T1

R303.2

E

k

klog


RESONANCE

CHEMISTRY



26. The difference between standard electrode potential (reduction) of metal-metal insoluble salts of AgCl andAgBr is x. Calculate the ratio of the solubility product of AgCl and AgBr.

(A) anti log

059.0

x(B) anti log

x2 0.059

(C) anti log

4x0.059

(D) None of these

27. Hydrolysis of XeF4 and CaNCN gives respectively :

(A) XeO3 and CaCO

3(B) XeO

2 and CaCN

2(C) XeOF

3 and CaCN

2(D) XeOF

2 and CaCO

3

28. The aromatic electrophilic substitution reaction is :

(A) /OCu/NH 23

(B) /SOH.Dil 42

(C) )H()ii(

fusion,NaOH)i(

(D) 42SOMe/NaOH

29. When 50ml of HCl is treated with excess of K2Cr

2O

7. The volume of Cl

2 liberated is 5.6 litres at STP. which the

following option is/are correct.(A) Molarity of HCl = 5 M (B) Molarity of HCl = 10 M(C) Molarity of HCl = 13.33 M (D) Molarity of HCl = 23.33 M

SECTION - IIMultiple Correct Answer Type

This section contains 6 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out ofwhich ONE OR MORE is/are correct.

RESONANCE

CHEMISTRY



30. Select the correct option(s) for the following statements.(A) Bimolecular elimination of alkyl halides is a stereospecific reaction.(B) In S

N2 reaction a single isomer is the only product.

(C) Alcohol dehydrate in strongly basic conditions by E1 mechanism.(D) 3 hydroxypropanal dehydrates in strong basic condition by E1 cb mechanism.

31. Which of the following statement are correct(A) Strength of H-bonding : HF > H

2O > NH

3

(B) Strength of H-bonding : .... .... ....F H O O H O F H F

(C) Boiling point : 2 3H O HF NH

(D) Dipole moment : 2 3HF H O NH

32. When 2 2 7K Cr O is treated with H2O

2 then

(A) In strong acidic medium deep blue-violet complex 2 2CrO O is formed

(B) In less acidic medium violet, coloured complex

2CrO O OH is formed

(C) In alkaline medium 3

2 4Cr O

is formed

(D) In ammonical solution 3 43NH CrO dark red-brown compound is formed.

33. Which of the following orders of bond angle is/are not correct.

(A) 3 3 3NH PH AsH (B) 2 2 2Cl O OF H O

(C) 4 4 4CH SiH GeH (D) XeO3 > XeF

4 > XeOF

4

34. Which of the following is/are correct option for the reaction

2 ,5 3 2,5 R R Hex en diol 4KMnO.Cold dil

31. HCO H

(M) + (N)

(X) + (Y)22 . H O

(A) (X) and (Y) are optically active (B) (M) and (N) are optically active(C) (M) and (N) are enantiomers (D) (X) & (Y) are diastereoisomers

RESONANCE

CHEMISTRY



35. The correct statements are :

(x) + base

(y) OH/Zn)ii(

O)i(

2

3 (z) +

(A) If (x) is PhCH=O, then (z) is also PhCH=O

(B) If (x) is PhCH=O, then (y) is Ph�CH=CH�CH=CH�COOH

(C) If (z) is , then (y) is

(D) x can be CH3�CH=O.


This section contains 1 paragraphs. Based upon each paragraph, there are 2 questions. Each question has4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Question Nos.36 & 37

Depressing in freezing point is that the solution always freezes at lower temperature than the freezing point

of solvent. f fT k m for non-electrolytes. where as for electrolytes we have to use the vant Hoff factor (i).

36. A saturated solution of a sparingly soluble metal chloride MCl2 has a vapour pressure of 31.78mm of Hg at

30ºC, while aquesous tension of water at 30ºC is 31.82mm of Hg. The solubility product of salt is

(A) 3.1 x 10-5 (B) 4.1 x 10-5 (C) 5.1 x 10-5 (D) 6.1 x 10-5

37. 1000g of 3 molal aqueous solution of Urea is cooled at -4ºC. Then the mass of

ice separated out is :[K

f(H

2O) = 1.86 K molal�1 ]

(A) 152 g (B) 446 g (C) 845 g (D) none of these

RESONANCE

CHEMISTRY



SECTION - IVMatrix - Match Type

This section contains 1 questions. Each question contains statements given in twocolumns, which have to be matched. The statements in Column-I are labelledA, B, C and D, while the statements in Column-II are labelled p, q, r, s and t. Anygiven statement in Column-I can have correct matching with ONE OR MOREstatement(s) in Column-II. The appropriate bubbles corresponding to the answersto 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 ofbubbles will look like the following :

38. Column-I Column-II

(A) OH (p) Aromatic ring substitution

(B) OH/OCHCH3 (q) Nucleophilic addition

(C) 423 SOHHNO (r) Condensation reaction

(D) H/KCN (s) Formation of more than one organic products

(t) Self redox reaction.

RESONANCE

CHEMISTRY




This section contains 4 questions. The answer to each of the questions is a doubledigit integer, ranging from 00 to 99. The appropriate bubble below the respectivequestion number in the ORS have to be darkened.

39. A 5g sample containing Fe3O

4 (FeO + Fe

2O

3) and an inert impurity is treated with excess of KI solution in the

presence of dilute H2SO

4. The entire iron converted to Ferrous ion along with liberation of Iodine. The resulting

solution is diluted to 100 mL. 20 mL of the diluted solution requires 10 mL of 0.5M Na2S

2O

3 solution to reduce

the iodine present. Calculate approximate percentage of Fe2O

3?

40. Isomeric alkynes having the molecular formula C3FClBrI have the following characteristics �P� = number of

positional isomers, �R� = number of fractions obtained on fractional distillation of a mixture of all possible

alkyne. What is the sum of �P� and �R�?

41. OH (Y) [No. of isomeric product obtained].

42. Balance the given below reaction

2 3 3 3 4 2 4 2xAs S yNaOH zNaClO aNa AsO bNa SO cNaClO dH O Calculate the value of

x y z a b c , when the molar coefficient are in simplest whole number ratio.


MATHEMATICS

PART- III - MATHEMATICS


This section contains 8 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out ofwhich ONLY ONE is correct.

43. Position vectors of vertices A, B, C of ABC are c,b,a

respectively and |a�b|3|a�c|

from C, CD is

drawn perpendicular to the bisector of angle A then(A) line BC is perpendicular bisector of AD(B) BC bisects AD

(C) PAB and PCD are congruent(here �p� is the point of intersection of bisector with side BC)(D) none of these

44. For x 2 ,3 and y R the number of ordered pair satisfying equation

23 sinx cos x 3y 6y 5 0 will be

(A) 8 (B) 4 (C) 6 (D) 3

45. If a b

tan .tana b

then value of a bcos2 a bcos2 is

(A) 1 (B) Independent of � �

(C) Independent of and both (D) None of these

46. If 5

sin3x A sin2x Bsin xf x ,x 0

x

then the value of f 0 A B equal to (Considering f(x) to be

continuous at x 0 )(A) 0 (B) 2 (C) � 2 (D) None of these


Kishalay Raj

Pencil

Remember Angle bisectors divide the side they cut in the ratio of the opposite side.


MATHEMATICS


47. A plane P passes through (1, 0, 0) and (0, 1, 0) and makes positive intercept on the z-axis if the plane P

makes 4

angle with the plane x + y = 3 ; then direction ratios of the plane Q through origin such that it

contains line of intersection of plane �P� and the given plane, are

(A) 4 4

, , 23 3

(B) 2,2, 2 (C) 2 2

, , 23 3

(D) 2,2, 2

48. If function f(x) = |x2 + a|x| + b| has exactly three points of non differentiability then which of the following canbe true(A) b = 0, a < 0 (B) b < 0, a R (C) b > 0 , a R (D) all of these

49. A function y = f(x) satisfies the differential equation 0x

xsinxcosy�xsin

dxdy

2

2

such that x

lim f(x) = 0

then which fo the following is not true

(A)

2/

02

dx)x(f1 (B) f(x) is an odd function

(C) 0xlim

f(x) = 2 (D) both (B) & (C)

50. The least value of �a� for which equation 4 1

sin 1 sina

x x

has atleast one solution in the interval

2,0 is

(A) 3 (B) 11 (C) 7 (D) 9

SECTION - IIMultiple Correct Answer Type

This section contains 6 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out ofwhich ONE OR MORE is/are correct.


MATHEMATICS


51. Let a, b, c be the distinct complex numbers such that cba and aa�cb then considering A, B,

C as their geomertical images -(A) a + c = 0 (B) b + c = 0(C) (AB) is perpendicular to (AC) (D) (BC) is perpendicular to (AB)

52. The sides of a right angled triangle form a geometric progression then cosine of the acute angles will be

(A) 5 12

(B) 5 12

(C) 2

5 1(D)

5 12

53. For the function x

0

dt|t|2)x(f , the equation of tangents which are parallel to 2x � 2y + 3 = 0 will be

(A) 21

xy (B) 21

�xy (C) 41

�xy (D) 41

xy

54. The possible negative values of real number �a� such that

0

a

t�t2� 0dt)9.2�9( is

(A) �2013 (B) 2013

2 (C) �2 (D) �1

55. L1 :

1 2 32 3 4

x y z

L2 :

2 4 53 2 5

x y z

be two given lines, point P lies on L1 and Q lies on L

2 then distance between

P and Q can be

(A) 31

(B) 91

(C) 15 (D) 30


MATHEMATICS


56. The locus of z such that 2 i3 1

zz

, represents a circle than the values of can be

(A) 23

(B) 1 (C) 4 (D) 2


This section contains 1 paragraphs. Based upon each paragraph, there are 2 questions. Each question has4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Question Nos. 57 to 58

If 1/ 2 1/ 410 10 10log x + log x + log x +.... = y and

10

1+ 3 + 5 +....+ upto y term 20=

4 + 7 +10 +....+ upto y term 7log xthen

57. The value of �x� equals to(A) 10 (B) 103 (C) 105 (D) none of these

58. The value of �y� equals to

(A)107

(B) 10 (C) 510 (D) none of these

SECTION - IV

Matrix - Match TypeThis section contains 1 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 drakened 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 :


MATHEMATICS


59. Column - I Column - II

(A) Number of ordered pair (x, y) satisfying (p) 82

sin2 cos2 sinx x y when x & y ∈ -2 , 2

(B) If f(x) = tan�1(x2 � 18x + a) and (q) 68

1

g x = + n f xf x

then least integral value

of �a� so that g(x) is defined for all real �x�

(C) The value of

80ð-1

0

cos cosx dx

- 2

(r) 70

(where [.] denotes greatest integer function)

(D) Number of n-digit numbers in which digits 3, 5 (s) 80are present but 0, 1, 8, 9 are not present comesout to be of the form (An � 2.Bn + Cn) then where

A > B > C 10A 2B C equals to (t) 74


This section contains 4 questions. The answer to each of the questions isa double digit integer, ranging from 00 to 99. The appropriate bubble belowthe respective question number in the ORS have to be darkened.


MATHEMATICS

60. What are the number of possible integral values of �a� such that the polynomial f(x) = ax3 + bx

2 + cx + d,

(b,c,d Z) equals to 1 at x = 19 and equal to 2 at x = 62.

61. All concurrent chords to the curve 3x2 � y2 � 2x + 4y = 0 , which subtends right angle to the origin passthrough (a, b) then |a| + |b| equals to

62. A circle passes through the point A(1, 0), B(5, 0) and touches y-axis. If C(0, h) is on y-axis and ACB ismaximum then find the value of [|h|] (where [.] is greatest integer function)

63. If the area of the region bounded by point (x, y) satisfying the condition

2x,y ;0 y x 1,0 y x 1,x 0,x 2,y 0 is A (unit)2 then23A

equals to


Name of the Candidate Roll Number

I have read all the instructions andshall abide by them.

-------------------------------- Signature of the Invigilator

I have verified all the informationfilled in by the Candidate.

-------------------------------- Signature of the Candidate

(Space for rough work)

JEE PREPARATORY TEST-1 (JPT-1) (JEE ADVANCED)

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Transcript of JEE PREPARATORY TEST-1 (JPT-1) (JEE ADVANCED)