Ct 3 Paper 1 Code 0 Jee Advanced 12-05-2013

8/12/2019 Ct 3 Paper 1 Code 0 Jee Advanced 12-05-2013

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PAPER 1INSTRUCTIONSA. General :

1. This Question Paper contains 66 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 Top-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 ballpoint 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 of Four

Sections.

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(s) in this section.

18. For each question in SectionIII, you will be awarded 3 marks if you darken the bubble corresponding to

the correct choice for the answer and zero mark if no bubbled is darkened. There is no negative marking

for incorrect answer(s) in this section.

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

the correct choice for the answer and zero mark if no bubbled is darkened. There is no negative marking

for incorrect answer(s) in this section.

DONOTBREAKTHESEA

LSWITHOUTBEING

INSTRUCTEDTODOSOB

YTHEINVIGILATOR

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

Date : 12-05-2013 Duration : 3 Hours Max. Marks : 228

O E0

CUMULATIVE TEST-3 (CT-3)-JEE (ADVANCED)

TARGET : JEE (ADVANCED)-2013 COURSE : REVISION CLASSES


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PHYSICS

Space for Rough Work

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PART I : PHYSICS

SECTION - I

Straight Objective TypeThis section contains 8 multiple choice questions. Each question has choices (A), (B), (C) and (D), out

of which ONLY ONEis correct.

1. At shown instant a thin uniform rod AB of length L = 1m and mass m = 1 kg is coincident with y-axissuch that centre of rod is at origin. The velocity of end A and centre O of rod at shown instant are

i2VA !"!

m/s and i10Vo "!

m/s respectively. Then the kinetic energy of rod at the shown instant is :

A

O

B

y

x

(A) 42 J (B) 56 J (C) 74 J (D) None of these

2. A particle of mass 2kg is moving such that at time t, its position vector, in metre, is given by jt2i5r 2!"!

.

The angular momentum of the particle at t = 2 second about origin in kg.m2sec1is :

(A) k40! (B) k80! (C) k80 (D) k40


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PHYSICS


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3. A block is suspended by a spring initially in natural length

"o. Take initial position of block as zero reference level for

gravitational potential energy of block. The block is

released from rest at its initial position. Now as the block

comes down till the maximum downward displacement

of the block for the first time, the sum of the elastic

potential energy of the spring and the gravitational potential

energy of the block:

/////////////////////////

0

x

zero gravitationalP.E. level

Initial positionof block

(A) increases

(B) decreases

(C) can either increase or decrease depending on the spring constant

(D) decreases first then increases

4. A particle of mass m0, travelling at speed v0, strikes a stationary particle of mass 2m0. As a result, the

particle of mass m0is deflected through 45 and has a final speed of 2

v0. Then the speed of the particle of

mass 2m0after this collision is :

(A)2v0 (B)

22v0 (C)

0v2 (D) 2v0

5. AB is small object dipped in water at a depth of d. Its length is ". It is

seen from air at near normal incidence. The length of the image is:

(A) " (B) #"

(C) "/ # (D) #$1"


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6. Figure %given below shows a glass vessel, partially filled with water. A narrow beam of light is incidentvertically down into the water and passes straight through. Figure %%shows the vessel glass tilted until theangle &, such that the light is refracted along the lower surface of the glass. If refractive indices of air, water

and glass are 1,3

4and 1.5 respectively then :

water

AIR

Glass

Figure 1

&

Figure II

(A) sin &=4

3(B) cos &=

4

3(C) sin &=

9

8(D) cos &=

9

8

7. An insect moves along a semi-circular transparent track of radiusR, with a constant speed V

0. It is start from point O. A point soure

of light is fixed at the centre of the circle. What is the velocity of

shadow of the insect on the surface at time t.

(A) V0sin '

(

)*+

,R

tV0(B) V

0cosec2 '

(

)*+

,R

tV0

(C) V0sec2 ''

(

)**+

,

tV

R

0(D) V

0sec2 '

(

)*+

,R

tV0


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PHYSICS


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8. Amplitude of simple pendulum is 60. Find the tension in string when str ing makes an angle of 30 with

vertical.

(A) mg2

3(B) 233 ! mg (C) mg '

'(

)**+

,!1

2

33(D) none of these

SECTION - II

Multiple Correct Answers TypeThis 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.

9. When two blocks connected by a stretched spring (as shown) start moving from rest towards each

other under mutual interaction. Then (pickup the correct alternative or alternatives)

(A) their velocit ies are equal and opposite. (B) their accelerat ions are equal and opposite.

(C) the force acting on them are equal and opposite. (D) their momentum are equal and opposite

10. A wedge is moved rightwards. A block of mass 10kg is placed on it. Friction

coefficient between wedge and block is 0.8. [take g = 10 m/s2]

(A) If wedge is moving with constant velocity then friction acting

on block is 64N.

(B) If wedge is moving with constant velocity then acceleration

of block is zero.

(C) If wedge is moving with a = 2 ( i ) m/s2then friction acting on block is 44N.

(D) If wedge is moving with a = 10 ( i ) m/s2 then friction is zero.


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11. A particle which can move along x-axis is released from rest at the position x = x0. The potential energy (U)

of block is described below :

U =/01

2

3!

0x;bx

0x;ax2

Which of the following statement is/are correct:

(A) The subsequent motion is simple harmonic

(B) The subsequent motion is periodic(C) The speed is a continuous function of time

(D) The magnitude of acceleration is a continuous function of time

12. A rigid body undergoing pure rolling encounters horizontal rigid tracks AB and BC as shown. AB is smooth

surface and BC is rough surface with #= 1. Which of the following statements is/are correct :

(A) Angular momentum of the rigid body is conserved only about a point on the horizontal surface.

(B) Angular momentum of the rigid body is conserved about every point in space.(C) In part BC, there will be no frictional force on the rigid body.

(D) In part BC, frictional force will act opposite to velocity of rigid body.

13. A uniform disc (with block) is rotating with constant angular

speed 4about vertical axis passing through its centre asshown in diagram. A small block of mass 'm' does not slip

on disc and this block is also performing uniform circular

motion with angular speed 4. Which of the followingstatements is/are correct :

(A) Power delivered by disc to the block is zero

(B) Acceleration vector of block is not constant with time

(C) Torque of normal force on block about vertical axis is zero(D) Torque of friction force on the block about vertical axis is zero



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14. Two persons A and B wear glasses of optical powers (in air) P1= + 2 D and P2= + 1D respectively. The

glasses have refractive index 1.5. Now they jump into a swimming pool and look at each other. B appears

to be present at distance 2m (from A) to A. A appears to be present at distance 1m (from B) to B. then

(A) Refractive index of water is 1.2

(B) Acctual distance between A and B is3

200cm

(C) Acctual distance between A and B is 50 cm

(D) Combined power of two glass (when placed in contanct in air) is +3D

SECTION - III

Comprehension TypeThis section contains 2 paragraphs. Based upon each paragraph, 2 multiple choice questions have to

be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Question Nos. 15 to 16

Three massless rods are f ixed to form a right angled triangular frame such that AB = BC = " = 22 m.

Two identical small objects each of mass m = 1kg are fixed at A and C. The f rame is hinged about Bsuch that the frame can rotate in vertical plane about an horizontal axis without friction. Initially AB is

vertical and BC is horizontal and the system is released from rest.

15. The maximum shift of centre of mass of two mass system from its initial position is

(A) 4 m (B) 22 m (C) zero (D) 24 m

16. The tangential acceleration of mass A when the rod AC becomes horizontal is :

(A) g (B) g2 (C) 3 (D) zero


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A point object 'O' is placed in a cylindrical solid glass rod on axis as shown in figure. One end of the rod is in

spherical shape of radius of curvature 20 cm and the other end is plane surface. Apparent distance (for near

normal incidence when observed from just outside the surface) of object when observed from plane surface

and curved surface are 10 cm and 20 cm respectively. Here n represents the refractive index of medium.

17. Actual distance of object from plane surface

(A) 40 cm (B) 30 cm (C) 20 cm (D) 20/3 cm

18. Actual distance of object from curved part :

(A) 45 cm (B) 60 cm (C) 20 cm (D) cannot be calculated

SECTION - IV

Integer Answer Type

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

single digit integer, ranging from 00 to 99. The appropriate bubble below the

respective question number in the ORS have to be darkened.


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19. The system shown is in equilibrium in vertical plane. All the rods and the

supports A & B are light and friction coefficient between supports and

horizontal rod is #. If maximum value of angle 5is 37 then find the value of4#. Assume light rod exerts force only along the rod.

20. In figure shown minimum mass of block B (at a particular angle between horizontal and

string AP) to just slide the block A on rough horizontal surface is2

mas shown in figure.

If #is the coefficient of friction between block A and ground then 21

#will be :

21. The blocks of mass m1= 1 kg and m

2= 2 kg are connected by an ideal spring, rest on a rough horizontal

surface. The spring is unstressed. The spring constant of spring is K = 2 N/m. The coefficient of friction

between blocks and horizontal surface is # "2

1. Now the left block is imparted a velocity u towards right as

shown. The largest value of u (in m/s) such that the block of mass m2never moves is (Take g = 10m/s2)

22. An object lies in front of a thick parallel glass slab (nglass= 3/2), the bottom of which is polished. If the

distance between first two images formed by bottom surface is 4cm, if the thickness of the slab isx mm then x is. [Assume paraxial rays only ]


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CHEMISTRY

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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

Straight Objective Type

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

23. If series limit (in nm) of a series of hydrogen spectrum which contains a photon of wavelength 1278.35 nm is

expressed asx

1240, then x is : (Given : hc = 1240 eV-nm)

(A) 1.51 eV (B) 2 eV (C) 3.4 eV (D) 0.66 eV

24. The order of first electron affinity of O, S and Se is :

(A) O > S > Se (B) S > Se > O (C) Se > O > S (D) S > O > Se

25. The gaseous decomposition of Cl2O7(gas) takes place according to following reaction

Cl2O

7(g) !"! Cl

2(g) + 7/2 O

2(g)

When decomposition is carried out in a closed container, pressure measured after 15 minute and after a very

long time were found to be 375 mm of Hg and 900 mm of Hg respectively, the ratio of partial pressure of Cl2gas after a very long time and after 15 minute is :

(A) 6 (B) 4 (C) 5 (D) 1

26. Potassium dichromate on heating does not gives :

(A) O2

(B) Cr2O

3(C) K

2O (D) K

2CrO

4

27. The SRP for S2(aq) /CuS/Cu half-cell is ?

Given : Ksp

(CuS) = 1035and0

Cu/Cu2E

# = 0.34 V

(A) 1.034 V (B)1.034 V (C)0.694 V (D) 0.694 V



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CHEMISTRY

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28. Boron can be obtained by various methods but not by :

(A) thermal decomposition of B2H

6(B) pyrolysis of BI

3(van Arkel)

(C) reducing BCl3with H

2(D) electrolysis of fused BCl

3

29. Amongst the following which is correct statements about the metal sulphide sols?

(A) The sol particles are positively charged due to preferential adsorption of metal ions.

(B) The sol particles are negatively charged due to preferential adsorption of sulphide ions.

(C) The anion of added electrolytes are effective in causing the coagulation of the sol.

(D) The sol is unstabilized due to both the electric charge and hydration of the particles.

30. The preparation of SO3(g) by reaction SO

2(g) +

2

1O

2(g) SO

3(g)

is an exothermic reaction. If the preparation follows the following temperaure-pressure relationship for its %

yield, then for temperatures T1, T

2and T

3. The correct

(A) T3> T

2> T

1

(B) T1> T

2> T

3

(C) T1= T

2= T

1

(D) Nothing could be predicted about temperature through given information

SECTION - II

Multiple Correct Answer Type

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

whichONE OR MORE is/are correct.


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CHEMISTRY

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31. Which of the following statements is/are correct ?(A) White precipitate of silver chloride turns yellow on treatment with sodium arsenite solution.(B) Cu is formed in the borax bead test of Cu2+ion in reducing flame.(C) Mercury(II) nitrate solution gives white precipitate with sodium sulphate solution.(D) Solid zinc oxide and 23 ml of cobalt nitrate solution on heating in oxidising flame in the charcoal cavityproduces green mass.

32. Which is (are) the correct order of molar entropy among the following :

(A) X(s) < X(l) < X(g) (B) diamond > graphite(C) white phosphorous > black phosphorous (D) H2(g) < D

2(g)

33. Saturated hydrocarbon gas is evolved by hydrolysis of carbide(s) is/are :

(A) CaC2

(B) Al4C

3(C) Mg

2C

3(D) Be

2C

34. An ideal gas is taken from the same initial pressure P1to the same final pressure P2by three differentprocesses. If it is known that point 1 corresponds to a reversible adiabatic and point 2 corresponds to asingle stage adiabatic then

(A) Point 3 may be a two stage adiabatic process.(B) The average K.E. of the gas is maximum at point 1(C) Work done by surroundings in reaching points 1 or 2 will be positive(D) The points 3 and 4 may lie along the process having PV2= constant

35. Select correct option(s) :(A) Both PCl3F2and PCl2F3are polar moleculars(B) B2Cl4is a planar molecule

(C) Both benzene and borazine (inorganic benzene) are isoelectronic and have same dipole moment(D) Hybridisation state of central atoms in $Cl2

and $3is different.


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CHEMISTRY

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36. Which of the following statements are correct?

(A) Liquid oxygen sticks to the poles of magnet.

(B) AIF3and AgF are water soluble compound.

(C) The ionization energy of silver is less than that of gold.

(D) Many peroxides are coloured because of the presence of superoxides.

SECTION - III

Comprehension TypeThis section contains 2 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.


A previously evacuated isothermal chamber is divided

in two compartments, each of equal volume 2 Lit, by

a freely movable, massless, frictionless piston as

shown in the figure. Initially, this piston is held locked.

Bulb 1 contains a volatile liquid L (P = 500 torr)

while bulb 2 contains a volatile solid S (P = 300 torr),

filled completely with 1 mol each of L and S

respectively. In the first question, assume the

condensed phases to be always present and to have

negligible volume as compared to that of vapour. The

amount in vapour phase may be assumed to be

negligible as compared to the liquid phase.

The stopper of bulbs 1 and 2 are opened with a remote control at time t = 0. [Take 17 = 4.125]

37. The sum of pressure inside compartments I & II after sufficient time has passed is :

(A) 500 torr (B) 300 torr (C) 400 torr (D) 800 torr

38. If the compartments initially contained air at 800 torr pressure and piston is released, the volume of

compartment-I after sufficient time has been passed, is :

(A) 2 Lit. (B) 1.75 Lit. (C) 1.5 Lit. (D) 2.25 Lit.


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CHEMISTRY

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According to MOT, two atomic orbitals overlap resulting in the formation of molecular orbitals. Number of

atomic orbitals overlapping together is equal to the molecular orbital formed. The two atomic orbital thus

formed by LCAO (linear combination of atomic orbital) in the same phase or in the different phase are known

as bonding and antibonding molecular orbitals respectively. The energy of bonding molecular orbital in lower

than that of the pure atomic orbital by an amount%. This is known as the stabilization energy. The energy of

antibonding molecular orbital is increased by %, (destabilisation energy).

39. Which of the following statements is not correct regarding bonding molecular orbitals ?

(A) Bonding molecular orbitals possess lesser energy than the atomic orbitals from which they are formed

(B) Bonding molecular orbitals have low electron density between the two nuclei.

(C) Electron in bonding molecular orbital contributes to the attraction between atoms.

(D) They are formed when the lobes of the combining atomic orbitals have the same sign.

40. If x-axis is the molecular axis, then &-molecular orbitals are formed by the overlap of :

(A) s + pz

(B) px+ p

y(C) p

z+ p

z(D) p

x+ p

x

SECTION - IV

Integer Answer Type

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.

41. A sample of calamine ore (ZnCO3) contains clay as impurity. Clay impurity loses some amount of its weight

as moisture on prolong heating. If the total loss in weight of ore on heating (due to CO2and H

2O) is 28% and

the percentage purity of ore is 62.5%, then the % loss in weight of clay is :(Given Atomic masses : Zn = 65, C = 12 , O =16)


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42. An element X (atomic weight = 24 gm/mol) forms a face centered cubic lattice. If the edge length of the lattice

is 4 108cm and the observed density is 2.40 103kg/m3, then the percentage occupancy of lattice points

by element X is : (Use NA= 6 1023) :

43.

Arrangement -I Arrangement -II

The difference in height of the mercury column in two arms of U tube manometer in arrangement$is h1= 660

mm. In another arrangement$$at same temperature, 222 gm of CaCl2is dissolved in 324 gm of water and

difference in height of mercury column in two arms is found to be h2= 680 mm. If the value of degree of

dissociation for CaCl2in arrangement$$is'then the value of 64 'is : [Atmospheric pressure = 1 atm]

44. The value of equilibrium constant (Kf) for the reaction :

Zn2+(aq) + 4OH(aq) Zn(OH)4

2(aq) is represented in scientific notation as p10q,

then q is :

Given : Zn2+(aq) + 2e !"! Zn (s) ; E =0.76 V

Zn(OH)42(aq) + 2e !"! Zn (s) + 4OH(aq) ; E =1.36 V

2.303F

RT= 0.06


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MATHEMATICS

PART- III - MATHEMATICS

SECTION - I

Straight Objective Type

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

45. If a pair of variable straight lines 0xyy4x22 !"" (where is a real parameter) cut the ellipse 4y4x 22 !"

at two points A and B, then the locus of the point of intersection of tangents at A and B is

(A) 0xy8y4x22 !"# (B) $ % $ % 0yx2yx2 !"#

(C) 0xy4y4x22 !"# (D) $ %$ % 0y2xy2x !"#

46. Ifb

c

c

b2

bc

a"!# , where a, b, c > 0, then family of lines ax by c 0" " ! passes through the fixed

point given by(A) (1, 1) (B) (1, -2) (C) (-1, 2) (D) (-1, 1)

47. If |z - 1| = 1 and $ % and0zwhere,zarg &! is acute, thenz

21# is equal to

(A) tan (B) tani (C) 2

tan

(D)2

tan

48. In 222 a2cbif,ABC !"' , then value ofCcotBcot

Acot

"is

(A)2

1(B)

2

3(C)

2

5(D)

3

5



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MATHEMATICS


49. The abscissa of point on curve ay2= x3, normal at which cuts off equal intercepts from the coordinate

axes is

(A)9

a2(B)

9

a4(C)

9

a4# (D)

9

a2#

50. Let $ %f : X Y, f x sinx cosx 2 2( ! " " is invertible, then YX( is / are

(A) ) *23,24

5,4

(+,-.

/0 (B) ) *23,2

43,

4(+

,-.

/0#

(C)3

, 2, 3 24 4

1 10 - 0 -(. + / ,/ ,(D) ) *23,2

4,

4

3(+

,

-./

0##

51. The number of values of c such that the straight line 3x + 4y = c touches the curvex4

2= x + y is:

(A) 0 (B) 1 (C) 2 (D) 4

52. Let a curve $ % $ % Rx0xf,xfy 234! has property that for every point P on the curve length of subnormal isequal to abscissa of P. If f(1) = 3, then f(4) is equal to

(A) 62# (B) 62 (C) 53 (D) 0

SECTION - II

Multiple Correct Answer Type

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

whichONE OR MORE is/are correct.


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MATHEMATICS


53. If the sum to n terms of the series ,Sis....3.4.2

5

2.3.2

4

1.2.2

3n321

""" then

(A) 2Slim nn

!5(

(B) $ %1n2

11S

nn "#! (C) $ %1n2

12S

nn "#! (D) 1Slim n

n!

5(

54. Let f(x) = $ %67

68

9

#:;&::#

!1

1xor1xforxx)0x(1x1forsinx

0xfor0

x2

, then:

(A) f(x) is an odd function (B) f(x) is an even function

(C) f(x) is neither odd nor even (D) f3f x max 2 x , 2 x , then! # #

(A) f(x) is continuous Rx 23 (B) f(x) is differentiable Rx 23

(C) f(x) is non-differentiable at one point only (D) f(x) is non-differentiable at 4 points only


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MATHEMATICS


58. The point of inflection for the curve1x

1xy

2 "

"! is

(A)1 3

2 3,4

? @## #A BA B

C D(B)

BB

D

@

AA

C

? ##"#

4

31,32

(C) B

B

D

@

A

A

C

? ""#

4

31

,32 (D) (1, 1)

SECTION - III

Comprehension TypeThis section contains 2 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.


A coplanar beam of light emerging from a point source have equation $ % R,012yx 2!""# . The rays ofthe beam strike inner part of an elliptical surface and get reflected. The reflected rays form another conver-

gent beam having equation $ % R,012yx 2!#"# . Further it is found that the foot of the perpendicular

from the point (2, 2) upon any tangent to the ellipse lies on the circle 05y4yx22 !##" .

Now answer the following questions :

59. The area of the largest triangle that an incident ray and the corresponding reflected ray can enclose with theaxis of the ellipse is equal to

(A) 54 (B) 52 (C) 5 (D) none of these

60. Total distance travelled by an incident ray and the corresponding reflected ray is the least if the point ofincidence coincides with(A) an end of the minor axis (B) an end of the major axis(C) an end of the latus rectum (D) anywhere on ellipse


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P1CT312513C0-19

MATHEMATICS



Let r!

is a position vector of a variable point in Cartesian OXY plane such that

$ %2 2

1 2 r . 10 j 8i r 40 and p max r 2i 3 j , p min r 2i 3 j

9 E 9 E# # ! ! " # ! " #8 F 8 F

7 G 7 G

! ! ! !

. A tangent line is drawn to the

curve 2x

8y! at the point A with abscissa 2. The drawn line cuts x - axis at a point B.

Now answer the following questions :

61. p1+ p

2is equal to

(A) 2 (B) 10 (C) 18 (D) 5

62. OB.AB is

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

SECTION - IV

Integer Answer Type

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.


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P1CT312513C0-20

MATHEMATICS

63. Let $ % $ % $ %kj5iCandk2j3iB,k5j3i2A """"#"" are vertices of a triangle and its median through A isequally inclined to the positive directions of the axes. The value of H+ is equal to

64. If 6-digit number abcdef is multiplied with 6 and the resulting number is defabc. Then a + b + c + d + e + f is

65. Suppose that the side lengths of a triangle are three consecutive integers and one of the angles is twiceanother. The perimeter of such a unique triangles is

66. If f(x + y + z) = f(x) + f(y) + f(z) with f(1) = 1 and f(2) = 2 and x, y, z R2 , then evaluate

$ % $ %n

r 1

3n

3 4r f 3r

limn

!

(5

I

is equal to



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Ct 3 Paper 1 Code 0 Jee Advanced 12-05-2013

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