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FILENO:IIT-1337/29(28/11/09) HYD-HG/SR IIT SPARK/PAPER-2

CODE Magna

I I

GRAND TEST 1XII STD Spark PAPER 2

Time: 3 hours Maximum marks: 240

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

INSTRUCTIONS

A. General:

1. This booklet is your Question Paper containing 57 questions. The

booklet has 14 pages.2. The question paper CODE is printed on the right hand top corner

of this booklet.

3. Blank papers, clipboards, log tables, slide rules, calculators,cellular phones, pagers, and electronic gadgets in any form are notallowed to be carried inside the examination hall.

4. The answer sheet, a machinereadable Objective Response Sheet(ORS), is provided separately.

5. DO NOT TAMPER WITH / MUTILATE THE ORS OR THEBOOKLET.

B. Filling the ORS

6. On the lower part of the ORS, write in ink, your name in box L1,

your Registration No. in box L2 and Name of the Centre in box L3.Do not write these anywhere else.

7. Write your Registration No. in ink, in the box L4 provided in thelower part of the ORS and darken the appropriate bubble UNDER

each digit of your Registration No. with a good quality HB pencil.

8. The ORS has a CODEprinted on its lower and upper parts.

9. Make sure the CODE on the ORS is the same as that on this booklet and put your signature in ink in box L5 on the ORSaffirming that you have verified this.

10. IF THE CODES DO NOT MATCH, ASK FOR A CHANGE OF

THE BOOKLET.

C. Question paper format:

11. The question paper consists of3 parts (Part I: Chemistry, PartII: Mathematics, Part III: Physics). Each part has 4 sections.

12. Section I contains 4 multiple choice questions. Each question has 4choices (A), (B), (C) and (D), out of which only one is correct.

13. Section II contains 5 multiple correct answer type questions. Eachquestions has 4 choices (A), (B), (C) and (D), out of which one ormore answers are correct.

14. Section III contains 2 questions. Each question has four statements(A, B, C and D) given in column I and five statements (p, q, r, sand t) in column II. Any given statement in column I can havecorrect matching with one or more statements(s) given in columnII. For example, if for a given question, statement B matches withthe statements given in q and r, then for that particular question,against statement B, darken the bubbles corresponding to q and r inthe ORS.

15. Section IV contains 8 questions. The answer to each of thequestions is a single-digit integer, ranging from 0 to 9. The answer

will have to be approximately bubbled in the ORS as per theinstructions given at the beginning of the section.

D. Marking Scheme:

16. For each question in Section I, you will be awarded 3 marks ifyou have darkened only the bubble corresponding to the correctanswer and zero mark if no bubble is darkened. In case of bubblingof incorrect answer, minus one (1) markwill be awarded.

17. For each question in Section II, you will be awarded 4 marks ifyou have darkened all the bubble(s) corresponding to the correctchoice(s) for the answer, and zero markif no bubble is darkened.In all other cases, minus one (-1) mark will be awarded.

18. For each question in Section III, you will be awarded 2 marksfor 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 is no negativemarking for incorrect answer(s) for this section.

19. For each questions in Section IV, you will be awarded 4 marks ifyou darken the bubble corresponding to the correct answer, and

zero mark if no bubble is darkened. In all other cases, minus one (-1) mark will be awarded.

Name of the Student Roll Number

I have read all the instructions and shall abide by them

..

Signature of the Candidate

I have verified all the information filled in by the

Candidate

..

Signature of the Invigilator

NARAYANA IIT JEE ACADEMY

HYD-HG

Test Date : 30 11 - 2009

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CODE : Magna HYD-HG/SR IIT

SPARK/PAPER-2

PART:1 - C H E M I S T R Y

SECTION I

Straight Objective Type

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

which ONLY ONE is correct.

1) In the reaction sequence [ ]X is ketone;

a

)

a)

b) c) d)

2) 3 2CH O CH CH NO 1 =

2 2

2

2 2

CH =CH NO 2CH =CH Cl 3CH =CH 4

Which of the following is the correct order of C C bond length among these compounds?

a) 1 2 3 4> > > b) 4 3 2 1> > > c) 1 3 2 4> > > d) 2 3 1 4> > >

3) In a reaction a Aproducts, the rate is doubled when the concentration of A is increased 4 times.

If 50% of the reaction occurs in 1414 sec , how long would it takes for the completion of 75%

reaction.

a) 4242sec b) 2825 sec c) 2414 sec d) 2121 sec

4)

The oE in the given diagram is

a) 0.52 V b) 0.61 V c) 0.74 V d) 0.83 V

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SECTION II

Multiple Correct Answer 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 MORE5) Which of the following statements are true?

a) 3 2 2CH CH CH I will react more readily than ( )3 2CH CHI for NS 2 reactions

b) 3 2 2CH CH CH Cl will react more readily than 3 2 2 NCH CH CH Br for S 2 reactions

c) 3 2 2 2CH CH CH CH OH will react more readily than ( )3 2 N3CH C CH OH for S i reactions in the presence of pyridine

d) 3 6 5CH O C H Br will react more readily than 2 6 5 2 NNO C H CH Br for S 2 reactions

6) 3(s) (s) 2(g)MCO MO CO+ the equilibrium pressure ofo o

2CO at 127 C and 147 C are 0.14 and

0.35 bar respectively.

a) The enthalpy of the reaction is nearly +64 kj / mole

b) increase in temperature decreases the yield of 2CO gas at equilibrium

c) it is endothermic reaction

d) on addition of 3MCO at equilibrium, the equilibrium shifts towards right

7) Which of the following statements are correct with respect to [ ] ( )2

4 3 22NiCl and Ni PPh Cl

?

a) [ ]2

4NiCl is tetrahedral

b) ( )3 22Ni PPh Cl is tetrahedral

c) ( )3 22Ni PPh Cl is square planar d) [ ]2

4NiCl is square planar

8) Select the correct option against mentioned property

a)

a)

(Rate of reaction with 3CH I )

b)

(Basic nature)

c)

Rate of reaction with 2 4H SO

d) I F > (Nucleofugacity)

9) White phosphorous ( )4P hasa) six P-P single bonds b) covalency of phosphorus, 5

c) four lone pairs of electrons d) PPP angle of 60O

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SECTION III

Matrix Match Type

This section contains 3 questions. Each question contains statements given in two

columns which have to be matched. Statements (A, B, C, D) in Column I have to be

matched with statements (p, q, r, s, t) in Column II. Any statement in Column I can

have correct matching with ONE OR MORE statement(s) in column II. The answers to

these questions have to be appropriately bubbled as illustrated in the following example.

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

then the correctly bubbled matrix should be as shown:

10. Match the following

Column I Column II

(A) Alc.KOH3 2 3 3 3CH CH CH CH CH CH CH CH

|

Cl

= (p) shows Hydrogen effect

(B) (q) doesnt showHydrogen effect

(C) CH2Cl

CH3

Et OH

EtO

(r) shows solvent

isotopic effect

(D) Alc.KOH3 2 3CH CH CH C Ph CH CH CH C Ph

| || ||

Cl O O

= (s) does show elemental

effect

(t) carbanion formation

11. Match the reactions mentioned in Column-I with the nature of the reaction/characteristic(s) of theproducts mentioned in Column-II

Column I Column II

(A) strongly heated3 2H PO (p) One of the products acts as reducing

agent

(B) 2i)H O3 ii)

PCl

(q) One of the products is tribasic

(C)2 2 NO H O+

(r) Dehydration

(D) 3 4 10HNO P O

+ (s) In one of the products the central atomis in +5 oxidation state(t) Disproportionation

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SECTION IV

Integer Answer Type Questions

This section contains 8 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 toquestions numbers 1, 2, 3, 4 and 5 (say) are 2, 1, 4, 2 and 3, respectively then the correct

darkening of bubbles will look like the following.

12)A

Zx in the above nuclear disintegration the number of nuclides having same

isotopic number

13) The hydrolysis constant of the aqueous solution of the salt 2ZnCl is calculated from the expression

( )

( )

x

h y

KwK

Kb

= . The sum of the values of x and y is ___

(Kw=ionic product of water, Kb = dissociation constant of ( )2

Zn OH ) .

14) A flask has N gas molecules out of whichN

10molecules are moving at Zms

-1 ,N

30at yms-1

and the remaining ones are moving at Xms-1 . If rms velocity of the gas is 4.89 ms-1 under sameconditions. What is X?

15)heat

2 6 3 23B H 6NH 3X 2Y 12H+ + . In the anionic part of the intermediate X the covalency ofthe central atom is __.

16) Green vitriolO

300 C anhydrous salthigh

tempL M N + + . If oxidation state of the central atom in

L,M,N are X,Y,Z respectively (X

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Part-II : M A T H E M A T I C S

SECTION I


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

which ONLY ONE is correct.

20) If ( )

2

sin cosecA B 2

2 21 12 2

A A Bt dt 1

A dt,B dt then e B 1 ?1 t t 1 t

1 A B 1

+= = =

+ ++

a) sin b) cosec c) 0 d) 121) The curves

2 2

1 2C : y x 3 ; C : y kx ,k 1= = < intersect each other at two different points. The

tangent drawn to 2C , at one of the points of intersection ( ) ( )1A a, y a 0= > meets 1C again at

( ) ( )2 1 2B 1, y . y y . Then value of a ___?=a) 4 b) 3 c) 2 d) 1

22) Let A(1, 2), B(3, 4) be two points and C(x, y) be a point such that area of ABC is 3 sq.units

and ( ) ( ) ( ) ( )x 1 x 3 y 2 y 4 0 + = . Then maximum number of positions of C, in the xy planeis

a) 2 b) 4 c)8 d) none of these

23) If ( ) ( )2 2sin cos cos sin msin cos then = =

a)1

| m |2

b)1

| m |2

c) | m | 1 d)| m | 1

SECTION II



(C) and (D), out of which One Or More Than One Correct

24) Thirteen persons are sitting in a row. Number of ways in which four persons can be selected so

that no two of them are consecutive is equal to ____

a) number of ways in which all the letters of the word M A R R I A G E are permutated if no

two vowels are never together.

b) number of numbers lying between 100 and 1000 using only the digits 1,2,3,4,5,6,7 without

repetition.

c) number of ways in which 4 alike chocolates can be distributed among 10 children so that each

child getting at most one chocolate.

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d) number of triangles can be formed by joining 12 points in a plane, of which 5 are collinear.

25) Given2 2 2| ax bx c | | Ax Bx C |, x R, a,b,c A,B,C R and d=b 4ac 0 and+ + + + >

2D=B 4AC 0 > . Then which of the following statements are truea) | a | | A | b) | d | | D | c) | a | | A |d) if D,d are not necessarily positive then roots of 2 2ax bx c 0 and Ax Bx C 0+ + = + + =

may not be equal

26) If ( ) 21 1 x

2f x xf 2f 2 sin x 4cos x cos , x R {0}x 4 2 x

+ + = +

then which of the

following statement(s) is/are true?

a) ( )1

f 2 f 12

+ =

b) ( ) ( )f 2 f 1 0+ = c) ( ) ( )1

f 2 f 1 f 2

+ =

d) ( ) ( )1

f 1 f f 2 12

=

27) If each of a,b,c is orthogonal to the sum of the other two vectors and a 3, b 4, c 5= = = then

which of the following statement(s) is/are true

a) ifa

makes angles of equal measures with x,y,z axes, then tangent of this angle is 2

b) range of [ ]| a b | is 1, 7 c) range of [ ]| b c | is 1, 9 d) | a b c | =2 5+ +

28) Which of the following is true.

a) There exists a point in the plane of a parabola through which no real normal can be drawn to the

parabola.

b) If P,Q,R are co-normal points of a parabola then circumcircle of PQR passes through thevertex of the parabola.

c) The circum circle of triangle formed by three tangents of a parabola passes through focus of the

parabola.

d) length of subnormal at any point on a parabola is equal to latus rectum of the parabola.

SECTION IIIMatrix Match Type

This section contains 3 questions. Each question contains statements given in two







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29. We are given M urns, numbered 1 to M and n balls (n

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SECTION IV



integer, ranging from 0 to 9. The appropriate bubbles below the respective questionnumbers in the ORS have to be darkened. For example, if the correct answers to

questions numbers 1, 2, 3, 4 and 5 (say) are 2, 1, 4, 2 and 3, respectively then the correct


31) Number of pairs of positive integers (p,q) whose LCM (Least common multiple) is 8100, is K.

Then number of ways of expressing K as a product of two co-prime numbers is ____

32) If 2 2

tan x 4 tan xsin 4x e dx c A cos x.e then A=___ =

33) The tangents drawn from the origin to the circle 2 2 2x y 2rx 2hy h 0+ + = are perpendicularthen sum of all possible values of

h

ris ___

34) Shortest distance between the z-axis and the line x y 2z 3 0+ + = 2x 3y 4z 4= + + is ___

35) If a , b , c

be non-coplanar unit vectors equally inclined to one another at an acute angle , and if

a b b c p a q b r c then p r=__

+ = + + (p,q,r R)

36) Differential equation, having ( ) ( )2

1 1y sin x A cos x B = + + where A and B are arbitary constants

is ( )2

2

2

d y xdyp x q then p+q=__

dx dx =

37) Given that

( ) ( )y 1 y

1 1 1 2 1 1 2

1 y 1sec x dx then sec x tan x 1 dx sec x tan x 1 dx ___(| y | 1)

= + =

equals to ( )y a b then a+b=___

38) If - 1 2 32 2

< < < < , then number of values of ,

2 2

satisfying

( ) ( ) ( )( ) ( ) ( )

1 2 3

1 2 3

tan tan tan tan tan tan

tan tan tan tan tan tan 0 is___

=

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Part III : P H Y S I C S

SECTION I


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

of which ONLY ONE is correct.

39. Two coherent radio point sources separated by 4.0m are placed at points A and B along a straight

line as shown. Both are emitting waves in phase of 1.0 m wave length. A

detector moves in a circular path around the two sources in a plane containing

them.

Point A and B lie on the diameter of the circle and they are at equidistant from

the center of the circle O as shown. Find the number of maxima counted by the

detector in one full circle.

a) 9 b) 10 c) 15 d) 16

40. A resistor and an inductor in series are connected to a battery through a

switch. After the switch has been closed, what is the magnitude of current

flowing when the rate of the increase of magnetic energy stored in the coil

is at a maximum?

a)V

4Rb)

V

3Rc)

V

2Rd)

V

R

41. Four charges of equal magnitudes but different signs are arranged at the corners of a square, as

shown here. In which arrangement is the magnitude of the electric field at point P a maximum? (Pis the mid point of the side).

a) b) c) d)

42. A particle is dropped along the axis from a heightf

2on a concave mirror of

focal f length f as shown in the figure. The acceleration due to gravity is g.

Find the maximum speed of image.

a) gf b) 3 3fg4

c) 2gf d) 1 2gf4

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SECTION II



(C) and (D), out of which ONE OR MORE THAN CORRECT ANSWER

43. A man stretches a horizontal spring attached to the front wall of a railway carriage over a distance

l in a train moving with uniform velocity. During this time, the train covers a distance L. The

man stretches the spring opposite to the direction of motion of the train. The co-ordinate system

attached to earth is 1s and the co-ordinate system attaches to train is 2s . Then the work preformed

by man in stretching the spring is

a)2

1

1kl in s

2b)

2

2

1kl in s

2c) 1

1kl(L l) in s

2 d) 2 1

1k(L l) in s

2

44. Find the true statements

a) it is easier to launch a satellite into an eastward orbit than into a westward one.

b) effect of friction on an orbiting satellite (assuming the height of the orbit is small so that

atmosphere is present) would finally result in increasing its speed.

c) An astronaut feels weightlessness as the astronauts acceleration is zero.

d) The earth is in free fall under the action of the net gravitational force of the sun and the planets(neglect the effect of other astronomical objects)

45. Charge Q is uniformly distributed on a thin insulating ring of mass m; Which is initially at rest. A

magnetic field perpendicular to the plane of the ring which can attain its maximum value B is

switched on. Let the final angular velocity attained by ring be . then(neglect magnetic field produced by the rotating ring)

a) Magnitude of does not depend on the radius of the ringb) direction of is opposite to the direction of magnetic field, if Q is negativec) Magnitude of depends on the radius of the ringd) Direction of is opposite to the direction of magnetic field, if Q is positive.

46. For piston-cylinder arrangement and different types of ideal gases, a plot of work done (W )

verses heat supplied (Q) is plotted. It is known that one of the straight

lines in the fig. is an isotherm and the other two are isobars of two gases.

The initial states of the two gases are same. It is known that one gas is

helium and the other is 2CO .

a) straight line 3 corresponds to isothermal process

b) straight line 1 corresponds to isothermal process

c) straight line 2 corresponds to He (helium)

d) straight line 2 corresponds to 2CO

47. A particle is subjected to two simple harmonic motion along x and y-directions according to the

equations 4sin 100x t= and 3sin 100 .y t= Choose the correct statementsa) Motion of particle will be on a ellipse b) motion of the particle will be on a straight line

c) particle will execute SHM of amplitude 5. d) particle will not execute SHM.

SECTION III

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Matrix Match TypeThis section contains 3 questions. Each question contains statements given in two







48. A charged particle passes through a region that could have uniform electric field only or uniform

magnetic field only or both uniform electric and uniform magnetic fields or none of these fields.

Some possible paths of motion of the particle inside the given region are mentioned in Column-II.

Match each path in Column-II with the related information in Column-I:

Column I Column II

(A) Both electric and magnetic fields (p

)

Parabola

(B) Electric field only (q

)

Circle

(C) Magnetic field only (r) Straight line

(D) No field (s) Cycloid

(t) Helix

49. An open capillary tube contains a drop of water. When the tube is in vertical position, it forms a

column of water. The internal diameter of the capillary tube is 1mm. Take coefficient of surface

tension of water as 0.075 N/m, density of water as3 310 kg / m and

2g 10m / s= . Assume wetting iscomplete. In column-I length of water column is given. In column-II information about lower

meniscuses is given. Match Column-I with Column-II

Column I Column II

(A) 1.5 cm (p) Shape of the meniscus is convex

(B) 2 cm (q) Shape of the meniscus is concave

(C) 3 cm (r) Shape of the meniscus is flat

(D) 4.5 cm (s) Radius of curvature is 1 mm

(t) Radius of curvature is 1.5 mm

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SECTION IV



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

questions numbers 1, 2, 3, 4 and 5 (say) are 2, 1, 4, 2 and 3, respectively then the correct


50. In the figure a 19 Kg cart is connected by means of a coiled spring to a 38 Kg cart. The two carts

are moving to the right at a speed of 25 m/s when the spring suddenly

becomes uncoiled and propels the 19 Kg cart forward with a speed of

27 m/s. find the speed of the second cart (in m/s) in centre of mass

frame.

51. There is an infinite grid of resistors shown in the diagram. The

resistance of each resistance is R. The equivalent resistance of the

grid between two neighboring grid points is given by2R

nwhen the

resistor joining them is removed. Then find the value of n.

52. A reinforced-concrete column is subjected to compression by a certain load. Assume that modulus

of elasticity of concrete is one-tenth of that of iron and the cross sectional area of the iron is one-

twentieth of that of concrete. IfC

I

Fn

F= . Where CF is the part of the load acting on concrete and IF

is the part of the load acting on iron, then find the value of n

53. Water is being poured in a vessel at a constant volume rate of" " . There is a small hole of area a at the bottom of the tank. If the maximum level in the vessel is proportion to

nm

a

, then find the

product mn.

54. A radioactive material consists of nuclides of 3 isotopes which decay by emission ,emission and deuteron emission respectively. Their half lives are

1 2 3T 400sec, T 800sec and T 1600sec= = = respectively. At t=0, probability of getting , and

deuteron from radio nuclide are equal. If the probability of emission at t=1600 seconds is n13,

then find the value of n.

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55. A small positively charged ball of mass m suspended by an insulated thread of

negligible mass. Another positively charged small ball is moved very slowly

from a large distance until it is in the original position of the first ball. As a

result, the first ball rises by h. If the work done by external agent is Kmgh,

then find the value of K.

56. Two soap bubble with radii of curvature 1R and 2R , where 2 1R R< are brought into contact as shown in figure . R is the radius of

curvature of film between them. If the contact angle of the films is

=12

nradian, then find the value of n.

57. A parallel plate capacitor consists of two square plates of side length

a=6 cms. There is dielectric slab in the shape of a cylinder of parabolic

cross-section between the plates, as shown in figure. The dielectric

constant of the material is K=2. The length of latus rectum of the parabola

is equal to the side length of the plate. Then the capacitance is given by2

04 N 10 farad , then fin d the value of N.

Paper Setters : HYD-HG

Mathematics : SRI. A.N.S - 9703945494

Physics : SRI. PRASAD - 9959555698

Chemistry : SRI. V.KUMAR - 9848691015

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