GRAND TEST Q.P I

FILE NO. IIT-777/66 (31/01/09) CODE VSSS.

IIT JEE – 2009

NARAYANA GRANDTEST-10PAPER – I

Time: 3 hours Max. Marks:207 DATE: 02– 02 – 09

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

INSTRUCTIONSA. General:

1. This booklet is your Question Paper containing 48 questions. The booklet has ____ 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 not allowed to be carried inside the examination hall.

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

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

B. Filling the ORS6. On the lower part of the ORS, write in ink, your

Registration Number in box L ,Test No. in box L

,Date in box L ,Your Name in box L ,Signature of

the candidate in box L ,Signature of Invigilator with

name in box L and Name of the Center in L .Do not write these anywhere else.

7. Write your Registration No. in ink, in the box Lprovided in the Upper 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 CODE printed 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 L

on the ORS affirming 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 of 3 parts (Part I: Physics: Part II: Chemistry, Part III: Maths). Each part has 5 sections.

12. Section I contains 6 multiple choices questions. Each question has 4 choices (A), (B), (C) and (D), out of which only one is correct.

13. Section II contains 3multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which one or more answer/s is/ are correct.

14. Section III contains 1 paragraph based upon paragraph 3 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which only one is correct.

15. Section IV contains 2 subjective or numerical or ICR model type questions

16. Section V contains 2 questions .each question contains statements given in 2 columns .Statement in the Column I have to be matched with the statement/s in the Column II. The answers to these questions have to be appropriately bubbled in the ORS as per the instructions given at the beginning of the section.

D. Marking Scheme:17. For each questions in Section I, you will be awarded

3 marks if you have darkened only 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.

18. For each question in Section II, you will be awarded +5 marks if you have darkened only 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

19. For each question in Section III, you will be awarded +4 marks if you darkened only 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.

20. For each question in Section IV, you will be awarded +6 marks if you darkened all the bubble corresponding only to the correct answer. No negative mark will be awarded for an Incorrectly bubbled answer

21. For each question in Section V, you will be awarded +6 marks if you darkened all the bubble corresponding only to the correct answer. No negative mark will be awarded for an Incorrectly bubbled answer

FILE NO. IIT-572/48 (30/12/2008)

Useful DataGas Constant R = 8.314 J K1 mol1

= 0.0821 Lit atm K1 mol1 = 1.987 2 Cal K1 mol1

Avogadro's Number Na = 6.023 1023

Planck’s constant h = 6.625 1034 J s= 6.625 10–27 erg s

1 Faraday = 96500 Coulomb1 calorie = 4.2 Joule1 amu = 1.66 10–27 kg 1 eV = 1.6 10–19 J

Atomic No: H = 1, D = 1, Li = 3, Na = 11, K = 19, Rb = 37, Cs = 55, F = 9, Ca = 20, He = 2, O = 8, Au = 79, Ni = 28, Zn = 30, Cu = 29, Cl = 17, Br = 35, Cr = 24, Mn = 25, Fe = 26, S = 16, P = 15, C = 6, N = 7, Ag = 47.

Atomic Masses: He = 4, Mg = 24, C = 12, O = 16, N = 14, P = 31, Br = 80, Cu = 63.5, Fe = 56, Mn = 55, Pb = 207, Au = 197, Ag = 108, F = 19, H = 1, Cl = 35.5, Sn = 118.6, Na = 23, D = 2, Cr = 52, K = 39, Ca = 40, Li = 7, Be = 4, Al = 27, S = 32.1

PHYSICS

PART – I

SECTION – IStraight Objective Type

This section contains 6 multiple choice questions, numbered 1 to 6 .Each question has four choices (A),(B),(C) and (D),out of which ONLY ONE is correct.

1. As shown in the figure, initially both the springs are in normal length . At , the block is given a rightward velocity 2 m/s. the mass of the

block is (14/3) kg. How much distance does the block cover before it comes to rest for the first time?(The spring constant of the left spring is and that of the right spring is not constant and varies as where x is the compression in the spring)

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

2. Two identical rods of length l and mass m are welded together at right angles and then suspended from a knifeedge as shown. Angular frequency of small oscillation of the system in its own plane about the point of suspension is

(A) (B)

(C) (D)

CODE: VSSS3. A sonic source starts falling under gravity at time towards detector lying

on the ground vertically below it as shown. velocity of sound. If is the frequency of the source, then the apparent frequency recorded by the detector corresponding to sound wave emitted at is

(A) (B)

(C) (D)

4. Two parallel straight rails of negligible resistance are l apart. At one end they are connected with each other by a resistanceless wire as shown in figure. A uniform magnetic field of induction B exists in the space, normal to the plane of rails. An isosceles right angled triangle abc, made of a uniform wire of resistance per unit length slides along rails with constant velocity v. Force required to pull it, is:

(A) (B)

(C) (D)

5. A particle moves in the x - y plane under the action of a force such that the value of its linear momentum at time t is:

and . The angle between and at time t will be:(A) (B) (C) (D)

CODE: VSSS

6. If the width of slit S in Young’s double slit experiment is gradually increased:(A) Bright fringes become brighter and dark fringes become darker.(B) Bright fringes become less bright dark fringes become less dark.(C) Bright fringes become brighter, dark fringes lighter.(D) Bright fringes become less bright, dark fringes darker.

SECTION – IIMultiple Correct Answer Type

This section contains 3 multiple choice questions, numbered 7 to 9. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE is/are correct.

7. A gas in a container A is in thermal equilibrium with another gas of the same mass in container B. If corresponding pressures and volumes are denoted by the suffixes A and B, then which of the following statements is / are possible?(A) (B) (C) (D)

8. A conductor is made of an isotropic material (resistivity ) has rectangular cross section. Horizontal dimension of the rectangle decreases linearly from 2x at one end to x at the other end and vertical dimension increases from y to 2y as shown in figure. Length of the conductor along the axis is equal to l. A battery is connected across this conductor. Then:(A) Resistance of the conductor is equal to (B) Rate of generation of heat per unit length ismaximum at middle cross

section.(C) Drift velocity of conduction electrons is minimum at middle section.(D) At the ends of the conductor, electric field intensity is same.

9. Y and Z are two partially reflecting thin glass sheets, a distance l a part in air. White light falls normally on Y; the light emerging from Z is analysed by a spectrometer. A dark band is observed in the spectrum at wavelength . Possible values of l is / are:

CODE: VSSS

(A) (B)

(C) (D)

SECTION – IIILinked Comprehension Type

This section contain 1 paragraph. Based upon paragraph, 3 multiple choice questions, numbered 10 to 12. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct

Paragraph for Questions Nos. 10 to 12

A block of mass M is kept in elevator (lift) which starts moving upward with constant acceleration ‘b’ as shown in figure. Initially elevator at rest. The block is observed by two observers A and B for a time interval to . Observer B is at rest with respect to elevator and observer A is standing on the ground.

10. The observer A finds that the work done by gravity on the block is (A) (B) (C) (D)

11. The observer A finds that work done by normal reaction acting on the block is

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

12. According to observer B(A) The work done by gravity on the block is zero(B) The work done by normal reaction on the block is zero(C) The work done by pseudo force on the block is zero(D) All the above are correct.

Section – IVSection – IVSubjective /Numerical Type /ICR Model Type Questions

This section contains 2 Subjective /Numerical Type /ICR Model Type Questions numbered 13 and 14.if your answer is<1.5 then the correct answer is 1 and it can be marked in ORS Sheet as 000000001.if the answer is 1.5 then the correct answer is 2, it can be marked in ORS Sheet as 000000002.if your answer is 225 then it can be marked in ORS Sheet as 000000225.

CODE: VSSS

13. A source of sonic oscillations with frequency and a reciver are located at the same point. At the moment the source starts receding from the reciver with constant acceleration . Assuming the velocity of sound to be equal to . The oscillation frequency registered by the stationary reciver at after the start of motion is …….Hz.

14. A cylindrical rod of length and cross sectional radius is placed at a distance 50 r from an infrared point source S of power 1.25 kW as shown in the figure. The lateral surface of the rod is perfectly insulated from the surroundings. The crosssection A, absorbs of the incident energy, has temperature in steady state. The surface B is radiating energy into space and the wavelength emitted by it with maximum energy density is . The value of if conductivity varies with temperature as is (Assume that the rate of flow of heat through the rod is steady)……..

CODE: VSSS

Section – VMatrix–Match Type

This section contains 2 questions, numbered 15 and 16. 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) in Column II. The answers to these questions have to be appropriately bubbles as illustrated in the following example. If the correct matches are A–p,B–q, B–r, C–p, C–q and D–s, then the correctly bubbled 4 × 4 matrix should be as follows :

15. A square loop of uniform conducting wire is as shown in figure. A current I (in amperes) entres the loop from one end and exits the loop from opposite end as shown in figure. The length of one side of square loop of l metre. The wire has uniform cross section area and uniform linear mass density. In four situations of column I, the loop is subjected to four different uniform and constant magnetic field. Under the conditions of column I, match the column I with corresponding results of column II ( in column I is a positive nonzero constant)

Column I Column II(A) in tesla (p) magnitude of net force on loop is l N(B) in tesla (q) magnitude of net force on loop is zero(C) in tesla (r) magnitude of net torque on loop about its

centre is zero(D) in tesla (s) magnitude of net force on loop is

l

CODE: VSSS

16. Match the statements in column I with the results in columnI I and indicate your answer by darkening appropriate bubbles in the 4 X 4 matrix given in OMR.

Column I Column II(A) A thin uniform spherical shell of surface

area ‘S’ has an initial temperature more than its surrounding atmosphere. Then magnitude of rate of change of its temperature with time

(p)

is independent of ‘S’

(B) A soap bubble initially in equilibrium is given a cange Q, which distributes uniformly over its surface. The centre of the bubble is always fixed. For the duration the bubble having surface area ‘S’ expands, the magnitude of electric potential at a fixed point always lying outside the bubble

(q)

depends on ‘S’

(C) A container with open top and filled with ideal liquid is placed at rest on a smooth horizontal table. A small hole of area ‘S’ is drilled at the bottom of a side wall of container. The magnitude of force exerted by escaping liquid on the container

(r) remains constant

(D) An infinitely long straight current carrying wire liesalong the axis of a closed cylindrical surface of total surface area ‘S’ in space. As the magnitude of current in the wire is continuously increased, the magnitude flux through the surface of this cylinder

(s)

decreases with time

CODE: VSSSCHEMISTRY

PART IISECTION – I

Straight Objective TypeThis section contains 6 multiple choice questions, numbered 17 to 22 .Each question has four choices (A),(B),(C) and (D),out of which ONLY ONE is correct.

17. EMF of the cell, Pt(s)|H2(1 atm)|H+(0.1 M)||KCl(aq)|Hg2Cl2(s)|Hg(l) is 0.045 V at 298 K and the temperature coefficient of the cell is 3.4 10-4 V K-1. The entropy change of the cell in J K-1 mol-1 is(A) 65.2 (B) 60 (C) 33.1 (D) 69.2

18. Incorrect statement among the following is(A) Vapour pressure is not a colligative property.(B) Vapour pressure does not not depend on the quantity of the liquid taken

and the surface area of the liquid.(C)Vapour pressure of a liquid always increases with temperature.(D) Vapour pressure depends only on temperature and not on the nature of

the liquid.19. In which of the following sets central atom of each molecule is sp3d

hybridized?(A) IO4−, ICl4−, IF4+ (B) IF5, PCl5, Fe(CO)5

(C) I3−, ClF3, SF4 (D) SO42−, PO43−, XeO4

20. NaCN is sometimes added in the froth floatation process when mineral contains both ZnS and PbS because(A) Pb(CN)2 is precipitated while there is no effect on ZnS and hence it can

float with froth.(B) PbS forms a soluble complex Na2[Pb(CN)4] while ZnS floats with froth.(C) silicious impurities settle down on the bottom.(D) ZnS forms a soluble complex Na2[Zn(CN)4] while PbS doesn’t and hence it

floats with froth.

Space for rough work

CODE: VSSS21. 2-Phenylcycloprop-2-en-1-one is allowed to react with phenyl magnesium

bromide and the reaction mixture is then treated with perchloric acid. The product formed is(A)

(B)

(C)

(D)

22. Following reaction can be effected by

(A)H2/Ni (B) B2H6/THF followed by acidification

(C) Na/alcohol (D) All of these


This section contains 3 multiple choice questions, numbered 23 to 25. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE is/are correct.

23. CaCO3 is often added during the extraction of lead from galena. Which of the following may the probable function(s) of CaCO3?(A) It removes silica as fusible slag.(B) It prevents formation of undesired lead silicate.(C) It removes iron impurity as fusible slag.(D) It oxidizes PbS to PbO.


CODE: VSSS24. One mole of an ideal diatomic gas (Cv = 5 cal) was transformed from initial

25°C and 1 L to the state at which the temperature is 100°C and volume 10 L. Then for this process (R = 2 cal mol-1K-1)(A) H = 525(B) U = 525

(C) S =

(D) G of the process can not be calculated using given information25. Which of the following can not be used to produce Grignard’s reagent?

(A)

(B)

(C)

(D)


This section contain 1 paragraph. Based upon paragraph, 3 multiple choice questions ,numbered 26 to 28. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Questions Nos. 26 to 28In monosubstituted benzene derivatives, if the substituent group provides electron density to the ring by its resonance effect, it is always ortho-para directing. The arenes astabilize the arenium ion by +I and hyperconjugative effect so are also activating and ortho-para directing. If the substituted group withdraws electron density by resonance effect the it is meta directing. In case of disubstituted benzenes, the strongly activating group dominates over weakly activating or deactivating groups in deciding the orientation of major product. There is often little substitution between two groups that are meta to each other due to steric repulsion.


CODE: VSSS26. Major product of the following reaction is

(A) (B)

(C) (D)

27. Select the correct statement regarding the reaction

(A)Bromine substitutes the hydrogen meta to both –NO2 and –NO groups as both are deactivating groups.

(B)Bromine replaces the hydrogen ortho to –NO but para to –NO2 as –NO group is activating.

(C)Bromine replaces the hydrogen para to –NO but ortho to –NO2 as –NO is a +R group.

(D) No reaction occurs as Br+ is too weak an electrophile to compete with the deactivating ability of –NO2 group.


CODE: VSSS28. Which of the following compound forms a six membered ring most readily

when treated with anhydrous AlCl3?(A) (B)

(C) (D)

SECTION – IVSECTION – IVSubjective /Numerical Type /ICR Model Type Questions

This section contains 2 Subjective /Numerical Type /ICR Model Type Questions ,numbered 29 and 30.if your answer is<1.5 then the correct answer is 1 and it can be marked in ORS Sheet as 000000001.if the answer is 1.5 then the correct answer is 2, it can be marked in ORS Sheet as 000000002.if your answer is 225 then it can be marked in ORS Sheet as 000000225.

29. What is the osmotic pressure of a solution(in Torr) made by mixing 20 mL of 0.01 M BaCl2 and 30 mL of 0.01 M NaF at 27°C? Ksp of BaF2 is 2.4 10−5, R = 0.082 L atm mol−1 K−1, 1 atm = 760 Torr.

30. Linus Pauling wanted to determine the electron gain enthalpy (electron affinity) of an unknown element X. He took one mole of atoms of X and found that on absorption of 410 kJ of energy half of X-atoms transfer one electron to the other half. To convert all the resulting X− ions to X+ ions, an additional energy of 735 kJ was required. What was the electron gain enthalpy of X as obtained by Linus Pauling? Report your answer in kJ mol-1

SECTION – VSECTION – VSpace for rough work

CODE: VSSSMatrix–Match Type

This section contains 2 questions, numbered 31 and 32. Each question contains statements given in two column which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (p, q, r, s) in Column II. The answers to these questions have to be appropriately bubbles as illustrated in the following example.If the correct matches are A–p,B–q, B–r, C–p, C–q and D–s, then the correctly bubbled 4 × 4 matrix should be as follows :31. Match the particulars given in column I with appropriate chemical reagents in

column II.Column I Column II

(A)Al3+, Cu2+ and Fe3+ can be distinguished by (p) KI solution

(B)PbS, CuS and CdS dissolve in (q) Aqeous NH3

(C)Pb2+ gives yellow precipitate with (r) 50 % HNO3 solution

(D) Bi3+ gives black precipitate with (s) K2CrO4 solution

32. Match the reactions mentioned in column I with the nature of the reaction/characteristic(s) of the products mentioned in column II.

Column I Column II(A)H3PO3 (p) One of the products is a reducing agent

(B)PCl3 + H2O (q) One of the products is tribasic acid and non-reducing

(C)NO2 + H2O (r) Dehydration

(D) HNO3 + P4O10 (s) At least one of the products contains central atom in +5 oxidation state

MATHEMATICS


CODE: VSSSPART – IIISECTION – I

Straight Objective TypeThis section contains 6 multiple choice questions, numbered 33 to 38 .Each question has four choices (A),(B),(C) and (D),out of which ONLY ONE is correct.

33. (x 1)2 + (y 3)2 = 9 and (x 7)2 + (y + 5)2 = 25 are two circles then the area of the hexagon formed by the points of contact of direct common tangents and the two centres is

A) 25 sq.units B) 50 sq.units C) 45 sq.units D) 48 sq.units

34. If the odd against an event E are 4 : 7 and the odds in favour of another event F independent of E are 6 : 7. Then the probability that exactly one of them occurs if it is given that at least one of them occurred is

A) B) C) D)

35. If , then the value of ‘n’ when nC0 + 2.nC1 + 3.nC2 + …. +

(n+1)nCn = 1280, is A) 7 B) 8 C) 9 D) 10

36. Number of ways of giving away 10 different gifts to 5 students so that each get at least one and a particular student gets at least 5 gifts is

A) 5040 B) 60480 C) 65520 D) 10080


CODE: VSSS

37. Suppose , then is equal to

A) B)

C) D)

38. If a, b, c are distinct positive real numbers in H.P., but not in G.P., the value of the expression is equal to

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


This section contains 3 multiple choice questions ,numbered 39 to 41. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE is/are correct.

39) Which of the following statements is/are TRUE ?

A) If f has domain [0, ) and has no horizontal asymptotes then or

B) If f is continuous on [1, 1] and f(1) = 4 and f(1) = 3, then there exist a number r such that |r| < 1 and f(r) = .

C) does not exist

D) For all values of m R the line ymx + m1 = 0 cuts the circle x2 + y2 2x 2y + 1 = 0 orthogonally.


CODE: VSSS

40) If z1 and z2 are two complex numbers satisfying then

A) B) C) D)

41) Let and then

A) 3Q = 4P B) 3P = 4Q C) P + 2Q = 5 D) 2(Q + P) = 7


This section contains 1 paragraph. Based upon paragraph, 3 multiple choice questions ,numbered 42 to 44. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct

Paragraph for Questions Nos. 42 to 44Consider three vectors , and and let be a unit vector, then

42) are A) linearly dependent

B) can form the sides of a possible triangle

C) such that the vector is orthogonal to

D) such that each one of these can be expressed as a linear combination of other two

43) If , then (p + q + r) equal to A) 8 B) 2 C) 2 D) 4


CODE: VSSS

44) The magnitude of the vector is A) 4 B) 8 C) 18 D) 2

SECTION – IVSECTION – IVSubjective /Numerical Type /ICR Model Type Questions

This section contains 2 Subjective /Numerical Type /ICR Model Type Questions, numbered 45 and 46.if your answer is<1.5 then the correct answer is 1 and it can be marked in ORS Sheet as 000000001.if the answer is 1.5 then the correct answer is 2, it can be marked in ORS Sheet as 000000002.if your answer is 225 then it can be marked in ORS Sheet as 000000225.

45. If are nonzero numbers such that ‘r’ and ‘s’ are roots of and are the roots of , then find the value of .

46. Let

Then find the value of .

SECTION – VSECTION – VMatrix–Match Type

This section contains 2 questions, numbered 47 and 48. Each question contains statements given in two column which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (p, q, r, s) in Column II. The answers to these questions have to be appropriately bubbles as illustrated in the following example.If the correct matches are A–p,B–q,B–r,C–p,C–q and D–s, then the correctly bubbled 4 × 4 matrix should be as follows :


CODE: VSSS

47) If and , [0, 2]. The quantity f() g()

in the interval given in column-I, match with column-II. Column-I Column-II

A)

p)

negative

B)

q)

positive

C)

r)

non-negative

D)

s)

non-positive

48) Consider the following four pair of lines in column-I and match them with one or more entries in column-II

Column-I Column-IIA)

L1 : x = 1 + t, y = t, z = 2 5t L2 :

p)

non-coplanar lines

B) L1 :

L2 :

q)

lines lie in a unique plane

C)

L1 : x = 6t, y = 1 + 9t, z = 3t L2 : x = 1 + 2s, y = 4 3s, z = s

r)

infinite planes containing both the lines

D) L1 :

L2 :

s)

lines are not intersecting


CODE: VSSS

PAPER SETTER: HYD – CO

Maths Dr.Saini 9885206477

Physics Mr. Siva Sanker 9000822524

Chemistry Mr. Lawrence 9703804794


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GRAND TEST Q.P I