BRILLIANTS HOME BASED FULL-SYLLABUS SIMULATOR TEST SERIES FOR OUR STUDENTS TOWARDS IIT-JOINT ENTRANCE EXAMINATION, 2009 QUESTION PAPER CODE Time: 3 Hours Maximum Marks: 243 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. INSTRUCTIONS: Name: . Enrollment No.: ⊗ Brilliant Tutorials Pvt. Ltd. IIT/STS VII/MPC/P(II) - 1 7 A. General 1. This booklet is your Question Paper containing 66 questions. The booklet has 26 pages. 2. This question paper CODE is printed on the right hand top corner of this sheet and on the back page (page no. 26) of this booklet. 3. This question paper contains 2 blank pages for your rough work. No additional sheets will be provided for rough work. 4. 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. 5. Fill in the boxes provided below on this page and also write your Name and Enrollment No. in the space provided on the back page (page no. 26) of this booklet. 6. The answer sheet, a machine-readable Objective Response Sheet (ORS), is provided separately. 7. DO NOT TAMPER WITH/MUTILATE THE ORS OR THE BOOKLET. 8. Do not break the seals of the questions-paper booklet before being instructed to do so by the invigilators. B. Filling the ORS 9. On the lower part of the ORS, write in ink, your name in box L1, your Enrollment No. in box L2 and Name of the Centre in box L3. Do not write these anywhere else. 10. The ORS has a CODE printed on its lower and upper parts. 11. Make sure the CODE on the ORS is the same as that on this booklet and put your signature in ink in box L4 on the ORS affirming that you have verified this. 12. IF THE CODES DO NOT MATCH, ASK FOR A CHANGE OF THE BOOKLET. C. Question paper format: Read the instructions printed on the back page (page no. 26) of this booklet. D. Marking scheme: Read the instructions on the back page (page no. 26) of this booklet. SEAL SEAL DO NOT BREAK THE SEALS ON THIS BOOKLET, AWAIT INSTRUCTIONS FROM THE INVIGILATOR MATHEMATICS − PHYSICS − CHEMISTRY PAPER II I have read all the instructions and shall abide by them. ............................................... Signature of the Candidate I have verified all the informations filled in by the Candidate. ............................................... Signature of the Invigilator IIT- JEE 2009 STS VII/MPC/P(II)/QNS
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BRILLIANTSHOME BASED FULL-SYLLABUS SIMULATOR TEST SERIES
FOR OUR STUDENTSTOWARDS
IIT-JOINT ENTRANCE EXAMINATION, 2009
QUESTION PAPER CODE
Time: 3 Hours Maximum Marks: 243
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.
A. General1. This booklet is your Question Paper containing 66 questions. The booklet has 26 pages.2. This question paper CODE is printed on the right hand top corner of this sheet and on the back page
(page no. 26) of this booklet.3. This question paper contains 2 blank pages for your rough work. No additional sheets will be provided
for rough work.4. 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.5. Fill in the boxes provided below on this page and also write your Name and Enrollment No. in the
space provided on the back page (page no. 26) of this booklet.6. The answer sheet, a machine-readable Objective Response Sheet (ORS), is provided separately.7. DO NOT TAMPER WITH/MUTILATE THE ORS OR THE BOOKLET.8. Do not break the seals of the questions-paper booklet before being instructed to do so by the invigilators.
B. Filling the ORS9. On the lower part of the ORS, write in ink, your name in box L1, your Enrollment No. in box L2 and
Name of the Centre in box L3. Do not write these anywhere else.10. The ORS has a CODE printed on its lower and upper parts.11. Make sure the CODE on the ORS is the same as that on this booklet and put your signature in ink in
box L4 on the ORS affirming that you have verified this.12. IF THE CODES DO NOT MATCH, ASK FOR A CHANGE OF THE BOOKLET.
C. Question paper format: Read the instructions printed on the back page (page no. 26) of this booklet.D. Marking scheme: Read the instructions on the back page (page no. 26) of this booklet.
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MATHEMATICS − PHYSICS − CHEMISTRY
PAPER II
I have read all the instructionsand shall abide by them.
...............................................Signature of the Candidate
I have verified all the informations filled in by the Candidate.
...............................................Signature of the Invigilator
IIT-JEE 2009STS VII/MPC/P(II)/QNS
2
PART A : MATHEMATICS
SECTION I
Straight Objective Type
This section contains 9 multiple choice questions numbered 1 to 9. Each question has4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
1. If ω is an imaginary fourth root of unity ∑s = 1
4ls + m ω
s 1 is equal to
(A) 4 m
3(B)
12 m
2ω(C)
4l
ω 1(D)
10 a
ω
2. The value of 0.25
log0.5
1
5+ 1
52
+ 1
53
+ ... to ∞
is
(A) 1
4(B)
5
8(C)
1
16(D)
3
4
3. If the equations λ x2 − x − 1 = 0 and x2 + x − λ = 0 have a common root, then thevalue of λ = ..... (λ ≠ 0)
(A) 1 (B) − 1 (C) 2 (D) − 2
4. The remainder when 17215 is divided by 29 is(A) 12 (B) 7 (C) 1 (D) 18
5. The maximum positive integral value of n such that xn divides
6. A bag contains four tickets numbered as 223, 231, 322 and 333. One ticket isdrawn at random from the bag. If Ei is the event that the ith digit on the ticket is
3, then
(A) E1 and E2 are independent
(B) E1 and E2 are mutually exclusive
(C) E2 and E3 are mutually exclusive
(D) E1, E2, E3 are independent
7. Number of solutions of the equation x3 + 3x2 + 20x + sin x = 0 in [0, 2π] is
(A) 2 (B) 1 (C) 4 (D) infinite
8. ∫0
3
x3 5x
2+ 6x dx is equal to
(A) 9
4(B) 3 (C)
16
3(D)
37
12
9. In a right-angled ∆ABC, C = 90° and AB = p. Then,
This section contains 4 questions numbered 10 to 13. Each question containsSTATEMENT 1 (Assertion) and STATEMENT 2 (Reason). Each question has 4 choices(A), (B), (C) and (D), out of which ONLY ONE is correct.
(A) Statement 1 is True, statement 2 is True; statement 2 is a correctexplanation for statement 1.
(B) Statement 1 is True, statement 2 is True; statement 2 is not a correctexplanation for statement 1.
(C) Statement 1 is True, statement 2 is False.
(D) Statement 1 is False, statement 2 is True.
10. Statement 1: The number 6 lies between the roots of the equation x2 − 18x + 9 = 0
and
Statement 2: The number k lies between the roots of the equation
f(x) ≡ ax2 + bx + c = 0 if the discriminant > 0 and f(k) < 0
11. Statement 1:2 4 51 2 13 6 4
= 0
and
Statement 2: The value of a determinant is zero, if two rows or two columnscoincide.
13. Statement 1: The function f(x) = 2x3 + 6x2 + 7x + cos x is one-one
andStatement 2: An strictly increasing or strictly decreasing function is one-one
SECTION IIILinked Comprehension Type
This section contains 2 paragraphs. Based upon each paragraph, 3 multiple choicequestions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out ofwhich ONLY ONE is correct.
Paragraph for Question Nos. 14 to 16Four letters of the word EARTHQUAKE are to be permuted.
14. The maximum number of different ways of the above permutation is(A) 5040 (B) 2694 (C) 1938 (D) 2190
15. The number of ways of the above permutation if the first and the last letters arerespectively A and E, is(A) 56 (B) 70 (C) 420 (D) None of these
16. The number of ways of the above permutation if the end letters are E and T(A) 168 (B) 84 (C) 24 (D) 86
Paragraph for Question Nos. 17 to 19
A hyperbola passes through the focus of the ellipse x2
25+ y
2
4= 1 and its
transverse and conjugate axes coincide with the x and y coordinate axes respectively.Also the eccentricity of the hyperbola is the reciprocal of the eccentricity of the ellipse.
Matrix-Match TypeThis section contains 3 questions. Each question contains statements given in twocolumns which have to be matched. Statements (A, B, C, D) in Column I have to bematched with statements (p, q, r, s) in Column II. The answers to these questionshave to be appropriately bubbled as illustrated in the following example.If the correct matches are A-p, A-s, B-q, B-r, C-p, C-q and D-s, then the correctlybubbled 4 × 4 matrix should be as follows:
21. The function in Column I is the solution of the differential equation in Column II. Column I Column II
(A) 4xy = y4+ c (p)
x dy
x2+ y
2= y
x2+ y
2 1 dx
(B) c y + 1 = e
x2+ 2x2
(q) xdx
dy+ y = x
2+ y
2
(C) y = x tan (c − x) (r) x y3 dy
dx+ y = 0
(D) x2 = c2 + 2cy (s) dy
dx= xy + x + y + 1
22. Column I Column II(A) The Cartesian equation of the (p) 6x + 3y + 2z − 18 = 0
plane through P i 2 j 4kperpendicular to the line joiningP and Q 3i + j + 2k is
(B) The equation of the plane through (q) 2x + 3y + 6z + 28 = 02i + j k passing through the line of intersection of the planesr ⋅ i + 3 j k = 0 andr ⋅ j + 2k = 0 is
(C) The equation of the plane (r) x + 9y + 11z = 0containing the line r = 2i + λ j k andperpendicular to the planer ⋅ i + k = 3 is
(D) The equation of the plane making (s) x − y − z − 2 = 0intercepts OA, OB, OC on thex, y, z axes where the centroid of the ∆ABC is i + 2 j + 3k is
This section contains 9 multiple choice questions numbered 23 to 31. Each questionhas 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
23. Two wires are bent (shown as joint-circle) with radius r (in xy plane).
The upper half has resistance of 2R Ω and the lowerhalf of R Ω. A current I is passed into circle as shown.The magnetic field at centre is
(A) µ
0I
rz (B)
µ0I
2rz
(C) zero (D) µ
0I
12 rz
24. A sample is kept in a strong neutron-flux to make it temporarily radioactive. Twodifferent decay processes are observed with equal activity when the incident fluxis removed and with activities that differ by a factor of e = 2.718 one hour later.The difference in the decay rates of the two radioactive species is
(A) e seconds (B) 1
es1
(C) one hr−1
(D) 1 s−1
25. The electronic energy of helium atom is − 79 eV. Its first ionisation potential is
26. A person of weight W1 is in an elevator of weight W1. The elevator accelerates
vertically up at a rate a and at a certain instant has speed v1. The person climbs
a vertical ladder within the elevator at a speed v2 relative to the elevator. The
persons rate of expenditure of energy is
(A) W1 (B) W1
1 + a
gv
1+ v
2
(C) W1
1 a
gv
2(D) W
11 + a
gv
2
27. An alternating voltage is applied to the circuit shown.The circuit has resonant angular frequency (or
frequencies) given by (where r =C
1
C2
)
(A) 1
LC1
only (B) 1
LC2
only
(C) 1
LC1
and 1
LC2
1 + r (D) 1
LC2
and 1
LC2
1 + 1
r
28. In an Youngs double slit experiment, the two slits are spaced by 3 × 10−3
m andfringe pattern is formed on a screen at a distance 150 cm. The light used was ofwavelength 6667 Å. The third fringe is at 1 mm from central fringe. Then, screenis moved 0.5 m away from source. The distance between central fringe to eighthdark fringe will be
29. The graph in Figure shows stress - straincurves I, II and III for three differentmaterials taken to fracture limit. Which ofthem will be for a copper (Cu) wire andwhich of them is for glass fibre (G)?
(A) (Cu − I) (G − II)
(B) (Cu − III) (G − I)
(C) (Cu − II) (G − I)
(D) (Cu − I) (G − III)
30. In an experiment (such as being conducted at Large Hadron Collider i.e., LHC inEurope), a proton of energy 10 GeV theoretically acquires a velocity v → c (i.e.,velocity of light). The guiding magnetic field is 1.5 T. The radius of theaccelerating machine called Proton-Synchrotron is (given that 10 GeV is
equivalent to 1.95 × 10−26
kg) (nearly)
(A) 9 m (B) 1.5 m (C) 24 m (D) 18 m31. The angular separation between two distant stars is 1 arc-second. The effective
wavelength of light is 5500 Å. If the stars are to be just resolved, the diameter ofthe objective of a telescope is to be(A) 8.84 cm (B) 13.76 cm (C) 25 cm (D) 5.5 cm
SECTION IIReasoning Type
This section contains 4 questions numbered 32 to 35. Each question containsSTATEMENT 1 (Assertion) and STATEMENT 2 (Reason). Each question has 4 choices(A), (B), (C) and (D), out of which ONLY ONE is correct.
(A) Statement 1 is True, statement 2 is True; statement 2 is a correctexplanation for statement 1.
(B) Statement 1 is True, statement 2 is True; statement 2 is not a correctexplanation for statement 1.
32. Statement 1: For supersonic waves also, Doppler-formula is applicable
and
Statement 2: In case of supersonic waves, source advances more than the wave.
33. Statement 1: Heat loss due to friction is irreversible
and
Statement 2: Reversible process must be extremely slow.
34. Statement 1: In the circuit shown, the value of I willbe minimum if the circuit elementshave the following values:
ε = 10 V, f = 50 Hz, R = 10 Ω, L = 0.2 Hand C = 50.7 F
and
Statement 2: The circuit will be purely resistive in those conditions.
35. Statement 1: Except for the peaks in the Intensity versus Wavelength graphs,X-ray production can be regarded as inverse photoelectric effect
and
Statement 2: Work functions are much smaller than accelerating potentialsin X-ray tubes.
SECTION III
Linked Comprehension Type
This section contains 2 paragraphs. Based upon each paragraph, 3 multiple choicequestions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out ofwhich ONLY ONE is correct.
Paragraph for Question Nos. 36 to 38
A particle of mass m is acted upon by a resistive force (in N) given by
Millikans oil drop experiment provides experimental evidence for the quantisationof charge.
The drops are charged by X-ray ionisation of air. They normally fall under theaction of gravity but an electric field can be applied to the horizontal plates A and B tomonitor the movement of the drops. The terminal velocity of the drop can be measuredby suitable means. Given that η is the coefficient of viscosity of air and r is the radiusof the oil drop.
39. In Millikans apparatus, a negatively charged oil-drop is observed to be falling atuniform speed for a period of 4 s, after which time, the electric field is appliedvertically downwards. Which of the following is correct variation (qualitatively)of velocity v of oil drop with time t?
40. In a Milliken experiment, a positively charged oil-drop is observed to fall at auniform speed of 4v when the electric field between the plates is zero. Onapplying an electric field ε0, the drop rises at a uniform speed of 2v. On changing
the electric field, the drop is observed to fall at a uniform speed of v. If the changeon the drops remained same, the magnitude and direction of final field are(neglect the upthrust from air)
(A) ε0, vertically upwards (B) ε
0
2, vertically downwards
(C) ε
0
2, vertically upwards (D)
ε0
4, vertically upwards
41. A negatively charged drop is held stationary between the plates with upper plateas positive. The drop acquires additional negative charge. In order to keep thedrop stationary:
(A) reverse the charges on plates.
(B) give positive plate more positive charge.
(C) decrease the potential difference between plates.
(D) move plates closer to each other.
SECTION IV
Matrix-Match Type
This section contains 3 questions. Each question contains statements given in twocolumns which have to be matched. Statements (A, B, C, D) in Column I have to bematched with statements (p, q, r, s) in Column II. The answers to these questionshave to be appropriately bubbled as illustrated in the following example.
44. The quantities given in Column I below are as follows about different mechanicalsystems.n = number of equations relating masses and initial velocities in an elastic
collision between two particles in three dimensionsm = number of equations needed to find final velocities in above collisionl0 = length (in metre) of an open pipe if its second overtone has same frequency
as first overtone of a 2 m long closed pipef = possible number of linear vibrations in system shown below having three
springs S1, S2, S3 and two masses P1, P2
Column I Column II(A) m (p) 6(B) n (q) 1(C) l0 (r) 4
This section contains 9 multiple choice questions numbered 45 to 53. Each questionhas 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
45. A sample of hard water contains 244 ppm of HCO3
ions. What is the minimum
mass of CaO required to remove HCO3
ions completely from 1 kg of such water
sample?
(A) 112 mg (B) 56 mg (C) 224 mg (D) 100 mg
46. Specific heat of certain elementary gas at constant volume is 315 J kg−1
K−1
and
that at constant pressure is 441 J kg−1
K−1
. 7.0 g of the gas is found to occupy avolume of 4.1 L at 27°C and 1 atm pressure. The atomic mass of the gas is
(A) 42 (B) 21 (C) 63 (D) 100
47. How many mol of butane must be burnt to heat 10 dm3 of water from 30°C to
100°C? Given: ∆Hcombustion of butane is 2.879 × 103 kJ mol−1
, density of water is
1.0 g cm−3
, specific heat of water is 4.184 JK−1
g−1
.
(A) 1.017 mol (B) 2.017 mol
(C) 3.017 mol (D) 2.034 mol
48. Among the following the incorrect statement is
49. The number and type of bonds between two carbon atoms in calcium carbide are
(A) two sigma, two pi (B) two sigma, one pi
(C) one sigma, one pi (D) one sigma, two pi
50. A certain diatomic molecule AB has a dipole moment 1.6 D and the internucleardistance is 100 pm. The fraction of electronic charge existing on the moreelectronegative atom is
This section contains 4 questions numbered 54 to 57. Each question containsSTATEMENT 1 (Assertion) and STATEMENT 2 (Reason). Each question has 4 choices(A), (B), (C) and (D), out of which ONLY ONE is correct.
(A) Statement 1 is True, statement 2 is True; statement 2 is a correct explanationfor statement 1.
(B) Statement 1 is True, statement 2 is True; statement 2 is not a correctexplanation for statement 1.
(C) Statement 1 is True, statement 2 is False.(D) Statement 1 is False, statement 2 is True.
54. Statement 1: All aldehydes in presence of aluminium ethoxide can besimultaneously oxidised to acid and reduced to alcohol to formester.
and
Statement 2: Aldehydes contain − CHO group.
55. Statement 1: Chloroform is always stored in brown bottles to cut off light.
and
Statement 2: CHCl3 → COCl2 + HCl
56. Statement 1: With the passage of time, the rate of radioactive disintegrationdecreases.
and
Statement 2: Radioactive disintegration follows zero order kinetics.
57. Statement 1: Cu(I) and Ni(II) do not form coloured complexes.
and
Statement 2: Ni(II) is 3d8
Cu(I) is 3d10
SECTION III
Linked Comprehension TypeThis section contains 2 paragraphs. Based upon each paragraph, 3 multiple choicequestions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out ofwhich ONLY ONE is correct.
Paragraph for Question Nos. 58 to 60
Halogenated hydrocarbon, commonly termed as alkyl halide, consists of an alkylgroup and a halogen. The physical properties of haloalkanes are strongly affected bythe polarization of the C − X bond and the polarizability of X. The SN2 reaction is
stereospecific and proceeds by backside displacement, thereby producing inversion ofconfiguration at the reaction centre.
58. The reactivity order of halides for dehydro-halogenation is
(A) R − F > R − Cl > R − Br > R − I
(B) R − I > R − Br > R − Cl > R − F
(C) R − I > R − Cl > R − Br > R − F
(D) R − F > R − I > R − Br > R − Cl
59. Compound C4H8Cl2 (A) on hydrolysis gives a compound C4H8O (B) which reacts
with hydroxylamine and does not give any test with Tollens reagent. A and Bare
63. The permitted cell to have spontaneous reaction is
(A) Ag | AgCl(s), KCl (0.2 M) || KBr (0.001 M), AgBr(s) | Ag
(B) Ag | AgBr(s), KBr (0.001 M) || KCl (0.2 M), AgCl(s) | Ag
(C) both A and B
(D) none of the above
SECTION IV
Matrix-Match Type
This section contains 3 questions. Each question contains statements given in twocolumns which have to be matched. Statements (A, B, C, D) in Column I have to bematched with statements (p, q, r, s) in Column II. The answers to these questionshave to be appropriately bubbled as illustrated in the following example.
If the correct matches are A-p, A-s, B-q, B-r, C-p, C-q and D-s, then the correctlybubbled 4 × 4 matrix should be as follows:
13. The question paper consists of 3 parts (Part A : Mathematics, Part B: Physics and Part C: Chemistry).Each part has 4 sections.
14. Section I contains 9 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out ofwhich only one is correct.
15. Section II contains 4 questions. Each question contains STATEMENT-1 (Assertion) and STATEMENT-2(Reason).
Bubble (A) if both the statements are TRUE and STATEMENT-2 is the correct explanation ofSTATEMENT-1.
Bubble (B) if both the statements are TRUE but STATEMENT-2 is not the correct explanation ofSTATEMENT-1.
Bubble (C) if STATEMENT-1 is TRUE and STATEMENT-2 is FALSE.
Bubble (D) if STATEMENT-1 is FALSE and STATEMENT-2 is TRUE.
16. Section III contains 2 paragraphs. Based upon each paragraph, 3 multiple choice questions have to beanswered. Each question has 4 choices (A), (B), (C) and (D), out of which only one iscorrect.
17. Section IV contains 3 questions. Each question contains statements given in 2 columns. Statements in the first column have to be matched with statements in the second column. The answers to these questions have to be appropriately bubbled in the ORS as per the instructions givenat the beginning of the section.
D. Marking scheme:
18. For each question in Section I, you will be awarded 3 marks if you darken only the bubblecorresponding to the correct answer and zero mark if no bubble is darkened. In all other cases, minusone (−1) mark will be awarded.
19. For each question in Section II, you will be awarded 3 marks if you darken only the bubblecorresponding to the correct answer and zero mark if no bubble is darkened. In all other cases, minusone (−1) mark will be awarded.
20. For each question in Section III, you will be awarded 4 marks if you darken only the bubblecorresponding to the correct answer and zero mark if no bubble is darkened. In all other cases, minusone (−1) mark will be awarded.
21. For each question in Section IV, you will be awarded 6 marks if you darken ALL the bubblescorresponding ONLY to the correct answer. No negative mark will be awarded for an incorrectlybubbled answer.