cpt_(12 std)_mpc_03-11-08_q.p

FILE NO. IIT – 181/23 (01/11/2008)CODE DEWALI

Common Practice Test XII Studying New [89 Batches]

Test Date: 3 t h NOV. 2008.

Time: 3 hours Maximum marks: 246

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

INSTRUCTIONSA. General:

1. This booklet is your Question Paper containing 69 questions. The booklet has 17 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 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 the lower 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 L5 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: Mathematics, Part

II: Physics, Part III: Chemistry). Each part has 4 sections.12. Section I contains 6 multiple choice questions. Each question has 4

choices (A), (B), (C) and (D), out of which only one is correct.

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

14. Section III contains 4 Reasoning type questions. Each question contains STATEMENT–1 AND STATEMENT–2.Bubble (A) if both the statements are TRUE and STATEMENT–2

is the correct explanation of STATEMENT–1.Bubble (B) if both the statements are TRUE but STATEMENT–2

is NOT the correct explanation of STATEMENT–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.15. Section IV contains 3 sets of Linked–Comprehension type question.

Each set consists of a paragraph followed by 3 questions. Each question has 4 choices (A), (B), (C) and (D), out which only one is correct.

D. Marking Scheme:16. 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.

17. For each question in Section II, you will be awarded 4 marks if you have darkened all the bubble(s) corresponding to the correct answer and zero mark for all other cases. If may be noted that there is no negative marking for wrong answer.

18. For each question in Section III, you will be awarded 3 marks if you darken 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 IV, you will be awarded 4 marks if you darken 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

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

South Delhi : 47–B, Kalu Sarai, New Delhi – 110016 Ph.: 011–46080612/13/14North/West Delhi : 15, Central Market, West Punjabi Bagh, New Delhi – 110026 Ph.: 011–45062651/52/53East Delhi : 32-E, Patparganj Village, Mayur Vihar Phase – I, Delhi – 110 091 Ph.: 011–22750043/52Gurgaon : M–21, Old DLF Colony, Sector–14, Gurgaon Ph.: 0124–3217791/92 Dwarka : 317/318, Vikas Surya Galaxy, Main Mkt, Sector–4, Dwarka, New Delhi – 110 075 Ph.: 011–45621724/25Faridabad : SCO-27, IInd Floor, Sector – 16, Faridabad, Haryana – 121002 Ph.: 0122-4074626, 4066938

MATHEMATICSPART – I

SECTION – IStraight Objective Type

This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

1. The sum of the factors of 9! Which are odd and are of the form 3m + 2, where m is a natural number is (A) 40 (B) 45(C) 51 (D) 48

2. The number of ways of dividing 15 men and 15 women into 15 couples, each consisting of a man and a woman, is (A) (B) (C) 1820 (D) 1240

3. A class contains 4 boys and g girls. Every Sunday five students, including at least three boys go for a picnic to Appu Ghar, a different group being sent every week. During, the picnic, the class teacher gives each girl in the group a doll. If the total number of dolls distributed was 85, then value of g is (A) 15 (B) 12(C) 8 (D) 5

4. Three critics review a book. Odds in favour of the book are 5 : 2, 4 : 3 and 3 : 4 respectively for the three critics. The probability that majority are in favour of the book is

(A) (B)

(C) (D)

5. The integers x and y are chosen at random simultaneously from the set {x : 0 x 10}, x Integer, then the probability for |x – y| 5 is

(A) (B)

(C) (D)

6. If P(A) = , P(B) = and P(A B) = then the events A and B are

(A) Mutually exclusive(B) Independent(C) Independent as well as mutually exclusive(D) None of these

SECTION – IIMultiple Correct Answer Type

This section contains 4 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.

7. If A and B are arbitrary events then

(A) P(A B) P(A) + P(B)(B) P(A B) P(A) + P(B)(C) P(A B) = P(A) + P(B)(D) P(A B) P(A) + P(B)

8. The number of non-negative integral solution of x + y + z = n (n is a positive integer) is (A) n + 2Cn (B) n + 4Cn

(C) n + 2C2 (D) Sum of first (n + 1) natural numbers

9. 6 different books of Maths and 6 different books of Physics are placed on a shelf. Let

P1, P2, P3 be the respective probabilities of the events E1, E2 and E3, where

E1 : all Physics books are together

E2 : no two Physics books are together

E3 : books of Maths and Physics are alternate. Then

(A) P1 = P2 (B) P1 = P3

(C) 2P1 = 7P3 (D) P2/P3 = 7/2

10. In the toss of two dice, the probability of getting a sum of 5 or 7 is

(A) (B)

(C) (D) None of these

SECTION – IIIReasoning Type

This section contains 4 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

CODE(A) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is a correct explanation for STATEMENT–1(B) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is NOT a correct explanation for STATEMENT–1(C) STATEMENT–1 is True, STATEMENT–2 is False(D) STATEMENT–1 is False, STATEMENT–2 is True

11. Statement – 1 : Number of permutations of n dissimilar things taken n at a time is nPn .Because Statement – 2 : n(A) = n(B) = n then the total number of functions from A to B are n!

12. Statement – 1 : nCr = nCp r = p or r + p = nBecause Statement – 2 : nCr = nCn–r

13. Statement – 1 : If A and B be two events such that P(A) = 0.3 and P(AB) = 0.8 also A and B are independent events P(B) is 0.5.

Because Statement – 2 : If A & B are two independent events then P(AB) = P(A).P(B).

14. Statement – 1 : The probability of occurence of a doublet when two identical dies are thrown is 2/7.

Because Statement – 2 : When two identical dies are thrown then the total number of cases are 21 in place of 36 (when two distinct dies are thrown) because the cases like (5, 6). (6, 5) are considered to be same.

SECTION – IVLinked Comprehension Type

This section contains 3 paragraphs. Based upon each paragraph, 3 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 Questions Nos. 15 to 17By using the principle of inclusion and exclusion or otherwise answer the following questions.

15. Five letters are put in 5 addressed envelops randomly, number of ways in which no letters goes to the correct envelop is (A) 41 (B) 43(C) 44 (D) 46

16. The number of positive integers 100 which are not divisible by 2, 3 or 5 is (A) 25 (B) 26(C) 29 (D) 30

17. The number of integral solution of x1 + x2 + x3 + x4 = 30 such that 0 xi < 10, is (A) 87 (B) 88(C) 89 (D) 90

Paragraph for Questions Nos. 18 to 20

A player ‘A’ plays a game against a machine. At each round he deposits one rupee in a slot and then flips a coin which has a probability p of showing a head. If a head shows, he gets back the rupee he deposited and one more rupee from the machine. If a tail shows, he loses his rupee. Let A starts with 10 rupees and q = 1 – p

18. The probability that he is left with no money by the tenth round or earlier is

(A) q10 (B)

(C) pq9 (D) 1 – p10

19. The probability that he will be drained out of his rupee exactly at the eleventh round is (A) q11 (B) 1 – p11

(C) pq10 + q11 (D) 0

20. The probability that all his money will be finished exactly at the twelfth round is (A) q12 (B) 1 – p12

(C) 10C1 pq11 (D) 12C2 p2 q10


The number of ways in which (m + n + p) items can be divided into unequal groups containing m, n,

p items is . Again the number of ways to distribute (m + n + p) items

among 3 persons in the groups containing m, n and p items is = (No. of ways to divide) × (No. of groups)

21. The number of ways in which 12 balls be divided into groups of 5, 4 and 3 respectively is

(A) (B)

(C) (D) none of these

22. The number of ways in which 12 balls be divided between 2 boys, one receives 5 and the other 7 balls, is(A) 1560 (B) 1584(C) 1284 (D) none of these

23. How many numbers each lying between 1000, 10,000 can be formed with the digits 0, 1, 2, 3, 4, 5 without repetition? (A) 540 (B) 300(C) 635 (D) 1079

PHYSICSPART – II

SECTION – IStraight Objective Type

This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

24. The planet mercury is revolving in an elliptical orbit around the sun as shown in the figure. K.E. of mercury will be greatest at

sun A

B

C

D

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

25. Figure shows the elliptical path of a planet about the sun. The two shaded parts have equal areas. If t1 and t2 be the time taken by the planet to go from a to b and from c to d respectively.

(A) t1 < t2 (B) t1 = t2

(C) t1 > t2

(D) insufficient information to deduce the relation between t1 and t2

26. An ornament weighing 36 g in air, weighs only 34 g in water. Assuming that some copper is mixed with gold to prepare the ornament, amount of copper will be (Specific gravity of gold is 19.3 and that of copper is 8.9).(A) 2.2g (B) 2g(C) 4.4 g (D) 4g

27. A cubical metal block of edge 12 cm floats in mercury with one fifth of the height inside the mercury. Water is poured till the surface of the block is just immersed in it. Height of the water column will be (Specific gravity of mercury = 13.6).(A) 10.4 cm (B) 12 cm(C) 10 cm (D) None

28. A cube of ice of edge 4 cm is placed in an empty cylindrical glass plate of inner diameter 6 cm. Assume that the ice melts uniformly from each side so that it always retains its cubical shape. Side of ice cube will be when it will just leaves contact with the bottom of the glass.(A) 3 cm (B) 2 cm(C) 2.26 cm (D) None

29. An infinite number of masses, each of 1 kg, are placed on the positive x-axis at 1 m, 2 m, 4 m, 8 m, …. from the origin. The value of the gravitational field at the origin due to this distribution is (A) 2G (B) 4G/3 (C) 3G/4 (D)

SECTION – IIMultiple Correct Answer Type

This section contains 4 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.

30. Water flows through two identical tubes A and B. A volume V0 of water passes through the tube A and 2V0 through B in a given time. Which of the following may be correct ?(A) Flow in both the tubes are steady (B) Flow in both the tubes are turbulent(C) Flow is steady in A but turbulent in B (D) Flow is steady in B but turbulent in A

31. A closed vessel is half filled with water. There is a hole near the top of the vessel and air is pumped out from this hole.(A) The water level will rise up in the vessel(B) The pressure at the surface of the water will decrease(C) The force by the water on the bottom of the vessel will decrease(D) The density of the liquid will decrease

32. Let V and E denote the gravitational potential and gravitational field at a point it is possible to have(A) V = 0 and E = 0 (B) V = 0 and E 0(C) V 0 and E = 0 (D) V 0 and E 0

33. Which of the following quantities remain constant in a planetary motion (consider elliptical orbits) as seen from the sun(A) Speed (B) Angular speed(C) Kinetic energy (D) Angular momentum



CODE(A) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is a correct explanation for STATEMENT–1(B) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is NOT a correct explanation for STATEMENT–1(C) STATEMENT–1 is True, STATEMENT–2 is False(D) STATEMENT–1 is False, STATEMENT–2 is True

34. STATEMENT – 1 : If an object is projected from earth surface with escape velocity path of object will be parabola. and STATEMENT – 2 : When object is projected with velocity less than escape velocity from horizontal surface and greater than orbital velocity. Path of object will be ellipse.

35. STATEMENT – 1 : As wind flows left to right and a ball is spinned as shown, there will be a lift of the ball.and

STATEMENT – 2 : Decreases velocity of air below the ball, increases the pressure more than that above the ball.

36. STATEMENT – 1 : A sphere is kept at a height h above the earth’s surface having mass

. The time taken by the sphere to reach the earth’s surface is .

and STATEMENT – 2 : The mass of sphere is comparable with mass of earth, then both sphere earth move towards the centre of mass of the system.

37. STATEMENT – 1 : In the three cases shown in the figure force exerted by liquid on three vessel is same. and STATEMENT – 2 : Pressure at the bottom in each case is same.




The spouting can is something used to demonstrate the variation of pressure with depth. When the corks are removed from the tubes in the side of the can, water flows out with a speed that depends on the depth.

In a certain can, three tubes T1, T2 and T3 are set at equal distances a above the base of the can. When water contained in this can is allowed to come out of the tubes the distance on the horizontal surface are measured as x1, x2 and x3.

38. Speed of efflux is :

(A) (B)

(C) (D)

39. Distance x3 is given by(A) (B)

(C) (D)

40. The correct sketch is :

(A) (B)



A hollow sphere is completely filled with a liquid having a density (. The radius of sphere is R). now sphere is pulled with a constant horizontal acceleration ax = g on a horizontal surface. Take centre of sphere as origin of co-ordinate system as shown in the figure.

B

AX

41. Co-ordinate of point having minimum pressure is

(A) (B)

(C) (D)

42. Co-ordinate of point having maximum pressure is

(A) (B)

(C) (D)

43. Consider points A and B as shown in figure(a) PA = PB (b) PA > PB(c) PB > PA (d) PA = PB = 0


Sphere of mass M and radius R is surrounded by a spherical shell of same mass M and radius 2R as shown. A small particle of mass m is released from rest from a height h ( <<R) above the shell. There is a hole in the shell.

A

mh

B

R 2R

44. In what time will it enter the hole at A :

(A) (B)


45. What time will it take to move from A to B ?

(A) (B)


46. With what approximate speed will it collide at B ?

(A) (B)

(C) (D)

CHEMISTRYPART – IIISECTION – I

Straight Objective TypeThis section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

47. For preparing a buffer solution of pH 6 by mixing sodium acetate and acetic acid, the ratio of concentration of salt and acid (Ka = 10–5) should be(A) 1:10 (B) 10:1(C) 100:1 (D)1:100.

48. 1-butene on reaction with HBr gives mainly (A) 1-bromobutane (B) 2-bromobutane (C) ()-2-bromobutane (D) 3-bromobutane

49. Ethene on reaction with Br2 in H2O forms mainly(A) 1, 2-bromoethane (B) 2-bromoethanol (C) 1, 2-ethanediol (D) an equimolecular mixture of (A) and (B)

50. 1 ml of 0.1M HCl is added into 99 ml of water. Assume volumes are additive, what is pH of resulting solution.(A) 3 (B) 1(C) 2 (D) 4

51. Consider the following reaction.

Which of the following is not formed ?

(D) all of these

52. Which of the following is inert towards SN-1 reaction ?

(A) Tertiary chloride (B) Isopropyl chloride

SECTION – II

Multiple Correct Answer TypeThis section contains 4 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.

(D) None of the above

54. Which of the following statements are correct. (A) In SN

1 reaction 100% racemisation takes place (B) It is not always necessary that in SN2 reaction inversion of configuration would take place. (C) In SN

1 reaction racemisation takes place with very less proportions of inversion of configuration. (D) Primary halides undergo elimnation reaction on treatment with strong bulky bases e.g. (CH3)3C – O-

55. The possible product (s) of the following reaction is /are

56. In the Dow process for the manufacture of phenol, chlorobenzene is fused with NaOH at high temp and under pressure.

Which of the following statements are correct for above reaction ? (A) Phenol is formed via an intermediate that is aromatic.(B) Diphenylether is also formed as by product. (C) p-phenylphenol is also formed as by product. (D) Biphenylene is also formed as by-product.



Code(A) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is a correct explanation for STATEMENT–1

(B) STATEMENT–1 is True, STATEMENT–2 is True; STATEMENT–2 is NOT a correct explanation for STATEMENT–1

(C) STATEMENT–1 is True, STATEMENT–2 is False

(D) STATEMENT–1 is False, STATEMENT–2 is True

57. STATEMENT – 1 : Li+ ion has the lowest mobility in aqueous solution among alkali metal ions

STATEMENT – 2: Li has higher IP value

58. STATEMENT – 1: The solubility of fluorides of alkaline earth metals increases on descending down in family.

STATEMENT – 2: The fall in lattice energy is more rapid than fall in hydration energy in descending down in family.

59. STATEMENT – 1: Configuration is inverted in SN2 reaction.STATEMENT – 2: Intermediate is a carbocation and nucleophile attacks from same side.

60. STATEMENT – 1: SN2 reaction on A can take place with inversion.

STATEMENT – 2: Intermediate is a carbocation and nucleophile attacks from same side.




Acidity or alkalinity of a solution depend upon the concentration of hydrogen ion relative to that of hydroxyl ions. The product of hydrogen ion & hydroxyl ion concentration is given by

Kw = [H+] [OH–]the value of which depends only on the temperature & not on the individual ionic concentration. If the concentration of hydrogen ions exceeds that of the hydroxyl ions, the solution is said to be acidic; whereas, if concentration of hydroxyl ion exceeds that of the hydrogen ions, the solution is said to be alkaline. The pH corresponding to the acidic and alkaline solutions at 25ºC will be less than and greater than seven, respectively. To confirm the above facts 0.5 M CH3COOH is taken for the experiments.

[Given : Ka of acetic acid = 1.8 ×10–5]

61. Degree of dissociation of acetic acid is -(A) 66 × 10–2 (B) 6 × 10–3

(C) 3 × 10–3 (D) 5 × 10–3

62. pH of the solution will be -(A) 2.52 (B) 2.22(C) 5 (D) 3.92

(log 3 = 0.4771)

63. If pH of the solution is doubled, what will be the concentration of acetic acid -(A) 4.5 × 10–6 M (B) 1.0 M(C) 1.374 × 10–5 M (D) 1.25 × 10–3 M


Nucleophilic substitution reactions generally expressed as

where Nu– NucleophileR — L substrateL leaving group

The best leaving groups are those that become the most stable ions after they depart. Since most leaving groups leave as a negative ion, the best leaving groups are those ions that stabilize a negative charge most effectively. A good leaving group should bei) electron-withdrawing to polarize the carbon atom ii) stable once it has left (not a strong base)iii) polarisable – to maintain partial bonding with the carbon in the transition state (both SN1 and

SN2). This bonding helps to stabilise the transition state and reduces the activation energy.

64. Among the following which is feasible?

(A) X– + CH3—CH2—H CH3—CH2—X + H–

(B) X– + CH3—OH CH3 —X +

(C)

(D) X– + CH3—CH3 CH3 — X +

65.

The correct order of increasing leaving group capability of above compound is(A) III IV II I (B) II III I IV(C) II IV III I (D) I III II IV

66. Among the following which is not feasible?

(A)R—O—R + HI RI + ROH (B) R—Cl + NaI RI + NaCl

(C) R—O—R + KI RI + RO–K+ (D)R—O—H + HI RI + H2O

Paragraph for Questions Nos. 67 to 69Nucleophilic aliphatic substitution reaction is mainly of two types: SN1 and SN2. The SN1 mechanism is a two step process. Reaction velocity of SN1 reaction depends only on the concentration of the substrate. Since product formation takes place by the formation of carbocation, optically active substrate gives (+) and (–) forms of the product. In most of the cases the product usually consits of 5-20% inverted product and 80-95%racemised species. The more stable the carbocation, the greater is the proportion of racemisation. In solvolysis reaction, the more nucleophilic the solvent, the greater is the proportion of inversion.

67. Which one of the following compound will give SN1 reaction?

(A) (B)

(A) (B) All of these

68. Which of the following compounds will give SN1 reactions?I. C6H5 – CH2 – BrII. CH2 = CH – CH2 – BrIII. CH3 – CH2 – Br

IV.

Select the correct answer from the codes given below:(A) I, II and III (B) I, II and IV(C) II, III and IV (D) I, III and IV

69 For the given reaction

Which substrate will give maximum racemisation?

(A) (B)

(C) (D)

If you have any genuine question paper problems please contact the following subject concerned persons.Paper Setter : PUNJABI BAGH Mathematics : Mr. Rajeev Ranjan Gupta Mobile: 09999069846Physics : Mr. V.B. Singh Mobile: Chemistry : Mr. S. K. SINAH Mobile: 09968458361

cpt_(12 std)_mpc_03-11-08_q.p

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