FILE NO. IIT û 180-26 (01-11-2008) CPT_(79 CF)_XII STD_03-11 - 08 Qp

FILE NO. IIT – 180/26 (01/11/2008)CODE DHAMAKA

Common Practice Test XII Std C/F Other Than Spark [79 Batches]

Test Date: 03 R D 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

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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 value of a, b, c for which the matrix is orthogonal is

(A) (B)

(C) (D)

2. If a, b, c, d are real numbers and A= then a2 – (a + d)a is equal to

(A) (ad – bc)i (B) (bc – ad)i(C) (ac – bd)i (D) (ab – cd)i

3. If P(x), Q(x) and R(x) are polynomials of degree one and a1, a2, a3 be real numbers then

is equal to

(A) 1 (B) 0(C) – 1 (D) none of these

4. If the base of a triangle and the ratio of tangent of half the base angles are given then the locus of the vertex of the triangle is (A) parabola (B) ellipse(C) hyperbola (D) none of these

5. If then is (where R)

(A) a zero matrix (B) an identity matrix

(C) (D)

6. The solution of the equation is

(A) x 0 (B) x > 0(C) x (1, ) (D) none of these

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.

7. The equation of the asymptotes of the hyperbola xy – 3y – 2x = 0 is (A) x = y (B) x = 3(C) y = 1 (D) y = 2

8. If z1, z2, z3, z4 are the four complex numbers represented by the vertices of a quadrilateral

taken in order such that z1 – z4 = z2 – z3 and , then the quadrilateral is a

(A) Rhombus (B) square (C) Rectangle (D) cyclic quadrilateral

9. The value of is equal to

(A) (B)

(C) (D) 0

10. If A and B are invertible square matrices of the same order, then which of the following is correct?(A) adj(AB) = (adjB) (adjA)(B) (adjA) = (adjA) (C) |adj A| = |A|n – 1 , where n is the order of matrix A(D) adj(adjB) = |B|n – 2 B, where n is the order of matrix B

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 : If then

Because Statement – 2 : The inverse of a diagonal matrix is a diagonal matrix.

12. Statement – 1 : If A is a skew symmetric matrix of order 3 × 3, then det(A) = 0. Because Statement – 2 : If A is square matrix, then det(A) = det(A) = det(A).

13. Statement – 1 : , then coefficient of x in f(x) is zero.

Because Statement – 2 : If F(x) = A0 + A1x + A2x2 + ….. + Anxn. then A1 = F(0), where dash denotes

the differential coefficient. 14. Statement – 1 : If a, b, c are distinct and x, y, z are not all zero and ax + by + cz = 0,

bx + cy + az = 0, cx + ay + bz = 0, then a + b + c = 0.Because Statement – 2 : a2 + b2 + c2 > ab + bc + ca, if a, b, c are distinct.

SECTION – IV

Linked Comprehension TypeThis 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 17

If we rotate the axes of the rectangular hyperbola x2 – y2 = a2 through an angle /4 in the clockwise

direction, then the equation x2 – y2 = a2 reduces to (say). Since x = ct,

satisfies xy = c2. (x, y) = (ct, c/t) (t 0) is called

15. Let , be the roots of the equation t1x2 – 4x + 1 = 0 and , be the roots of t2x2 – 6x + 1 = 0 and , , , are in H.P. then the point of intersection of normals at ‘t1’ and ‘t2’ on xy = c2

(A) (B)

(C) (D) none of these

16. If e1 and e2 are the eccentricities of the hyperbolas xy = 9 and x2 – y2 = 25, then (e1, e2) lie on a circle C1 with centre origin then the square of the radius of the director circle of C1 is (A) 2 (B) 4(C) 8 (D) 16

17. If the normal at the point ‘t1’ to the rectangular hyperbola xy = c2 meets it again at the point ‘t2’, then the value of t1t2 is(A) (B) (C) (D)


Suppose a, b, c, d, be non-zero real numbers and ab > 0, and

18. Which statement is correct? (A) ac > 0 (B) ab <0(C) ad > 0 (D) none of these

19. The equation ax3 + bx2 + cx + d = 0 has (A) three positive roots (B) three negative roots (C) two positive and one negative roots (D) one positive and two negative roots

20. Rolle’s theorem can be applied for ax3 + bx2 + cx + d in the interval (A) [1, 2] (B) [0, 2](C) [1, 2] (D) none of these


Let A and B are two matrices of same order 3 × 3, where

21. If A is singular matrix, then tr(A + B) is equal to (A) 6 (B) 12(C) 24 (D) 17

22. If = 3, then (tr(AB) + tr(BA)) is equal to

(A) 34 (B) 42(C) 84 (D) 63

23. The correct statement is (A) (A + B) (A – B) = A2 + B2 – 2AB (B) (A + B)2 = A2 + B2 + AB + BA(C) (A + B)2 = A2 + B2 + 2AB (D) none of the above

PHYSICS

PART – IISECTION – 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.24. A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very

small compared to the mass of the earth:(A) The acceleration of S is always directed towards the centre of the earth.(B) The angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant. (C) The total mechanical energy of S varies periodically with time.(D) The linear momentum of S remains constant in magnitude.

25. A hydrogen atom is in an excited state of principle quantum number n. It emits a photon of wavelength when returns to the ground state. The value of n is (R = Rydberg constant)

(A) (B)

(C) (D)

26. In X-ray tube when the accelerating voltage V is halved, the difference between the wavelengths of K line and minimum wavelength of continuous X-ray spectrum (A) remains constant (B) becomes more than two times(C) becomes half (D) becomes less than two times

27. The activities of three lumps of a radioactive substance are in the ratio of 1 : 2 : 3 at any future date the ratio of their activities will be (A) 3 : 2 : 1 (B)(C) (D) .

28. Stopping potential increases with (A) decrease in momentum of incident photon(B) increase in the intensity of incident photon(C) increase in the work function of photo metal(D) increase in the frequency of incident light.

29. A neutron collides head-on with a stationary hydrogen atom in ground state. Which of the following statement is correct?(A) If kinetic energy of the neutron is less than 13.6eV, collision must be elastic. (B) If kinetic energy of the neutron is less than 13.6eV, collision may be inelastic.(C) Inelastic collision may take place only when initial kinetic energy of neutron is greater

than 13.6eV.(D) Perfectly inelastic collision cannot take place.

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. The X-ray beam coming from an X-ray tube will be(A) Monochromatic(B) Having all wavelengths between a minimum and a maximum wavelength(C) Having all wavelengths smaller than a certain maximum wavelength(D) Having all wavelengths larger than a certain minimum wavelength

31. When photoelectrons of energy 4.25 eV strike the surface of a metal A, the ejected photoelectrons have maximum kinetic energy TA eV and de-Broglie wavelength A. The maximum kinetic energy of photoelectrons liberated from another metal B by photons of energy 4.70 eV is TB = (TA 1.50)eV. If the de-Broglie wavelength of these photoelectrons is B = 2A, then(A) The work function of A is 2.25 eV (B) TA = 2.00 eV(C) The work function of B is 4.20 eV (D) TB = 2.75 eV

32. A small mass m is moved slowly from the surface of the earth to a height h above the surface. The work done (by an external agent) in doing this is (A) mgh, for all values of h (B) mgh, for h << R

(C) (D)

33. A solid sphere of uniform density and radius 4 units is located with its centre at the origin of coordinates, O. Two spheres of equal radii of 1 unit, with their centres at A ( 2, 0,0) and B (2,0,0) respectively, are taken out of the solid sphere, leaving behind spherical cavities as shown in the figure.

(A) The gravitational force due to this object at the origin is zero(B) The gravitational force at the point B(2,0,0) is zero(C) The gravitational potential is the same at all points of the circle y2 + z2 = 36(D) The gravitational potential is the same at all points on the circle y2 + z2 = 4


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

34. STATEMENT – 1 : In the photoelectric effect; the photoelectron current is increased when frequency of incident photons is doubled. andSTATEMENT – 2 : Photoelectric effect follows the Einstein equation hv = hv0 + KE.The KE of photoelectron is increased and not is the increase of number of photo electron.

35. STATEMENT – 1 : If the accelerating voltage is doubled; then minimum wavelength of emitted continues X–rays is halved. and STATEMENT – 2 : The wavelength of characteristic X–rays is independent of applied accelerating voltage.

36. STATEMENT – 1 : If a train is moving in straight line, and its frequency of whistle is f. An observer which lies on perpendicular of path of train. Observer is stationary; frequency hand by observer will be continuously increasing. and STATEMENT – 2 : If relative motion occur between source and observer then frequency observed by observer will be different from frequency produced by source.

37. STATEMENT – 1 : If an object is projected from earth surface with escape velocity path of object will be parabola. andSTATEMENT – 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.

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.


Two metallic plates A and B, each of area 5 × 104 m2, are placed parallel to each other at a separation of 1 cm. Plate B carries a positive charge of 33.7 × 10 12 C. A monochromatic beam of light , with photons of energy 5 eV each , starts falling on plate A at t = 0 so that 10 16 photons fall on it per square meter per second. Assume that one photoelectrons is emitted for every 106 incident photons. Also assume that all the emitted photoelectrons are collected by plate B and the work function of plate A remains constant at the value 2eV.

38. The number of photoelectrons emitted up to t = 10 s(A) 5 × 107 (B) 5 × 106

(C) 25 × 108 (D) None of these

39. The magnitude of the electric field between the plates A and B at t = 10 s(A) 1000 N/C (B) 200 N/C(C) 2000 N/C (D) Zero

40. The kinetic energy of the most energetic photoelectron emitted at t = 10 s when it reaches plate B.(A) 23eV (B) 25eV(C) 12 eV (D) 46eV

Paragraph for Questions Nos. 41 to 43Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium. The kinetic energy of the fastest photo-electrons emitted from sodium is 0.73 eV. The work function for sodium is 1.82 eV.

41. The energy of the photons causing the photo-electric emission (A) 2.40 eV (B) 2.55 eV(C) 0.85 eV (D) 0.73 eV

42. The quantum number of the photons causing the photo-electric emission.(A) 4 and 2 (B) 3 and 2(C) 4 and 1 (D) 3 and 1

43. The change in the angular momentum of the electron in the hydrogen atom in the above transition(A) 2h/ (B) 3h/(C) h/ (D) (3/2)h/


A single electron orbits a stationary nucleus of charge +Ze, where Z is a constant and e is the magnitude of electronic charge. It requires 47.2 eV to excite the electron from the second orbit to third Bohr orbit. Find

44. The value of z(A) 25 (B) 5(C) 20 (D) 10

45. The energy required to excite the electron from the third to the fourth Bohr orbit.(A) 36.5 eV (B) 16.53 eV(C) 20 eV (D) 30 eV

46. The wavelength of electromagnetic radiation required to remove the electron from first Bohr orbit to infinity.(A) 36.5 Ao (B) 13.6 A°(C) 42.7 A° (D) 73 A°

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. The standard oxidation potential of Ni/Ni2+ electrode is 0.236V. If this is combined with a hydrogen electrode in acid solution at what pH of the solution will the measured e.m.f. be zero at 25°C. Assume [Ni2+] = 1M and = 1 atm?(A)pH = 4 (B) pH = 2(C) pH = 3 (D)pH = 1

48. A hydrocarbon with minimum number of carbon atoms, capable of showing geometrical isomerism as well as optical isomerism is:(A)3-methylpentene (B) 3-methylpentene-2(C) 4-methylhexene-2 (D)4-methylheptene-3

49. Standard electrode potentials for the gain of one electron by the ions Cu+ (aq) and Cu2+ (aq) are as follows : Cu+ (aq) + e ® Cu(s) E° = + 0.52 VCu2+ (aq) + e ® Cu+ (aq) E° = + 0.16 VThe standard potential for the disproportion,

2 Cu+ (aq) ® Cu+2(aq) + Cu(s), would be (A) 0.68 V (B) 0.36 V

(C) + 0.36 V (D) + 0.68 V

50. For the calomel half-cell, Hg, Hg2Cl2 | Cl (aq) values of electrode potentials are plotted at different log [Cl]. Variation is represented by

51. The depression in freezing point of equimolal aqueous solution will be highest for :

(A)C6H5NH3Cl (B) Ca(NO3)2 (C) La(NO3)3 (D)C6H12O6

52. The plots of (where XA and YA are the mole fraction of liquid A in liquid and

vapour phase respectively) is linear with slope and intercepts respectively

(A) (B)

(C) (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.

53. What can be said about the volume and pressure of one mole of a real gas at STP if the volume correction is ignored and the pressure correction is ignored respectively (Pi = ideal gas pressure, Pr = real gas pressure) (A) Pi > Pr (B) Vi > Vr(C) Vr > Vi (D) Pr > Pi

54. Correct statements are (A) I.E. for hydrogen atom = 13.6 ev(B) I.E. of Li2+ in the first excited state is 30.6eV(C) I.E. of Be3+ in the first excited state is 54.4 eV(D) I.E. of Li2+ in the first excited state in 10.6 eV

55. When Na2S is added to sodium nitroprusside solution:(A) violet colour is produced (B) A complex [Fe(CN)5NOS]4- is formed (C) The complex Na4[Fe(CN)5NOS] is formed (D) Na2[Fe(CN)5NOS] is formed

56. Consider the following alkene and select correct alternate(s)

(A)A 3° alcohol is formed by acidic hydration(B) A 1° alcoholi s formed by hydroboration-oxidation(C) A racemic mixture of 2° alcohols is formed by oxymercuration-demercuration(D)A racemic mixture of 1° alcohols is formed by oxymercuration-demercuration


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

57. STATEMENT-1: Na+ ions are discharged in preference to hydrogen ions at the mercury cathode.STATEMENT-1: The nature of the cathode can affect the order of discharge of ions.

58. STATEMENT-1: 0.1 M solution of glucose has higher increment in the freezing point than 0.1 M solution of urea STATEMENT-2: Kf for their aqueous solution has same values.

59. STATEMENT-1: Geometry of SF4 molecule can be termed as distorted tetrahedron, a folded square or see saw. because STATEMENT-2: four fluorine atoms surround or form bond with sulphur atom.

60. STATEMENT-1: Electrophilic substitution reaction on cummene is slower than toluene. becauseSTATEMENT-2: Positive inductive effect of isopropyl group is lesser than methyl group.

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. 61 to 63Molar conductance is used to define as the conducting power of all the ions produced by one mole of the electrolyte in a given solution.

K = specific conduction, Cm = concentration at infinite dilution each ion makes it’s contribution towards equivalent conductance of the electrolyte and at infinite dilution equivalent conductance is given by sum of equivalent conductance of the conducting ions. where x and y number of ions per formulae unit of electrolyte. By measuring the conductance (i) we can calculate degree of dissociation and Ka and Kb value.

(ii) we can measure solubility product of sparingly soluble salt. If solute is sparingly soluble in a given solvent, its concentration is taken as its solution in the saturated solution.

( of salt will be calculated by Kohlrausch’s law) By knowing C we can calculate Ksp.

61. The value of ÙC for 0.0010 M aqueous solution of NH3 will be : (given Kb for NH3 = 1.6 × 105 , Ù0 = 2.3 × 102 S m2 mole1)

(A) 2.18 × 102 (B) 3.01 × 103

(C) 1.579 × 105 (D) 1.17 × 104

62. The degree of dissociation of water will be (given Ù0 (H+) = 3.4582 × 102, Ù0 (OH) = 1.98 × 102 Sm2 mol1 and K = 5.7 × 106 S m1)(A) 1.875 × 107 % (B) 3.457 × 102 %(C) 1.27 % (D) 2.165 × 105

63. The specific conductance of 0.0025 M Na2SO4 solution would be : (Given resistance of Na2SO4 = 326.0 ohm, when the same cell is filled with NaCl which has specific conductance of 0.2768 ohm1 m1, resistance of 82.4 ).(A) 0.07 ohm1 m1 (B) 1.7 ohm1 m1

(C) 0.037 ohm1 m1 (D) .00257 ohm1 m1


Force per unit area applied by vapour on the upper thrust on the container at equilibrium state i.e., when rate of evaporation is equal to rate of condensation; is called vapour pressure. It depends on temperature. The vapour pressure above a solution of 5.0 gm acetic acid and in 100 gm H2O ( torr

at 25°C) was 23.4 torr & in 100 gm C6H6 ( torr at 25°C) was 70 torr. According to Raoult’s Law the vapour pressure of a solution containing non–volatile solute is equal to the vapour pressure of pure solvent times the mole traction of the solvent i.e., Psolution = Psolvent Xsolvent The abnormal behavior of the solution is calculated by Van’t Hoff factor (i) When i > 1 (solute shows dissociative nature)

i < 1 (solute shows associative nature) i = 1 (solute shows neither dissociation nor association)

64. From the above data, acetic acid in water shows (A)dissociative nature (B) associative nature (C) neither dissociative nor associative nature (D)none of these

65. The molecular weight of acetic acid in benzene is (A)60 (B) 120 (C) 113.1 (D)121.1

66. The molality of aq. Solution of acetic acid is (A)0.83 (B) 0.50 (C) 0.30 (D)0.10

Paragraph for Questions Nos. 67 to 69Stability of alkenes can be compared by converting these compounds to a common product and comparing the amounts of heat given off. One possibility would be to measure heats of combustion from converting alkenes to CO2 and H2O. Heats of combustion are large numbers, however, and measuring small difference in these large numbers is difficult. Alkene of lowest heat of combustion among the isomeric alkenes is of lowest energy and most stable. Stability of alkenes are often compared by measuring the heat of hydrogenation the heat given off (H°) during catalytic hydrogenation. Heats of hydrogenation are smaller numbers and provide more accurate energy difference.For a compound containing more than one double bond we might expect a heat of hydrogenation that is the sum of the heats of hydrogenation of the individual double bonds. For non conjugated dienes

this additive relationship is found to hold. For conjugated dienes, however, the measured values are slightly lower than expected. Cumulated dienes even less stable than non-conjugated dienes.Stabler the alkene lower the heat of combustion and heat of hydrogenation. More highly substituted double bonds are usually more stable. In case of cycloalkenes compounds having higher angle strain are less stable.

67. In which among the following compounds heat of hydrogenation is maximum ?(A)CH2 = CH2 (B) CH2 = C = CH2

(C) CH2 = CH — CH = CH2 (D)CH2 = CH — CH2 — CH = CH2

68. Match the correct optionAlkene Heat of Hydrogenation (– ) Kcal/mol(a) 2 methyl – 2 butene (i) 27.6(b) trans 2-pentene (ii) 26.9(c) cis 2-penteen (iii) 30.3(d) 3 methyl 1 butene (iv) 28.6(A) (a) ® (i), (b) ® (iv), (c) ® (ii), (d) ® (iii)(B) (a) ® (ii), (b) ® (i), (c) ® (iv), (d) ® (iii)(C) (a) ® (ii), (b) ® (iv), (c) ® (iii), (d) ® (i)(D) (a) ® (iii), (b) ® (iv), (c) ® (i), (d) ® (ii)

69. Among the following pairs in which case the second compound has higher heat of hydrogenation than the first

(A) (B) cis 2-butene, trans-2-butene

(C) (D) 1-butene, 2-butene

If you have any genuine question paper problems please contact the following subject concerned persons.Paper Setter : PUNJABI BAGH Mathematics : Mr. B.P. Singh Mobile: 09958068784Physics : Mr. Rishi Jha Mobile: 09999972017Chemistry : Mr. Vikas Mani Tripathi Mobile: 09999596350

Common Practice Test XII Std C/F Other Than Spark [79 Batches]

ANSWER KEYMATHEMATICS PHYSICS CHEMISTRY

Q. No. Answer Q. No. Answer Q. No. Answers

1 A 24 A 47 A2 B 25 C 48 C3 B 26 B 49 C4 C 27 D 50 C5 A 28 D 51 C6 C 29 A 52 B7 BD 30 BD 53 AC8 CD 31 ABC 54 ABC9 CD 32 BC 55 ABC10 ABCD 33 ACD 56 ABC11 B 34 C 57 A12 C 35 B 58 D13 A 36 D 59 B14 A 37 B 60 C15 D 38 A 61 B16 C 39 C 62 A17 B 40 A 63 A

18 C 41 B 64 C

19 C 42 A 65 C20 B 43 C 66 A21 C 44 B 67 B22 A 45 B 68 B23 B 46 A 69 C

CPT-23_79(C/F)Other Than Spark (XII std) CODE : DHAMAKA - 1

Hints /Solution

MATHEMATICS

1. Let

now

a is orthogonal aat = i

equating the corresponding elements we get

2. a2 – (a + d)a + (ad – bc)i

3. Let p(x) = ax + bq(x) = mx + nr(x) = cx + d

required determinant reduces to

applying c1 ® c1 – c2, c2 ® c2 – c3 we get

= (a1 – a2)(a2 – a3)


4. clearly

(using compendo and dividendo)

constant

ca – ba = constant

9. Let

= tan–1 at + tan–1 bt + tan–1 ct

= tan–1 (0) = 0,

11.

|a| = abc

and adj

12.

a = a ( a is skewy symmetric) det (a) = det(a)

= det(a)= det a


det a = 0det a = det(a) is not true

det(a) = (1)3 det (a) = det a

13. Let f(x) = a0 + a1x + a2x2 + …. f (x) = 0 + a1 + 2a2 x + …. or f (0) = a1

= 0 + 0 + 0= 0

14.

= (a + b + c) (a2 + b2 + c2 – ab – bc – ca) = 0( a + b + c = 0) (non trivial)

and a2 + b2 + c2 – ab – bc – ca

{(a – b)2 + (b – c)2 + (c – a)2} > 0

15. …..(i)

and …..(ii)

also , , , are in h.p.

[from eq.(i)]

and [from eq. (ii)]

now, lie on t1x2 – 4x + 1 = 0

t1 = 3and lie on t2x2 – 6x + 1 = 0

t2 = 2normal at ‘t1’ is

…..(iii)and normal at ‘t2’ is


…..(iv)solving eqs. (iii) and (iv), we get point of intersection is

or

16. both xy = 9 and x2 – y2 = 25 are rectangular hyperbolas

(e1, e2) lie on x2 + y2 = 4 …..(i)director circle of eq. (i) is

x2 + y2 = 8 (radius)2 = 8

17. normal at ‘t1’ to the hyperbola xy = c2 is

but this passes through ‘t2’ then

or

18. Let f(x) = a2x3 + abx2 + acx + ad f(x) has one negative root

f(0) > 0 ad > 0

19. a2 x3 + abx2 + acx + ad = 0has three real roots

ax2 + bx2 + cx + d = 0has two positive and one negative real roots.

20. Clearly ax3 + bx2 + cx + d takes two turns in [0, 2].Hence x [0, 2]

21. a is singular

1(40 – 40) – 3(20 – 24) + ( + 2) (10 – 12) = 0 12 – 2 4 = 0 = 4


tr(a + b) = 4 + 6 + 14 = 24

22. for = 3

tr(ab) + tr(ba) = 2tr (ab)tr(ab) = c11 + c22 + c33 = 119

(tr (ab) + tr(ba)) = (238) = 34

23. (a + b)2 = (a + b) (a + b) = a2 + ab + ba + b2 = a2 + b2 + ab + ba

CHEMISTRY

47. (A)47.

– log [H+] = 4

48. (C)

49. (C)

49. Ecell for dispropotionation will be = .052 0.16 = 0.36 V.

50. (C)50.

51. (C)

52. (B) and


and

or

or

or y = mx + C

slope = m = and intercept

C =

53. AC

54. ABC

55. ABC

56. ABC

57. (A)

58. (D)

59. (B)

60. (C)

61. (B)61.

By Ostwald’s dilution law

(molar conductance at infinite dilution ) = 2.38 × 102 S m2 mol1

(molar conductance at a given concentration) == 0.1265 × 2.38 × 102 S m2 mol1= 3.01 × 103 S m2 mol1

62. (A)62. C (concentration of H2O) = 1000 g

L1 =


63. (A)

63. Specific conductance =

Cell constant = 0.2768 × 82.4Hence specific conductance of Na2SO4

Will be = 22.81/326 = 0.07 ohm1 m1

64. (C)

Torr, nH2O = mol

Psolution = 23.4 Torr, n ACOH =

MACOH = 60.05 g/mol The original value of MACOH = 60 g/mol. AcOH remains as monomer.

65. (C)

mACOH = 113.1 gmol–1

66. (A)

m =

=

67. (B)68. (B)69. (C)


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FILE NO. IIT û 180-26 (01-11-2008) CPT_(79 CF)_XII STD_03-11 - 08 Qp