**JEE Main (AIEEE) Past Exam Question Paper 2011 Set-Q**

**Physics**

1. The transverse displacement y (x, t) of a wave on a string is given by This represents a

(1) wave moving in – x direction with speed

(2) standing wave of frequency √b

(3) standing wave of frequency 1/√b

(4) wave moving in + x direction with

2. A screw gauge gives the following reading when used to measure the diameter of a wire.

Main scale reading : 0 mm

Circular scale reading : 52 divisions

Given that 1 mm on main scale corresponds to 100 divisions of the circular scale.

The diameter of wire from the above data is :

(1) 0.052 cm

(2) 0.026 cm

(3) 0.005 cm

(4) 0.52 cm

3. A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is

(1) g

(2)

(3) g/3

(4)

4. Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly (Surface tension of soap solution = 0.03 Nm^{−1}):

(1) 0.2π mJ

(2) 2π mJ

(3) 0.4 π mJ

(4) 4π mJ

5. A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc:

(1) continuously decreases

(2) continuously increases

(3) first increases and then decreases

(4) remains unchanged

6. Two particles are executing simple harmonic motion of the same amplitude A and frequency ω along the x-axis. Their mean position is separated by distance X_{0}(X_{0} > A). If the maximum separation between them is (X0 + A), the phase difference between their motion is:

(1) π/3

(2) π/4

(3) π/6

(4) π/2

7. Two bodies of masses m and 4 m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is:

(1) −4Gm/r

(2) −6Gm/r

(3) −9Gm/r

(4) zero

8. Two identical charged spheres suspended from a common point by two massless strings of length l are initially a distance d(d << 1) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity v. Then as a function of distance x between them,

(1) v ∝ x^{−}^{1}

(2) v ∝ x^{1/2}

(3) v ∝ x

(4) v ∝ x^{−}^{1/2}

9. A boat is moving due east in a region where the earth’s magnetic field is 5.0×10⁻⁵NA^{−}^{1} m^{−}^{1} due north and horizontal. The boat carries a vertical aerial 2m long. If the speed of the boat is 1.50 ms^{−}^{1}, the magnitude of the induced emf in the wire of aerial is:

(1) 0.75 mV

(2) 0.50 mV

(3) 0.15 mV

(4) 1 mV

10. An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by :

where v is the instantaneous speed. The time taken by the object, to come to rest, would be :

(1) 2 s

(2) 4 s

(3) 8 s

(4) 1 s

11. A fully charged capacitor C with initial charge q_{0} is connected to a coil of self inductance L at t = 0. The time at which the energy is stored equally between the electric and the magnetic field is :

(1)

(2) 2π√LC

(3) √LC

(4) π√LC

12. Let the x – z plane be the boundary between two transparent media. Medium 1 in z ≥ 0 has a refractive index of √2 and medium 2 with z < 0 has a refractive index of √ A ray of light in medium 1 given by the vector is incident on the plane of separation. The angle of refraction in medium 2 is

(1) 45°

(2) 60°

(3) 75°

(4) 30°

13. A current I flows in an infinitely long wire with cross section in the form of a semicircular ring of radius R. The magnitude of the magnetic induction along its axis is

(1)

(2)

(3)

(4)

14. A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats γ. It is moving with speed υ and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by :

(1)

(2)

(3)

(4)

15. A mass M, attached to a horizontal spring, executes S.H.M. with amplitude A_{1}. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude A_{2}. The ratio of (A_{1}/A_{2}) is :

(1)

(2)

(3)

(4)

16. Water is flowing continuously from a tap having an internal diameter 8 × 10^{−}^{3} The water velocity as it leaves the tap is 0.4 ms^{−}^{1}. The diameter of the water stream at a distance 2×10^{−1 }m below the lap is close to :

(1) 7.5 ×10^{−3 }m

(2) 9.6 ×10^{−3 }m

(3) 3.6 ×10^{−3 }m

(4) 5.0 ×10^{−3 }m

17. This question has Statement – 1 and Statement – 2. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement-1 : Sky wave signals are used for long distance radio communication. These signals are in general, less stable than ground wave signals.

Statement-2 : The state of ionosphere varies from hour to hour, day to day and season to season.

(1) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

(2) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

(3) Statement-1 is false, Statement-2 is true.

(4) Statement-1 is true, Statement-2 is false.

18. Three perfect gases at absolute temperatures T_{1}, T_{2} and T_{3} are mixed. The masses of molecules are m_{1}, m_{2} and m_{3} and the number of molecules are n_{1}, n_{2} and n_{3} Assuming no loss of energy, the final temperature of the mixture is :

(1)

(2)

(3)

(4)

19. A pulley of radius 2 m is rotated about its axis by a force F = (20t − 5t^{2}) Newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation made by the pulley before its direction of motion if reversed, is :

(1) more than 3 but less than 6

(2) more than 6 but less than 9

(3) more than 9

(4) less than 3

20. A resistor ‘R’ and 2μF capacitor in series is connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5 s after the switch has been closed.(log_{10}5 = 0.4 )

(1) 1.7 ×10^{5}Ω

(2) 2.7 ×10^{6}Ω

(3) 3.3 ×10^{7}Ω

(4) 1.3 ×10^{4}Ω

21. A Carnot engine operating between temperatures T_{1} and T_{2} has efficiency 1/6. When T_{2} is lowered by 62 K, its efficiency increases to 1/3. Then T_{1} and T_{2} are, respectively :

(1) 372 K and 330 K

(2) 330 K and 268 K

(3) 310 K and 248 K

(4) 372 K and 310 K

22. If a wire is stretched to make it 0.1% longer, its resistance will :

(1) increase by 0.2%

(2) decrease by 0.2%

(3) decrease by 0.05%

(4) increases by 0.05%

23. **Direction:**

The question has a paragraph followed by two statements, Statement – 1 and statement – 2. Of the given four alternatives after the statements, choose the one that describes the statements.

A thin air film is formed by putting the convex surface of a plane – convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film.

Statement-1 : When light reflects from the air-glass plate interface, the reflected wave suffers a phase change of π.

Statement-2 : The centre of the interference pattern is dark.

(1) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

(2) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

(3) Statement-1 is false, Statement-2 is true.

(4) Statement-1 is true, Statement-2 is false.

24. A car is fitted with a convex side-view mirror of focal length 20cm. A second car 2.8 m behind the first car is overtaking the first car at relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is:

(1) 1/15 m/s

(2) 10 m/s

(3) 15 m/s

(4) 1/10 m/s

25. Energy required for the electron excitation in Li^{++} from the first to the third Bohr orbit is :

(1) 36.3 eV

(2) 108.8 eV

(3) 122.4 eV

(4) 12.1 eV

26. The electrostatic potential inside a charged spherical ball is given by φ = αρ^{2} + b where r is the distance from the centre; a, b are constants. Then the charge density inside ball is

(1) −6aε_{0}r

(2) −24πaε_{0}r

(3) −6aε_{0}

(4) −24πaε_{0}

27. A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is:

(1)

(2)

(3)

(4)

28. 100g of water is heated from 30°C to 50°C. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4148 J/kg/K):

(1) 8.4 kJ

(2) 84 kJ

(3) 2.1 kJ

(4) 4.2 kJ

29. The half life of a radioactive substance is 20 minutes. The approximate time interval (t_{2 }− t_{1}) between the time t₂ when 2/3 of it has decayed and time t_{1} and 1/3 of it had decayed is:

(1) 14 min

(2) 20 min

(3) 28 min

(4) 7 min

30. This question has Statement – 1 and Statement – 2. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement-1 : A metallic surface is irradiated by a monochromatic light of frequency v > v0 (the threshold frequency). The maximum kinetic energy and the stopping potential are K_{max} and V_{0} respectively. If the frequency incident on the surface doubled, both the K_{max} and V_{0} are also doubled.

Statement-2 : The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.

(1) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

(2) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

(3) Statement-1 is false, Statement-2 is true.

(4) Statement-1 is true, Statement-2 is false.

**Chemistry**

31. Among the following the maximum covalent character is shown by the compound:

(1) SnCl_{2}

(2) AlCl_{3}

(3) MgCl_{2}

(4) FeCl_{2}

32. Among the following the maximum covalent character is shown by the compound:

(1) 2nd

(2) 3rd

(3) 4th

(4) 1st

33. Trichloroacetaldehyde was subjected to Cannizzaro’s reaction by using NaOH. The mixture of the products contains sodium trichloroacetate and another compound. The other compound is:

(1) Trichloromethanol

(2) 2, 2, 2-Trichloropropanol

(3) Chloroform

(4) 2, 2, 2-Trichloroethanol

34. Sodium ethoxide has reacted with ethanoyl chloride. The compound that is produced in the above reaction is:

(1) 2-Butanone

(2) Ethyl chloride

(3) Ethyl ethanoate

(4) Diethyl ether

35. The reduction potential of hydrogen half cell will be negative if:

(1) p(H_{2}) = 1 atm and [H^{+}] =1.0 M

(2) p (H_{2} )=2 atm and [H^{+} ] =1.0 M

(3) p (H_{2} ) = 2 atm and [H^{+}] = 2.0 M

(4) p (H_{2} ) =1 atm and [H^{+}] = 2.0 M

36. The strongest acid amongst the following compounds is:

(1) HCOOH

(2) CH_{3}CH_{2}CH(Cl)CO_{2}H

(3) ClCH_{2}CH_{2}CH_{2}COOH

(4) CH_{3}COOH

37. The degree of dissociation (α) of a weak electrolyte, A_{X}B_{Y} is related to van’t Hoff factor (i) by the expression:

(1)

(2)

(3)

(4)

38. `a’ and `b’ are van der Waals’ constants for gases. Chlorine is more easily liquefied than ethane because

(1) a and b for Cl_{2} < a and b for C_{2}H_{6}

(2) a for Cl_{2} < a for C_{2}H_{6} but b for Cl_{2} > b for C_{2}H_{6}

(3) a for Cl_{2} > a for C_{2}H_{6} but b for Cl_{2} < b for C_{2}H_{6}

(4) a and b for Cl_{2} > a and b for C_{2}H_{6}

39. A vessel at 1000 K contains CO_{2} with a pressure of 0.5 atm. Some of the CO_{2} is converted into CO on the addition of graphite. If the total pressure at equilibrium is 0.8 atm, the value of K is

(1) 3 atm

(2) 0.3 atm

(3) 0.18 atm

(4) 1.8 atm

40. Boron cannot form which one of the following anions?

(1) BH_{4}^{−}

(2) B(OH)_{4}^{−}

(3) BO_{2}^{−}

(4) BF_{6}^{3}^{−}

41. Which of the following facts about the complex [Cr (NH_{3})_{6}] Cl_{3} is wrong?

(1) The complex is paramagnetic

(2) The complex is an outer orbital complex

(3) The complex gives white precipitate with silver nitrate solution

(4) The complex involves d^{2}sp^{3} hybridization and is octahedral in shape.

42. Ethylene glycol is used as antifreeze in a cold climate. Mass of ethylene glycol which should be added to 4 kg of water to prevent it from freezing at −6°C will be:

[Kf for water = 1.86 K kg mol^{−}^{1} and molar mass of ethylene glycol = 62g mol^{−}^{1})

(1) 204.30 g

(2) 400.00 g

(3) 304.60 g

(4) 804.32 g

43. Which one of the following order represents the correct sequence of the increasing basic nature of the given oxides?

(1) MgO < K_{2}O < Al_{2}O_{3} < Na_{2}O

(2) Na_{2}O < K_{2}O < MgO < Al_{2}O_{3}

(3) K_{2}O < Na_{2}O < Al_{2}O_{3} < MgO

(4) Al_{2}O_{3} < MgO < Na_{2}O < K_{2}O

44. The rate of a chemical reaction doubles for every 10°C rise of temperature. If the temperature is raised by 50°C, the rate of the reaction increases by about :

(1) 24 times

(2) 32 times

(3) 64 times

(4) 10 times

45. The magnetic moment (spin only) of [NiCl_{4}]^{2}^{−} is

(1) 5.46 BM

(2) 2.83 BM

(3) 1.41 BM

(4) 1.82 BM

46. The hybridization of orbitals of N atom in NO_{3}^{−}, NO_{2}^{+} and NH_{4}^{+} are respectively :

(1) sp^{2}, sp, sp^{3}

(2) sp, sp^{3}, sp^{2}

(3) sp^{2}, sp^{3}, sp

(4) sp, sp^{2}, sp^{3}

47. In context of the lanthanoids, which of the following statements is not correct?

(1) All the members exhibit +3 oxidation state

(2) Because of similar properties the separation of lanthanoids is not easy.

(3) Availability of 4f electrons results in the formation of compounds in +4 state for all the members of the series.

(4) There is a gradual decrease in the radii of the members with increasing atomic number in the series.

48. A 5.2 molal aqueous solution of methyl alcohol, CH_{3}OH, is supplied. What is the mole fraction of methyl alcohol in the solution?

(1) 0.190

(2) 0.086

(3) 0.050

(4) 0.100

49. Which of the following statement is wrong?

(1) Nitrogen cannot form dπ – pπ bond.

(2) Single N- N bond is weaker than the single P – P bond.

(3) N_{2}O_{4} has two resonance structures

(4) The stability of hydrides increases from NH_{3} to BiH_{3} in group 15 of the periodic table

50. The outer electron configuration of Gd (Atomic No: 64 is:

(1) 4f^{8} 5d^{0} 6s^{2}

(2) 4f^{4} 5d^{4} 6s^{2}

(3) 4f^{7} 5d^{1} 6s^{2}

(4) 4f^{3} 4d^{5} 6s^{2}

51. Which of the following statements regarding sulphur is incorrect?

(1) The vapour at 200°C consists mostly of S_{8} rings

(2) At 600°C the gas mainly consists of S_{2} molecules

(3) The oxidation state of sulphur is never less than +4 in its compounds

(4) S_{2} molecule is paramagnetic

52. The structure of IF_{7} is:

(1) trigonal bipyramid

(2) octahedral

(3) pentagonal bipyramid

(4) square pyramid

53. Ozonolysis of an organic compound gives formaldehyde as one of the products. This confirms the presence of:

(1) a vinyl group

(2) an isopropyl group

(3) an acetylenic triple bond

(4) two ethylenic double bonds

54. A gas absorbs a photon of 355 nm and emits at two wavelengths. If one of the emissions is at 680 nm, the other is at:

(1) 325 nm

(2) 743 nm

(3) 518 nm

(4) 1035 nm

55. Silver Mirror test is given by which one of the following compounds?

(1) Acetone

(2) Formaldehyde

(3) Benzophenone

(4) Acetaldehyde

56. Which of the following reagents may be used to distinguish between phenol and benzoic acid?

(1) Tollen’s reagent

(2) Molisch reagent

(3) Neutral FeCl_{3}

(4) Aqueous NaOH

57. Phenol is heated with a solution of mixture of KBr and KBrO_{3}. The major product obtained in the above reaction is

(1) 3-Bromophenol

(2) 4-Bromophenol

(3) 2, 4, 6- Tribromophenol

(4) 2-Bromophenol

58. In a face centred cubic lattice, atom A occupies the corner positions and atom B occupies the face centre positions. If one atom of B is missing from one of the face centred points, the formula of the compound is:

(1) AB_{2}

(2) A_{2}B_{3}

(3) A_{2}B_{5}

(4) A_{2}B

59. The entropy change involved in the isothermal reversible expansion of 2 moles of an ideal gas from a volume of 10 dm³ to a volume of 100 dm^{3} at 27°C is:

(1) 35.8 J mol^{−}^{1} K^{−}^{1}

(2) 32.3 J mol^{−}^{1} K^{−}^{1}

(3) 42.3 J mol^{−}^{1} K^{−}^{1}

(4) 38.3 J mol^{−}^{1} K^{−}^{1}

60. Identify the compound that exhibits tautomerism.

(1) Lactic acid

(2) 2-Pentanone

(3) Phenol

(4) 2-Butene

**Mathematics**

61. The lines L_{1 }: y−x =0 and L₂: 2x+y=0 intersect the line L_{3 }: y+2=0 at P and Q respectively. The bisector of the acute angle between L_{1} and L_{2} intersect L_{3} at R.

Statement – 1: The ratio PR: RQ equals 2√2 : √5

Statement – 2: In any triangle, bisector of an angle divides the triangle into two similar triangles.

(1) Statement – 1 is true, Statement – 2 is true; Statement – 2 is not a correct explanation for Statement–1

(2) Statement – 1 is true, Statement– 2 is false

(3) Statement – 1 is false, Statement– 2 is true

(4) Statement – 1 is true, Statement – 2 is true; Statement – 2 is a correct explanation for Statement – 1

62. If A = sin^{2} x + cos^{4} x , then for all real x

(1)

(2) 1 ≤ A ≤ 2

(3)

(4)

63. The coefficient of x^{7} in the expansion of (1 – x – x^{2} + x^{3})^{6} is

(1) −132

(2) −144

(3) 132

(4) 144

64.

(1) equals √2

(2) equals −√2

(3) equals 1/√2

(4) does not exist

65. Statement – 1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ^{9}C_{3}

Statement – 2 : The number of ways of choosing any 3 places from 9 different places is ^{9}C_{3}.

(1) Statement – 1 is true, Statement – 2 is true; Statement – 2 is not a correct explanation for Statement – 1

(2) Statement – 1 is true, Statement– 2 is false.

(3) Statement – 1 is false, Statement– 2 is true.

(4) Statement – 1 is true, Statement – 2 is true; Statement – 2 is a correct explanation for Statement – 1

66.

(1)

(2)

(3)

(4)

67. If and y(0) = 2, then y(ln 2) is equal to

(1) 5

(2) 13

(3) −2

(4) 7

68. Let R be the set of real numbers

Statement – 1 : A = {(x, y) ∈ R × R : y – x is an integer} is an equivalence relation on R.

Statement – 2 : B ={(x, y) ∈ R × R : x = αy for some rational number α} is an equivalence relation on R.

(1) Statement – 1 is true, Statement – 2 is true; Statement – 2 is not a correct explanation for Statement−1

(2) Statement – 1 is true, Statement– 2 is false

(3) Statement – 1 is false, Statement– 2 is true

(4) Statement – 1 is true, Statement – 2 is true; Statement – 2 is a correct explanation for Statement

69.

(1)

(2)

(3) log 2

(4) πlog 2

70. Let α, β be real and z be a complex number. If z^{2} + αz + β = 0 has two distinct roots on the line Rez = 1, then it is necessary that

(1) β∈(−1, 0)

(2) β = 1

(3) β∈(1, ∞)

(4) β∈(0, 1)

71. Consider 5 independent Bernoulli’s trials each with probability of success p. If the probability of at least one failure is greater than or equal to 31/32, then p lies in the interval

(1)

(2)

(3)

(4)

72. A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after

(1) 19 months

(2) 20 months

(3) 21 months

(4) 18 months

73. The domain of the function is

(1) (0, ∞)

(2) (−∞, 0)

(3) (−∞,−∞) – {0}

(4) (−∞,∞)

74. If the angle between the line and the plane x + 2y + 3z = 4 is then λ equals

(1) 3/2

(2) 2/5

(3) 5/3

(4) 2/3

75.

(1) −3

(2) 5

(3) 3

(4) −5

76. Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (−3, 1) and has eccentricity is

(1) 5x^{2} + 3y^{2} – 48 = 0

(2) 3x^{2} + 5y^{2} – 15 = 0

(3) 5x^{2} + 3y^{2} – 32 = 0

(4) 3x^{2} + 5y^{2} – 32 = 0

77. Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equation where k > 0 is a constant and T is the total life in years of the equipment. Then the scarp value V(T) of the equipment is

(1)

(2)

(3) e^{−}^{kT}

(4)

78. The vector are not perpendicular and are two vectors satisfying Then the vector is equal to

(1)

(2)

(3)

(4)

79. The two circles x^{2} + y^{2} = ax and x^{2} + y^{2} = c^{2} (c > 0) touch each other if

(1) |a| = c

(2) a = 2c

(3) |a| = 2c

(4) 2|a| = c

80. If C and D are two events such that C ⊂ D and P(D) ≠ 0, then the correct statement among following is

(1) P(C | D) ≥ P(C)

(2) P(C | D) < P(C)

(3)

(4) P(C | D) = P(C)

81. The number of values of k for which the linear equations 4x + ky + 2z = 0 ; kx + 4y + z = 0 ; 2x + 2y + z = 0 possess a non-zero solution is

(1) 2

(2) 1

(3) zero

(4) 3

82. Consider the following statements

P : Suman is brilliant

Q : Suman is rich

R : Suman is honest

The negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as

(1) ~(Q↔(P∧~R))

(2) ~ Q↔~ P∧R

(3) ~(P∧~R)↔Q

(4) ~P∧(Q↔~R)

83. The shortest distance between line y−x=1 and curve x= y^{2} is

(1)

(2)

(3)

(4)

84. If the mean deviation about the median of the numbers a, 2a, …, 50a is 50, then |a| equals

(1) 3

(2) 4

(3) 5

(4) 2

85. Statement – 1 : The point A(1, 0, 7) is the mirror image of the point B(1, 6, 3) in the line

Statement – 2 : The line : bisects the line segment joining A(1, 0, 7) and B(1, 6, 3) .

(1) Statement – 1 is true, Statement–2 is true; Statement–2 is not a correct explanation for Statement – 1

(2) Statement – 1 is true, Statement– 2 is false.

(3) Statement – 1 is false, Statement– 2 is true.

(4) Statement – 1 is true, Statement – 2 is true; Statement – 2 is a correct explanation for Statement – 1

86. Let A and B be two symmetric matrices of order 3.

Statement – 1 : A(BA) and (AB)A are symmetric matrices.

Statement – 2 : AB is symmetric matrix if matrix multiplication of A and B is commutative.

(1) Statement – 1 is true, Statement – 2 is true; Statement – 2 is not a correct explanation for Statement– 1

(2) Statement – 1 is true, Statement– 2 is false.

(3) Statement – 1 is false, Statement– 2 is true.

87. If ω(≠ 1) is a cube root of unity, and (1+ ω)^{7} = A + Bω . Then (A, B) equals

(1) (1, 1)

(2) (1, 0)

(3) (−1, 1)

(4) (0, 1)

88. The value of p and q for which the function is continuous for all x in R, is

(1) p = 5/2, q = 1/2

(2) p = −3/2, q = 1/2

(3) p = 1/2, q = 3/2

(4) p = 1/2, q = −3/2

89. The area of the region enclosed by the curves y x, x e, y = 1/x and the positive x-axis is

(1) 1 square unit

(2) 3/2 square units

(3) 5/2 square units

(4) 1/2 square units

90. For Then f has

(1) local minimum at π and 2π

(2) local minimum at π and local maximum at 2π

(3) local maximum at π and local minimum at 2π

(4) local maximum at π and 2π

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