VITEEE Past Exam Paper 2009

Physics

1. When a wave traverses a medium the displacement of a particle located at x at a time t is given by y = a sin (bt – cx). Where a, b and c are constants of the wave. Which of the following is a quantity with dimensions?

(a) y/a

(b) bt

(d) b/c

Answer: (d)

2. A body is projected vertically upwards at time t = 0 and it is seen at a height H at time t₁ and t₂ second during its flight. The maximum height attained is (g is acceleration due to gravity)

(a)

(b)

(c)

(d)

Answer: (b)

3. A particle is projected up from a point at an angle θ with the horizontal direction. At any time t, if p is the linear momentum, y is the vertical displacement, x is horizontal displacement, the graph among the following which does not represent the variation of kinetic energy KE of the particle is

(a) graph (A)

(b) graph (B)

(d) graph (D)

Answer: (a)

4. A motor of power P₀ is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe n times, the power of the motor is increased to P₁. The ratio of P₁ to P₀ is

(a) n : 1

(b) n² : 1

(d) n⁴ : 1

Answer: (a)

5. A body of mass of 5 kg makes an elastic collision with another body at rest and continues to move in the original direction after collision with a velocity equal to 1/10th of its original velocity. Then the mass of the second body is

(a) 4.09 kg

(b) 0.5 kg

(d) 5.09 kg

Answer: (a)

6. A particle of mass 4 m explodes into three pieces of masses m, m and 2m. The equal masses move along X-axis and Y-axis with velocities 4 ms⁻¹ and 6 ms⁻¹ The magnitude of the velocity of the heavier mass is

(a) √17 ms⁻¹

(b) 2√13 ms⁻¹

(d) √13/2 ms⁻¹

Answer: (c)

7. A body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If R is the radius of the earth, maximum height attained by the body from the surface of the earth is

(a) R/6

(b) R/3

(d) R

Answer: (b)

8. The displacement of a particle executing SHM is given by

If T is the time period and the mass of the particle is 2g, the kinetic energy of the particle when t = T/4 is given by

(a) 0.4 J

(b) 0.5 J

(d) 0.3 J

Answer: (d)

9. If the ratio of lengths, radii and Young’s modulus of steel and brass wires shown in the figure are a, b and c respectively, the ratio between the increase in lengths of brass and steel wires would be

(a) b²a/2c

(b) bc/2a²

(d) a/2b²c

Answer: (d)

10. A soap bubble of radius r is blown up to form a bubble of radius 2r under is isothermal conditions. If T is the surface tension of soap solution, the energy spent in the blowing

(a) 3πTr²

(b) 6πTr²

(d) 24πTr²

Answer: (d)

11. Eight spherical rain drops of the same mass and radius are falling down with a terminal speed of 6 cm-s⁻¹. If they coalesce to form one big drop, what will be the terminal speed of bigger drop?

(Neglect the buoyancy of the air)

(a) 1.5 cm-s⁻¹

(b) 6 cm-s⁻¹

(d) 32 cm-s⁻¹

Answer: (c)

12. A clock pendulum made of invar has a period of 0.5 s, at 20° If the clock is used in a climate where the temperature averages to 30°C, how much time does the clock lose in each oscillation?

(For invar, α = 9 × 10⁻⁷/°C, g = constant)

(a) 2.25 × 10⁻⁶ s

(b) 2.5 × 10⁻⁷ s

(d) 1.125 × 10⁻⁶ s

Answer: (a)

13. A piece of metal weighs 45 g in air and 25 g in a liquid of density 1.5 × 10³ kg-m⁻³ kept at 30° When the temperature of the liquid is raised to 40°C, the metal piece weights 27g. The density of liquid of 40°C is 1.25 × 10³ kg-m³. The coefficient of linear expansion of metal is

(a) 1.3 × 10⁻³/°C

(b) 5.2 × 10⁻³/°C

(d) 0.26 × 10⁻³/°C

Answer: (c)

14. An ideal gas is subjected to a cyclic process ABCD as depicted in the p-V diagram given below:

Which of the following curves represents the equivalent cyclic process?

(a)

(b)

(c)

(d)

Answer: (a)

15. An ideal gas is subjected to cyclic process involving four thermodynamic states, the amounts of heat (Q) and work (W) involved in each of these states are

Q₁ = 6000 J, Q₂ = −5500 J; Q₃ = −3000 J; Q₄ = 3500 J

W₁ = 2500 J; W₂ = −1000 J; W₃ = −1200 J; W₄ = x J.

The ratio of the net work done by the gas to the total heat absorbed by the gas is η). The values of x and η respectively are

(a) 500; 7.5%

(b) 700; 10.5%

(d) 1500; 15%

Answer: (b)

16. Two cylinders A and B fitted with pistons contain equal number of moles of an ideal monoatomic gas at 400 K. The piston of A is free to move while that of B is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in A is 42 K, the rise in temperature of the gas in B is

(a) 21 K

(b) 35 K

(d) 70 K

Answer: (c)

17. Three rods of same dimensional have thermal conductivity 3 K, 2 K and K. They are arranged as shown in the figure below

Then, the temperature of the junction in steady state is

(a)

(b)

(d)

Answer: (a)

18. Two sources A and B are sending notes of frequency 680 Hz. A listener moves from A and B with a constant velocity u. If the speed of sound in air is 340 ms⁻¹, what must be the value of u so that he hears 10 beats per second?

(a) 2.0 ms⁻¹

(b) 2.5 ms⁻¹

(d) 3.5 ms⁻¹

Answer: (b)

19. Two identical piano wires have a fundamental frequency of 600 cycle per second when kept under the same tension. What fractional increase in the tension of one wires will lead to the occurrence of 6 beats per second when both wires vibrate simultaneously?

(a) 0.01

(b) 0.02

(d) 0.04

Answer: (b)

20. In the Young’s double slit experiment, the intensities at two points P₁ and P₂ on the screen are respectively I₁ and I₂. If P₁ is located at the centre of a bright fringe and P₂ is located at a distance equal to a quarter of fringe width from P₁, then I₁/I₂ is

(a) 2

(b) 1/2

(d) 16

Answer: (d)

21. In Young’s double slit experiment, the 10th maximum of wavelength λ₁ is at a distance of y₁, from the central maximum. When the wavelength of the source is changed to λ₂, 5th maximum is at a distance of y₂ from its central maximum. The ratio (y₁/y₂) is

(a) 2λ1/λ2

(b) 2 λ2/λ1

(d) λ2/2λ1

Answer: (a)

22. Four light sources produce the following four waves:

(i) y₁ = a sin(ωt + ϕ₁)

(ii) y₂ = a sin 2ωt

(iii) y₃ = a sin(ωt + ϕ₂)

(iv) y₄ = a sin(3ωt + ϕ)

Superposition of which two waves give rise to interference?

(a) (i) and (ii)

(b) (ii) and (iii)

(d) (iii) and (iv)

Answer: (c)

23. The two lenses of an achromatic doublet should have

(a) equal powers

(b) equal dispersive powers

(d) sum of the product of their powers and dispersive power equal to zero

Answer: (d)

24. Two bar magnets A and B are placed one over the other and are allowed to vibrate in a vibration magnetometer. They make 20 oscillations per minute when the similar poles of A and B are on the same side, while they make 15 oscillations per minute when their opposite poles lie on the same side. If M_A and M_Bare the magnetic moments of A and B and if M_A < M_B, the ratio of M_A and M_B is

(a) 4 : 3

(b) 25 : 7

(d) 25 : 16

Answer: (b)

25. A bar magnet is 10 cm long is kept with its north (N)-pole pointing north. A neutral point is formed at a distance of 15 cm from each pole. Given the horizontal component of earth’s field is 0.4 Gauss, the pole strength of the magnet is

(a) 9 A-m

(b) 6.75 A-m

(d) 1.35 A-m

Answer: (d)

26. An infinitely long him straight wire has uniform linear charge density of 1/3 cm⁻¹. Then, the magnitude of the electric intensity at a point 18 cm away is (given ε₀ = 8.8 × 10⁻¹² C² Nm⁻²)

(a) 0.33 × 10¹¹ NC⁻¹

(b) 3 × 10¹¹ NC⁻¹

(d) 1.32 × 10¹¹ NC⁻¹

Answer: (a)

27. Two point charges –q and +q are located at points (0, 0, −a) and (0, 0, a) respectively. The electric at a point (0, 0, z), where z > a is

(a)

(b)

(c)

(d)

Answer: (c)

28. In the adjacent shown circuit, a voltmeter of internal resistance R, when connected across B and C reads Neglecting the internal resistance of the battery, the value of R is

(a) 100 kΩ

(b) 75 kΩ

(d) 25 kΩ

Answer: (c)

29. A cell in secondary circuit gives null deflection for 2.5 m length of potentiometer having 10 m length of wire. If the length of the potentiometer wire is increased by 1 m without changing the cell in the primary, the position of the null point now is

(a) 3.5 m

(b) 3 m

(d) 2.0 m

Answer: (c)

30. The following series L-C-R circuit, when driven by an emf source of angular frequency 70 kilo-radians per second, the circuit effectively behaves like

(a) purely resistive circuit

(b) series R-L circuit

(d) series L-C circuit with R = 0

Answer: (c)

31. A wire of length l is bent into a circular loop of radius R and carries a current I. The magnetic field at the centre of the loop is B. The same wire is now bent into a double loop of equal radii. If both loops carry the same current I and it is in the same direction, the magnetic field at the centre of the double loop will be

(a) Zero

(b) 2 B

(d) 8 B

Answer: (c)

32. An infinitely long straight conductor is bent into the shape as shown below. It carries a current of I ampere and the radius of the circular loop is R metre. Then, the magnitude of magnetic induction at the centre of the circular loop is

(a)

(b)

(c)

(d)

Answer: (c)

33. The work function of a certain metal is 3.31 × 10⁻¹⁹ Then, the maximum kinetic energy of photoelectrons emitted by incident radiation of wavelength 5000 Å is (Given, h = 6.62 × 10⁻³⁴ J-s, c = 3 × 10⁸ ms⁻¹, e = 1.6 × 10⁻¹⁹ C)

(a) 2.48 eV

(b) 0.41 eV

(d) 0.82 eV

Answer: (b)

34. A photon of energy E ejects a photoelectron from a metal surface whose work function is W₀. If this electron enters into a uniform magnetic field of induction B in a direction perpendicular to the field and describes a circular path of radius r, then the radius r is given by, (in the usual notation)

(a)

(b)

(c)

(d)

Answer: (d)

35. Two radioactive materials x₁ and x₂ have decay constants 10λ and λ If initially they have the same number of nuclei, then the ratio of the number of nuclei of x₁ to that of x₂ will be 1/e

(a) (1/10λ)

(b) (1/11λ)

(d) 1/(9λ)

Answer: (d)

36. Current flowing in each of the following circuit A and B respectively are

(a) 1A, 2A

(b) 2A, 1A

(d) 2A, 4A

Answer: (c)

37. A bullet of mass 0.02 kg travelling horizontally with velocity 250 ms⁻¹ strikes a block of wood of mass 0.23 kg which rests on a rough horizontal surface. After the impact, the block and bullet move together and come to rest after travelling a distance of 40 m. The coefficient of sliding friction of the rough surface is (g = 9.8 ms⁻²)

(a) 0.75

(b) 0.61

(d) 0.30

Answer: (c)

38. Two persons A and B are located in X-Y plane at the points (0, 0) and (0, 10) respectively. (The distance are measured in MKS unit). At a time t = 0, they start moving simultaneously with velocities respectively. The time after which A and B are at their closest distance is

(a) 2.5s

(b) 4s

(d)

Answer: (a)

39. A rod of length l is held vertically stationary with its lower end located at a point P, on the horizontal When the rod is released to topple about P, the velocity of the upper end of the rod with which it hits the ground is

(a)

(b)

(c)

(d)

Answer: (b)

40. A wheel of radius 0.4 m can rotate freely about its axis as shown in the figure. A string is wrapped over its rim and a mass of 4 kg is hung. An angular acceleration of 8 rad-s⁻² is produced in it due to the torque. Then, moment of inertia of the wheel is (g = 10 ms⁻²)

(a) 2 kg-m²

(b) 1 kg-m²

(d) 8 kg-m²

Answer: (a)

Chemistry

41. Given that ∆H_f(H) = 218 kJ/mol, express the H−H bond energy in kcal/mol.

(a) 52.15

(b) 911

(d) 52153

Answer: (c)

42. Identify the alkyne in the following sequence of reactions,

(a) H₃C – C – C – CH₃

(b) H₃C – CH₂ – C ≡ CH

(d) HC ≡ C – CH₂ – C ≡ CH

Answer: (a)

43. Fluorine reacts with dilute NaOH and forms a gaseous product A. The bond angle in the molecule of A is

(a) 104°4′

(b) 103°

(d) 109°28′

Answer: (b)

44. One mole of alkene X on ozonolysis gave one mole of acetaldehyde and one mole of acetone. The IUPAC name of X is

(a) 2-methyl-2-butene

(b) 2-methyl-1-butene

(d) 1-butene

Answer: (a)

45. The number of pπ – dπ ‘pi’ bonds present in XeO₃ and XeO₄ molecules, respectively are

(a) 3, 4

(b) 4, 2

(d) 3, 2

Answer: (a)

46. The wavelengths of electron waves in two orbits is 3 : 5. The ratio of kinetic energy of electrons will be

(a) 25 : 9

(b) 5 : 3

(d) 3 : 5

Answer: (a)

47. Which one of the following sets correctly represents the increase in the paramagnetic property of the ions?

(a) Cu²⁺ > V²⁺ > Cr²⁺ > Mn²⁺

(b) Cu²⁺ < Cr²⁺ < V²⁺ < Mn²⁺

(d) V²⁺ < Cu²⁺ < Cr²⁺ < Mn²⁺

Answer: (c)

48. Electrons with a kinetic energy of 6.023 × 10⁴ J/mol are evolved from the surface of a metal, when it is exposed to radiation of wavelength of 600 nm. The minimum amount of energy required to remove an electron from the metal atom is

(a) 2.3125 × 10⁻¹⁹ J

(b) 3 × 10⁻¹⁹ J

(d) 6.62 × 10⁻³⁴ J

Answer: (a)

49. The chemical entities present in thermosphere of the atmosphere are

(a) O₂⁺, O⁺, NO⁺

(b) O₃

(d) O₃, O₂⁺, O₂

Answer: (a)

50. The type of bonds present in sulphuric anhydride are

(a) 3σ and three pπ-dπ

(b) 3σ, one pπ – pπ and two pπ – dπ

(d) 2σ and two pπ – dπ

Answer: (b)

51. In Gattermann reaction, a diazonium group is replaced by X using Y. X and Y are

Answer: (a)

52. Which pair of oxyacids of phosphorus contains ‘P−H’ bonds?

(a) H₃PO₄, H₃PO₃

(b) H₃PO₅, H₄P₂O₇

(d) H₃PO₂, HPO₃

Answer: (c)

53. Dipole moment of HCl = 1.03 D, HI = 0.38 D. Bond length of HCl = 1.3 Å and HI = 1.6 Å. The ratio of fraction of electric charge, δ, existing on each atom in HCl and HI is

(a) 12 : 1

(b) 2.7 : 1

(d) 1 : 3.3

Answer: (c)

54. SiCl₄ on hydrolysis forms ‘X’ and HCl. Compound ‘X’ loses water at 1000°C and gives ‘Y’. Compounds ‘X’ and ‘Y’ respectively are

(a) H₂SiCl₆, SiO₂

(b) H₄SiO₄, Si

(d) H₄SiO₄, SiO₂

Answer: (d)

55. 1.5g of CdCl₂ was found to contain 0.9 g of Cd. Calculate the atomic weight of Cd.

(a) 118

(b) 112

(d) 53.25

Answer: (c)

56. Aluminium reacts with NaOH and forms compound ‘X’. If the coordination number of aluminium in ‘X’ is 6, the correct formula of X is

(a) [Al(H₂O)₄(OH)₂]⁺

(b) [Al(H₂O)₃ (OH)₃]

(d) [Al(H₂O)₆](OH)₃

Answer: (c)

57. The average kinetic energy of one molecules of an ideal gas at 27°C and 1 atm pressure is

(a) 900 cal K⁻¹ mol⁻¹

(b) 6.21 × 10⁻²¹ JK⁻¹ molecule⁻¹

(d) 3741.3 JK⁻¹ mol⁻¹

Answer: (b)

58. Assertion (A) : Rb and Cs form superoxides.

Reason (R): The stability of the superoxides increases from ‘K’ to ‘Cs’ due to decrease in lattice energy.

The correct answer is

(a) Both (A) and (R) are true and (R) is the correct explanation of (A)

(b) Both (A) and (R) are true but (R) is not the correct explanation of (A)

(d) (A) is not true but (R) is true

Answer: (c)

59. How many mL of perhydrol is required to produce sufficient oxygen which can be used to completely convert 2 L of SO₂ gas to SO₃ gas?

(a) 10 mL

(b) 5 mL

(d) 30 mL

Answer: (a)

60. pH of a buffer solution decreases by 0.02 units when 0.12 g of acetic acid is added to 250 mL of a buffer solution of acetic acid and potassium acetate at 27° The buffer capacity of the solution is

(a) 0.1

(b) 10

(d) 0.4

Answer: (d)

61. Match the following

List I List II

(a) Flespar (I) [Ag₃Sb₃]

(b) Asbestos (II) Al₂O₃ . H₂O

(d) Diaspore (IV) KAlSi₃O₈

(V) CaMg₃(SiO₃)₄

The correct answer is

(a) (A) – IV ; (B) – V ; (C) – II ; (D) – I

(b) (A) – IV ; (B) – V ; (C) – I ; (D) – II

(d) (A) – II ; (B) – V ; (C) – IV ; (D) – I

Answer: (b)

62. Which one of the following order is correct for the first ionization energies of the elements?

(a) B < Be < N < O

(b) Be < B < N < O

(d) B < O < Be < N

Answer: (c)

63. What are X and Y in the following reaction sequence?

(a) C₂H₅Cl, CH₃CHO

(b) CH₃CHO, CH₃CO₂H

(d) C₂H₅Cl, CCl₃CHO

Answer: (c)

64. What are A, B, C in the following reactions?

(a) A – C₂H₆ ; B – CH₃COCH₃ ; C – (CH₃CO)₂O

(b) A – (CH₃CO)₂O ; B – C₂H₆ ; C – CH₃COCH₃

(d) A – CH₃COCH₃ ; B – (CH₃CO)₂O ; C – C₂H₆

Answer: (c)

65. One per cent composition of an organic compound A is, carbon : 85.71% and hydrogen 14.29%. Its vapour density is 14. Consider the following reaction sequence

Identify C.

(a)

(b) HO – CH₂ – CH₂ – CO₂H

(d) CH₃ – CH₂ – CO₂H

Answer: (b)

66. How many tripeptides can be prepared by linking the amino acids glycine, alaniine and phenyl alanine?

(a) One

(b) Three

(d) Twelve

Answer: (c)

67. A codon has a sequence of A and specifies a particular B that is to be incorporated into a C. What are A, B, C?

(a) A – 3 bases ; B – amino acid ; C – carbohydrate

(b) A – 3 acids ; B – carbohydrate ; C – protein

(d) A – 3 bases : B – amino acid ; C – protein

Answer: (d)

68. Parkinson’s disease is linked to abnormalities in the levels of dopamine in the body. The structure of dopamine is

(a)

(b)

(c)

(d)

Answer: (c)

69. During the depression in freezing point experiment, an equilibrium is established between the molecules of

(a) liquid solvent and solid solvent

(b) liquid solute and solid solvent

(d) liquid solvent and solid solute

Answer: (a)

70. Consider the following reaction,

Which one of the following statements is true for X?

(I) It gives propionic acid on hydrolysis

(II) It has an ester functional group

(III) It has a nitrogen linked to ethyl carbon

(IV) It has a cyanide group

(a) IV

(b) III

(d) I

Answer: (b)

71. For the following cell reaction,

Ag|Ag⁺|AgCl|Cl^⊖| Cl₂, Pt

∆G°_f (AgCl) = −109 kJ/mol

∆G°_f (Cl⁻) = −129 kJ/mol

∆G°_f (Ag⁺) = 78 kJ/mol

E° of the cell is

(a) −0.60 V

(b) 0.60 V

(d) None of these

Answer: (a)

72. The synthesis of crotonaldehyde from acetaldehyde is an example of ……… reaction.

(a) nucleophilic addition

(b) elimination

(d) nucleophilic addition-elimination

Answer: (d)

73. At 25°C, the molar conductances at infinite dilution for the strong electrolytes NaOH, NaCl and BaCl₂ are 248 × 10⁻⁴, 126 × 10⁻⁴ and 280 × 10× 10⁻⁴ Sm² mol⁻¹ respectively, λ°_m Ba(OH)₂ in Sm² mol⁻¹ is

(a) 52.4 × 10⁻⁴

(b) 524 × 10⁻⁴

(d) 262 × 10⁻⁴

Answer: (b)

74. The cubic unit cell of a metal (molar mass =63.55 g mol⁻¹) has and edge length of 362 pm. Its density is 8.92 g cm-3. The type of unit cell is

(a) primitive

(b) face centred

(d) end centred

Answer: (b)

75. The equilibrium constant for the given reaction is 100.

N₂(g) + 2O₂(g) ⇌ 2NO₂(g)

What is the equilibrium constant for the reaction given below?

(a) 10

(b) 1

(d) 0.01

Answer: (c)

76. For a first order reaction at 27°C, the ratio of time required for 75% completion to 25% completion of reaction is

(a) 3.0

(b) 2.303

(d) 0.477

Answer: (c)

77. The concentration of an organic compound in chloroform is 6.15 per 100 mL of solution. A portion of this solution in a 5 cm polarimeter tube causes an observed rotation of −2°. What is the specific rotation of the compound?

(a) +12°

(b) −3.9°

(d) +61.5°

Answer: (c)

78. 230 ml of 0.1 M acetic acid is mixed with 50 mL of potassium acetate. K_a of acetic acid = 1.8 × 10⁻⁵ at 27° Calculate concentration of potassium acetate if pH of the mixture is 4.8.

(a) 0.1 M

(b) 0.04 M

(d) 0.02 M

Answer: (a)

79. Calculate ∆H° for the reaction,

Na₂O(s) + SO₃(g) → Na₂SO₄ (g)

given the following:

(a) +823 kJ

(b) −581 kJ

(d) +531 kJ

Answer: (b)

80. Which one of the following is the most effective in causing the coagulation of an As₂S₃ sol?

(a) KCl

(b) AlCl₃

(d) K₃Fe(CN)₆

Answer: (a)

Mathematics

81. If f : [2, 3] → R is defined by f(x) = x³ + 3x – 2 then the range f(x) is contained in the interval

(a) [1, 12]

(b) [12, 34]

(d) [−12, 12]

Answer: (b)

82. The number of subsets of {1, 2, 3, …., 9} containing at least one odd number is

(a) 324

(b) 396

(d) 512

Answer: (c)

83. A binary sequence is an array of 0’s and 1’s. The number of n-digit binary sequences which contain even number of 0’s is

(a) 2^{n – 1}

(b) 2ⁿ – 1

(d) 2ⁿ

Answer: (a)

84. If x is numerically so small so that x² and higher powers of x can be neglected, then is approximately equal to

(a)

(b)

(c)

(d)

Answer: (a)

85. The root of (x – a) (x – a – 1) + (x – a – 1) (x – a – 2) + (x – a) (x – a – 2) = 0 a ∈ R are always

(a) equal

(b) imaginary

(d) rational and equal

Answer: (c)

86. Let f(x) = x² + ax + b, where a, b ∈ If f(x) = 0 has all its roots imaginary, then the roots of f(x) + f'(x) + f”(x) = 0 are

(a) real and distinct

(b) imaginary

(d) rational and equal

Answer: (b)

87. If f(x) = 2x⁴ – 13x² + ax + b is divisible by x² – 3x + 2, then (a, b) is equal to

(a) (–9, –2)

(b) (6, 4)

(d) (2, 9)

Answer: (c)

88. If x, y, z are all positive and are the pth, qth and rth terms of a geometric progression respectively, then the value of the determinant equals

(a) log xyz

(b) (p – 1) (q – 1) (r – 1)

(d) 0

Answer: (d)

89. The locus of z satisfying the inequality where z = x + iy, is

(a) x² + y² < 1

(b) x² – y² < 1

(d) 2x² + 3y² < 1

Answer: (c)

90. If n is an integer which leaves remainder one when divided by three, then (1 + √3i)ⁿ + (1 – √3i)ⁿ equals

(a) −2^{n + 1}

(b) 2^{n + 1}

(d) −2ⁿ

Answer: (c)

91. The period of sin⁴x + cos⁴ x is

(a) π⁴/2

(b) π²/2

(d) π/2

Answer: (d)

92. If 3 cos x ≠ 2 sin x, then the general solution of sin² x- cos 2x = 2 – sin 2x is

(a)

(b)

(c)

(d) (2n – 1)π, n∈ Z

Answer: (c)

93.

(a) 19π/12

(b) 35π/12

(d) 43π/12

Answer: (d)

94. In a ∆ ABC equals

(a) cos²A

(b) cos²B

(d) sin²B

Answer: (c)

95. The angle between the lines whose direction cosines satisfy the equations l + m + n = 0, l² + m² – n² = 0 is

(a) π/6

(b) π/4

(d) π/2

Answer: (c)

96. If m₁, m₂, m₃ and m₄ are respectively the magnitudes of the vectors

then the correct order of m₁, m₂, m₃ and m₄ is

(a) m₃ < m₁ < m₄ < m₂

(b) m₃ < m₁ < m₂ < m₄

(d) m₃ < m₄ < m₂ < m₁

Answer: (a)

97. If X is a binomial variate with the range {0, 1, 2, 3, 4, 5, 6} and P(X = 2) = 4P(X = 4), then the parameter p of X is

(a) 1/3

(b) 1/2

(d) 3/4

Answer: (a)

98. The area (in square unit) of the circle which touches the lines 4x + 3y = 15 and 4x + 3y = 5 is

(a) 4π

(b) 3π

(d) π

Answer: (d)

99. The area (in square unit) of the triangle formed by x + y + 1 = 0 and the pair of straight lines x² – 3xy + 2y² = 0 is

(a) 7/12

(b) 5/12

(d) 1/6

Answer: (c)

100. The pairs of straight lines x² – 3xy + 2y² = 0 and x² – 3xy + 2y² + x – 2 = 0 form a

(a) square but not rhombus

(b) rhombus

(d) rectangle but not a square

Answer: (c)

101. The equations of the circle which pass through the origin and makes intercepts of lengths 4 and 8 on the x and y-axes respectively are

(a) x² + y² ± 4x ± 8y = 0

(b) x² + y² ± 2x ± 4y = 0

(d) x² + y² ± x ± y = 0

Answer: (a)

102. The point (3, −4) lies on both the circles x² + y² – 2x + 8y + 13 = 0 and x² + y² – 4x + 6y + 11 = 0

Then, the angle between the circles is

(a) 60°

(b) tan⁻¹ (1/2)

(d) 135°

Answer: (d)

103. The equation of the circle which passes through the origin and cuts orthogonally each of the circles x² + y² – 6x + 8 = 0 and x² + y² – 2x – 2y = 7 is

(a) 3x² + 3y² – 8x – 13y = 0

(b) 3x² + 3y² – 8x + 29y = 0

(d) 3x² + 3y² – 8x – 29y = 0

Answer: (b)

104. The number of normals drawn to the parabola y² = 4x from the point (1, 0) is

(a) 0

(b) 1

(d) 3

Answer: (b)

105. If the circle x² + y² = a² intersects the hyperbola xy = c² in four points (x₁, y₁) for i = 1, 2, 3 and 4, then y₁ + y₂ + y₃ + y₄ equals

(a) 0

(b) c

(d) c⁴

Answer: (a)

106. The mid point of the chord 4x – 3y = 5 of the hyperbola 2x² – 3y² = 12 is

(a) (0, −5/3)

(b) (2, 1)

(d) (11/4, 2)

Answer: (b)

107. The perimeter of the triangle with vertices at (1, 0, 0), (0, 1, 0) and (0, 0, 1) is

(a) 3

(b) 2

(d) 3√2

Answer: (d)

108. If a line in the space makes angle α, β and γ with the coordinates axes, then cos 2α + cos 2β + cos 2γ + sin² α + sin² β + sin² γ equals

(a) −1

(b) 0

(d) 2

Answer: (c)

109. The radius of the sphere x² + y² + z² = 12x + 4y + 3z is

(a) 13/2

(b) 13

(d) 52

Answer: (a)

110.

(a) e

(b) e²

(d) e⁵

Answer: (c)

111. If f : R → R is defined by

then the value of a so that f is continuous at 0 is

(a) 2

(b) 1

(d) 0

Answer: (d)

112. is equal to

(a) 0

(b) tan t

(d) sin t cos t

Answer: (c)

113. is equal to

(a) 1

(b) −1

(d) 2

Answer: (b)

114. is equal to

(a) −(n² + a²) y_n

(b) (n² – a²)y_n

(d) −(n² – a²)y_n

Answer: (c)

115. The function f(x) = x³ + ax² + bx + c, a² ≤ 3b has

(a) one maximum value

(b) one minimum value

(d) one maximum and one minimum value

Answer: (c)

116.

(a) −e^x cot x + c

(b) e^x cot x + c

(d) −2e^x cot x + c

Answer: (a)

117. If I_n = ∫sinⁿ x dx, then nI_n – (n – 1)I_{n – 2}equals

(a) sin^{n – 1} x cos x

(b) cos ^{n – 1} x sin x

(d) −cos^{n – 1} x sin x

Answer: (c)

118. The line x = π/4 divides the area of the region bounded by y = sin x, y = cos x and x-axis (0 ≤ x ≤ π/2) into two regions of areas A₁ and A₂. Then A₁ : A₂ equals

(a) 4 : 1

(b) 3 : 1

(d) 1 : 1

Answer: (d)

119. The solution of the differential equation is

(a) cosec(x + y) + tan(x + y) = x + c

(b) x + cosec (x + y) = c

(d) x + sec (x + y) = c

Answer: (b)

120. If p ⇒ (~ p ⋁ q) is false, the truth value of p and q are respectively

(a) F, T

(b) F, F

(d) T, T

Answer: (c)

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