JEE Main (AIEEE) 2012 Question Paper

JEE Main (AIEEE) 2012 Question Paper

Physics

1. A wooden wheel of radius R is made of two semicircular parts (see figure). The two parts are held together by a ring made of a metal strip of cross-sectional area s and length L. L is slightly less than 2πR. To fit the ring on the wheel, it is heated so that its temperature rises by ∆T and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is α and its Young’s modulus is Y, the force that one part to the wheel applies on the other part is:

(1)  2πSYα∆T

(2)  SYα∆T

(3)  πSYα∆T

(4)  2SYα∆T

Answer: (4)

2. The figure shows an experimental plot discharging of a capacitor in an R-C circuit. The time constant τ of this circuit lies between

(1)  150s and 200s

(2)  0 and 50s

(3)  50s and 100s

(4)  100s and 150s

Answer: (4)

3. In a uniformly charged sphere of total charge Q and radius R, the electric field E is plotted as function of distance from the centre. The graph which would correspond to the above will be

(1) 

(2) 

(3) 

(4) 

Answer: (3)

4. An electromagnetic wave in vacuum has the electric and magnetic fields E and B, which are always perpendicular to each other. The direction polarization is given by X and that of wave propagation by k. Then,

(1)  X || B and k || B × E

(2)  X || E and k || E × B

(3)  X || B and k || E×B

(4)  X || E and k || B×E

Answer: (2)

5. If a simple pendulum has significant amplitude (upto a factor of 1/e of original) only in the period between t = 0 s to t = τs, then τ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity with b as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds.

(1)  0.693/b

(2)  b

(3)  1/b

(4)  2/b

Answer: (4)

6. Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4. Then, the number of spectral lines in the emission spectra will be

(1)  2

(2)  3

(3)  5

(4)  6

Answer: (4)

7. A coil is suspended in a uniform magnetic filed with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil, it starts oscillating; it is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to

(1)  development of air current when the plate is placed

(2)  induction of electrical charge on the plate

(3)  shielding of magnetic lines of force as aluminium is a paramagnetic material

(4)  electromagnetic induction in the aluminium plate giving rise to electromagnetic damping

Answer: (4)

8. The mass of a spaceship is 1000 kg. It is to be launched from the earth’s surface out into free space. The value of g and R (radius of earth) are 10 m/s2 and 6400 km respectively. The required energy for this work will be

(1)  6.4 × 1011 J

(2)  6.4 × 108 J

(3)  6.4 × 109 J

(4)  6.4 × 1010 J

Answer: (4)

9. Helium gas goes through a cycle ABCDA (consisting of two isochoric and isobaric lines) as shown in figure. Efficiency of this cycle is nearly (Assume the gas to be close to ideal gas)

(1)  15.4%

(2)  9.1%

(3)  10.5%

(4)  12.5%

Answer: (1)

10. In Young’s double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit is double of that form other slit. If Im be the maximum intensity, the resultant intensity I when they interfere at phase difference ϕ, is given by

(1) 

(2) 

(3) 

(4) 

Answer: (4)

11. A liquid in a beaker has temperature θ(t) at time t and θ0 is temperature of surroundings, then according to Newton’s law of cooling, the correct graph between loge(θ – θ0) and t is

(1) 

(2) 

(3) 

(4) 

Answer: (1)

12. A particle of mass m is at rest at the origin at time t = 0. It is subjected to a force F(t) = F0e−bt in the x direction. Its speed v(t) is depicted by which of the following curves?

(1) 

(2) 

(3) 

(4) 

Answer: (3)

13. Two electric bulbs marked 25 W-220 V and 100 W-220 V are connected in series to a 440 V supply. Which of the bulbs will fuse?

(1)  Both

(2)  100 W

(3)  25 W

(4)  Neither

Answer: (3)

14. Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is

(1)  6%

(2)  zero

(3)  1%

(4)  3%

Answer: (1)

15. A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be

(1)  20√2 m

(2)  10 m

(3)  10√2 m

(4)  20 m

Answer: (4)

16. This question has statement 1 and statement 2. Of the four choices given the statements m choose the one that describes the two statements.

Statement 1: Davisson-Germer experiment established the wave nature of electrons.

Statement 2: If electrons have wave nature, they can interfere and show diffraction.

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

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

(3)  Statement 1 is true, Statement 2 is true. Statement 2 is the correct explanation for Statement 1

(4)  Statement is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1

Answer: (3)

17. A thin liquid film formed between a U-shaped wire and a light slider supports a weight of 1.5 × 10−2 N (see figure). The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is

(1)  0.125 Nm1

(2)  0.1 Nm1

(3)  0.05 Nm1

(4)  0.025 Nm1

Answer: (4)

18. A charge Q is uniformly distributed over the surface of non-conducting disc of radius R. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity ω. A a result of this rotation, a magnetic field of induction B is obtained at the centre of the disc. If we keep both the amount of charge placed on the disc and its angular velocity to be constant and vary the radius of the disc then the variation of the magnetic induction at the centre of the disc will be represented by the figure

(1) 

(2) 

(3) 

(4) 

Answer: (1)

19. Truth table for system of four NAND gates as shown in figure is

(1) 

(2) 

(3) 

(4) 

Answer: (1)

20. A radar has a power of 1 kw and is operating at a frequency of 10 GHz. It is located on a mountain top of height 500 m. The maximum distance upto which it can detect object located on the surface of the earth (Radius of earth = 6.4 × 106 m) is

(1)  80 km

(2)  16 km

(3)  40 km

(4)  64 km

Answer: (1)

21. Assume that a neutron breaks into a proton and an electron. The energy released during this process is (mass of neutron = 1.6725 × 10−27 kg, mass of proton = 1.6725 × 10−27 kg, mass of electron = 9 × 10−31 kg)

(1)  0.73 MeV

(2)  7.10 MeV

(3)  6.30 MeV

(4)  5.4 MeV

Answer: (1)

22. A Carnot engine, whose efficiency is 40%, take in heat from a source maintained at a temperature of 500 K. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be

(1)  Efficiency of Carnot engine cannot be made larger than 50%

(2)  1200 K

(3)  750 K

(4)  600 K

Answer: (3)

23. 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.

If two springs S1 and S2 of force constants k1 and k2, respectively are stretched by the same force, it is found that more work is done on spring S1 than on spring S2.

Statement 1: If stretched by the same amount, work done on S1, will be more than that on S2.

Statement 2:  k1 < k2

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

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

(3)  Statement is true, Statement 2 is true, Statement 2 is the correct explanation for Statement 1

(4)  Statement is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1

Answer: (1)

24. Two cars of masses m1 and m2 are moving in circles of radii r1 and r2, respectively. Their speeds are such that they make complete circles in the same time t. the ratio of their centripetal acceleration is

(1)  m1r1 : m2r2

(2)  m1 : m2

(3)  r1 : r2

(4)  1 : 1

Answer: (3)

25. A cylindrical tube, open at both ends, has a fundamental frequency, f, in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now

(1)  f

(2)  f/2

(3)  3f/4

(4)  2f

Answer: (1)

26. An object 2.4 m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate 1 cm thick, of refractive index 1.50 is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object shifted to be in sharp focus on film?

(1)  7.2 m

(2)  2.4 m

(3)  3.2 m

(4)  5.6 m

Answer: (4)

27. A diatomic molecule is made of two masses m1 and m2 which are separated by a distance r. If we calculate its rotational energy by applying Bohr’s rule of angular momentum quantization, its energy will be given by ( n is integer)

(1) 

(2) 

(3) 

(4) 

Answer: (4)

28. A spectrometer gives the following reading when used to measure the angle of a prism.

Main scale reading : 58.5 degree

Vernier scale reading : 09 divisions

Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data is

(1)  58.59 degree

(2)  58.77 degree

(3)  58.65 degree

(4)  59 degree

Answer: (3)

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

An insulating solid sphere of radius R has a uniform positive charge density ρ. As a result of this uniform charge distribution, there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at point outside the sphere. The electric potential at infinite is zero.

Statement 1: When a charge q is taken from the centre of the surface of the sphere its potential energy changes by qρ/3ε0.

Statement 2: The electric field at a distance r(r < R) from the centre of the sphere is ρr/3ε0.

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

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

(3)  Statement is true, Statement 2 is true, Statement 2 is the correct explanation for Statement 1

(4)  Statement is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1

Answer: (1)

30. Proton, deuteron and alpha particles of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively rp, rd and rα. Which one of the following relation is correct?

(1)  rα = rp = rd

(2)  rα = rp < rd

(3)  rα > rd > rp

(4)  rα = rd > rp

Answer: (2)

Chemistry

31. Which among the following will be named as dibromidobis- (ethylenediamine) chromium (III) bromide?

(1)  [Cr(en)3]Br3

(2)  [Cr(en)2Br2]Br

(3)  [Cr(en)Br4]

(4)  [Cr(en)Br2]Br

Answer: (2)

32. Which method of purification is represented by the following equation?

(1)  Zone refining

(2)  Cupellation

(3)  Polling

(4)  van-Arkel

Answer: (4)

33. Lithium forms body-centred cubic structure. The length of the side of its unit cell is 351 pm. Atomic radius of the lithium will be

(1)  75 pm

(2)  300 pm

(3)  240 pm

(4)  152 pm

Answer: (4)

34. The molecule having smallest bond angle is

(1)  NCl3

(2)  AsCl3

(3)  SbCl3

(4)  PCl3

Answer: (3)

35. Which of the following compounds can be detected by Molisch’s test?

(1)  Nitro compounds

(2)  Sugars

(3)  Amines

(4)  Primary alcohols

Answer: (2)

36. The incorrect expression among the following is

(1) 

(2)  In isothermal process, 

(3) 

(4)  K = e−∆G°/RT

Answer: (3)

37. The density of a solution prepared by dissolving 120 g of urea (mol. mass = 60 u) in 1000 g of water is 1.15 g/mL. The molarity this solution is

(1)  0.50 M

(2)  1.78 M

(3)  1.02 M

(4)  2.05 M

Answer: (4)

38. The species which can best serve as an initiator for the cationic polymerization is

(1)  LiAlH4

(2)  HNO3

(3)  AlCl3

(4)  BaLi

Answer: (3)

39. Which of the following on thermal decomposition yields a basic as well as acidic oxide?

(1)  NaNO3

(2)  KClO3

(3)  CaCO3

(4)  NH4NO3

Answer: (3)

40. The standard reduction potentials for Zn2+/Zn, Ni2+/Ni and Fe2+/Fe are −0.76, −0.23 and −0.44 V respectively. The reaction X + Y2 → X2 + Y will be spontaneous when

(1)  X = Ni, Y = Fe

(2)  X = Ni, Y = Zn

(3)  X = Fe, Y = Zn

(4)  X = Zn, Y = Ni

Answer: (4)

41. According to Freundlich adsorption isotherm which of the following is correct?

(1) 

(2) 

(3) 

(4)  All of the above are correct for different range of pressure

Answer: (4)

42. The equilibrium constant (Kc) for the reaction N2(g) + O2(g) → 2NO(g) at temperature T is 4 × 10−4. The value of Kc for the reaction NO(g) → ½ N2(g) + ½ O2(g) at the same temperature is

(1)  0.02

(2)  2.5 × 102

(3)  4 × 104

(4)  50.0

Answer: (4)

43. The compressibility factor for real gas at high pressure is

(1)  1 + (RT/pb)

(2)  1

(3)  1+(pb/RT)

(4)  1 – (pb/RT)

Answer: (3)

44. Which one of the following statements is correct?

(1)  All amino acids except lysine are optically active.

(2)  All amino acids are optically active.

(3)  All amino acids except glycine are optically active.

(4)  All amino acids except glutamic acids are optically active.

Answer: (3)

45. Aspirin is known as

(1)  acetyl salicylic acid

(2)  phenyl salicylate

(3)  acetyl salicylate

(4)  methyl salicylic acid

Answer: (1)

46. Ortho-nitrophenol is less soluble in water than p- and m-nitrophenols because

(1)  o-nitrophenol is more volatile steam than those of m- and p-isomers

(2)  o-nitrophenol shows intramolecular H-bonding

(3)  o-nitrophenol shows intermolecular H-bonding

(4)  melting point of o-nitrophenol is lower than those of m- and p –isomers.

Answer: (2)

47. How many chiral compounds are possible on monochlorination of 2-methyl butane?

(1)  8

(2)  2

(3)  4

(4)  6

Answer: (3)

48. Very pure hydrogen (99.9) can be made by which of the following processes?

(1)  Reaction of methane with steam

(2)  Mixing natural hydrocarbons of high molecular weight

(3)  Electrolysis of water

(4)  Reaction of slats like hydrides with water

Answer: (4)

49. The electrons identified by quantum numbers n and l

(1) n = 4, l = 1           (2) n = 4, l = 0

(3) n = 3, l = 2           (4)  n = 3, l = 1

(1)  (3) < (4) < (2) < (1)

(2)  (4) < (2) < (3) < (1)

(3)  (2) < (4) < (1) < (3)

(4)  (1) < (3) < (2) < (4)

Answer: (2)

50. For a first order reaction (A) → products the concentration of A changes from 0.1 M to 0.025 M in 40 min. The rate of reaction when the concentration of A is 0.01 M is

(1)  1.73 × 105 M/min

(2)  3.47 × 104 M/min

(3)  3.47 × 105 M/min

(4)  1.73 × 104 M/min

Answer: (2)

51. Iron exhibits +2 and +3 oxidation states. Which of the following statements about iron is incorrect?

(1)  Ferrous oxide is more basic in nature than the ferric oxide

(2)  Ferrous compounds are relatively more ionic than the corresponding ferric compounds

(3)  Ferrous compounds are less volatile than the corresponding ferric compounds

(4)  Ferrous compounds are more easily hydrolyzed than the corresponding ferric compounds

Answer: (4)

52. The pH of a 0.1 molar solution of the acid HQ is 3. The value of the ionization constant, Ka of the acid is

(1)  3 × 101

(2)  1 × 103

(3)  1 × 105

(4)  1 × 107

Answer: (3)

53. Which branched chain isomer of the hydrocarbon with molecular mass 72 u gives only one isomer of mono substituted alkyl halide?

(1)  Tertiary butyl chloride

(2)  Neopentane

(3)  Isohexane

(4)  Neohexane

Answer: (2)

54. Kf for water is 1.86 K kg mol−1. If your automobile radiator holds 1.0 kg of water, how many grams of ethylene glycol (C2H6O2) must you add to get the freezing point of the solution lowered to −2.8℃?

(1)  72 g

(2)  93 g

(3)  39 g

(4)  27 g

Answer: (2)

55. What is DDT among the following?

(1)  Green house gas

(2)  A fertilizer

(3)  Biodegradable pollutant

(4)  Non-biodegradable pollutant

Answer: (4)

56. The increasing order of the ionic radii of the given isoelectronic species is

(1)  Cl, Ca2+, K+, S2

(2)  S2, Cl, Ca2+, K+

(3)  Ca2+, K+, Cl, S2

(4)  K+, S2, Ca2+, Cl

Answer: (3)

57. 2-hexyne gives trans-2-hexene on treatment with

(1)  Pt/H2

(2)  Li/NH3

(3)  Pd/BaSO4

(4)  LiAlH4

Answer: (2)

58. Iodoform can be prepared from all except

(1)  ethyl methyl ketone

(2)  isopropyl alcohol

(3)  3-methyl-2-butanone

(4)  isobutyl alcohol

Answer: (4)

59. In which of the following pairs the two species are not isostructural?

(1) 

(2) 

(3)  PF5 and BrF5

(4) 

Answer: (3)

60. In the given transformation, which the following is the most appropriate reagent?

(1) 

(2)  Zn – Hg/HCl

(3)  Na, Liq. NH3

(4)  NaBH4

Answer: (1)

Mathematics

61. The equation esin x − e−sin x – 4 = 0 has

(1)  infinite number of real roots

(2)  no real roots

(3)  exactly one real root

(4)  exactly four real roots

Answer: (2)

62. Let  be two unit vectors. If the vectors  perpendicular to each other, then the angle between  is

(1)  π/6

(2)  π/2

(3)  π/3

(4)  π/4

Answer: (3)

63. A spherical balloon is filled with 4500π cu m of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72π cu m/min, then the rate (in m/min) at which the radius of the balloon decreases 49 min after the leakage began is

(1)  9/7

(2)  7/9

(3)  2/9

(4)  9/2

Answer: (3)

64. Statement 1: The sum of the series 1+(1 + 2+ 4) + (4 + 6 + 9) + (9 + 12 +16)+……….+(361 + 380 + 400) is 8000.

Statement 2 :  for any natural number n.

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

(2)  Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1.

(3)  Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.

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

Answer: (2)

65. The negation of the statement “If I become a teacher, then I will open a school”, is

(1)  I will become a teacher and I will not open a school

(2)  Either I will not become a teacher or I will not open a school

(3)  Neither I will become a teacher nor I will open a school

(4)  I will not become a teacher or I will open a school

Answer: (1)

66. If the integral  then a is equal to

(1)  −1

(2)  −2

(3)  1

(4)  2

Answer: (4)

67. Statement 1: An equation of a common tangent to the parabola y2 = 16√3x and the ellipse 2x2 + y2 = 4 is y = 2x + 2√3.

Statement 2: If the line  (m≠0) is a common tangent to the parabola y2 = 16√3x and ellipse 2x2 + y2 = 4, then m satisfies m4 + 2m2= 24.

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

(2)  Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1.

(3)  Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.

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

Answer: (3)

68. Let If u1 and u2 are column matrices such that  then u1 + u2 is equal to

(1) 

(2) 

(3) 

(4) 

Answer: (4)

69. If n is a positive integer, then (√3 + 1)2n – (√3 – 1)2n is

(1)  an irrational number

(2)  an odd positive integer

(3)  an even positive integer

(4)  a rational number other than positive integers

Answer: (1)

70. If 100 times the 100th term of an AP with non-zero common difference equals the 50 times its 50th term, then the 150th term of this AP is

(1)  −150

(2)  150 times its 50th term

(3)  150

(4)  zero

Answer: (4)

71. In a ∆PQR , if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then the angle R is equal to

(1)  5π/6

(2)  π/6

(3)  π/4

(4)  3π/4

Answer: (2)

72. An equation of a plane parallel to the plane x – 2y + 2z – 5 = 0 and at a unit distance from the origin is

(1)  x – 2y + 2z – 3 = 0

(2)  x – 2y + 2z + 1 = 0

(3)  x – 2y + 2z – 1 = 0

(4)  x – 2y + 2z + 5 = 0

Answer: (1)

73. If the line 2x + y = k passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then k equals

(1)  29/5

(2)  5

(3)  6

(4)  11/5

Answer: (3)

74. Let x1, x2….., xn be n observations and let  be their arithmetic mean and σ2 be the variance.

Statement 1:  Variance of 2x1, 2x2, . . . . , 2xn is 4σ2.

Statement 2:  Arithmetic mean 2x1, 2x2 …….., 2xn is 

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

(2)  Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1.

(3)  Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.

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

Answer: (4)

75. The population p(t) at time t of a certain mouse species satisfies the differential equation  If p(0) = 850, then the time at which the population becomes zero is

(1)  2 log 18

(2)  log 9

(3)  1/2 log 18

(4)  log 18

Answer: (1)

76. Let a, b ∈R be such that the function f given by f(x) = log|x| + bx2 + ax, x ≠ 0 has extreme values x = −1 and x = 2.

Statement 1: f has local maximum at x = −1 and at x = 2

Statement 2: a = ½ and b = −1/4

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

(2)  Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1.

(3)  Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.

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

Answer: (3)

77. The area bounded between the parabolas x2 = y/4 and x2= 9y and the straight line y = 2 is

(1)  20√2

(2)  (10√2)/3

(3)  (20√2)/3

(4)  10√2

Answer: (3)

78. Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is

(1)  880

(2)  629

(3)  630

(4)  879

Answer: (4)

79. If f : R → R is a function defined by  where [x] denotes the greatest integer function, then f is

(1)  continuous for every real x

(2)  discontinuous only at x = 0

(3)  discontinuous only at non-zero integral vales of x

(4)  continuous only at x = 0

Answer: (1)

80. If the line  interest, then k is equal to

(1)  −1

(2)  2/9

(3)  9/2

(4)  0

Answer: (3)

81. Three numbers are chosen at random without replacement from {1, 2, 3, ….8}. The probability that their minimum is 3, given that their maximum is 6, is

(1)  3/8

(2)  1/5

(3)  1/4

(4)  2/5

Answer: (2)

82. If z ≠ 1 and  is real, then the point represented by the complex number z lies

(1)  either on the real axis or on a circle passing through the origin

(2)  on a circle with centre at the origin

(3)  either on the real axis or on a circle not passing through the origin

(4)  on the imaginary axis

Answer: (1)

83. Let P and Q be 3 × 3 matrices P ≠ Q. If P3 = Q3 and P2Q = Q2P, then determinant of (P2 + Q2) is equal to

(1)  −2

(2)  1

(3)  0

(4)  −1

Answer: (3)

84. If  then g(x + π) equals

(1)  g(x)/g(π)

(2)  g(x) + g(π)

(3)  (g(x) − g(π))1/2

(4)  g(x) ∙g(π)

Answer: (2)

85. The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is

(1)  10/3

(2)  3/5

(3)  6/5

(4)  5/3

Answer: (1)

86. Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can formed such that Y ⊆ X, Z ⊆ X and Y ∩ Z is empty, is

(1)  52

(2)  35

(3)  25

(4)  53

Answer: (2)

87. An ellipse is drawn by taking a diameter of the circle (x – 1)2 + y2 = 1 as its semi-minor axis and a diameter of the circle x2 + (y – 2)2 = 4 is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is

(1)  4x2 + y2 = 4

(2)  x2 + 4y2 = 8

(3)  4x2 + y2 = 8

(4)  x2 + 4y2 = 16

Answer: (4)

88. Consider the function f(x) = |x – 2| |x – 5|, x ∈

Statement 1: f'(4) = 0

Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and f(2) = f(5).

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

(2)  Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1.

(3)  Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.

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

Answer: (3)

89. A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a ∆PQR, where O is the origin, if the area of the ∆PQR is least, then the slope of the line PQ is

(1)  −1/4

(2)  −4

(3)  −2

(4)  −1/2

Answer: (3)

90. Let ABCD be a parallelogram such that AB = q, AD = p and ∠BAD be an acute angle. If r is the vector that coincides with the altitude directed from the vertex B to the side AD, then r is given by

(1) 

(2) 

(3) 

(4) 

Answer: (2)

JEE Main (AIEEE) 2010 Question Paper

JEE Main (AIEEE) Past Exam Question Paper 2010

Physics

1. A rectangular loop has a sliding connector PQ of length ℓ and resistance R Ω and it is moving with a speed v as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents I1, I2 and I are

(1) 

(2) 

(3) 

(4) 

Answer: (2)

2. Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t₁ is the time taken for the energy stored in the capacitor to reduce to half its initial value and t2 is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio t1/t2 will be

(1)  1

(2)  1/2

(3)  1/4

(4)  2

Answer: (3)

Directions: Questions number 3 – 4 contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.

3. Statement1: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.

Statement2: Principle of conservation of momentum holds true for all kinds of collisions.

(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

Answer: (1)

4. Statement1: When ultraviolet light is incident on a photocell, its stopping potential is V0 and the maximum kinetic energy of the photoelectrons is Kmax. When the ultraviolet light is replaced by X-rays, both V0 and Kmax

Statement-2 : Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the 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

Answer: (4)

5. A ball is made of a material of density ρ where ρoil < ρ< ρwater with ρoil and ρwater representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position?

(1) 

(2) 

(3) 

(4) 

Answer: (2)

6. A particle is moving with velocity , where K is a constant. The general equation for its path is

(1)  y = x2 + constant

(2)  y2 = x + constant

(3)  xy = constant

(4)  y2 = x2 + constant

Answer: (4)

7. Two long parallel wires are at a distance 2d apart. They carry steady equal current flowing out of the plane of the paper as shown. The variation of the magnetic field along the line XX’ is given by

(1) 

(2) 

(3) 

(4) 

Answer: ()

8. In the circuit shown below, the key K is closed at t = 0. The current through the battery is

(1) 

(2) 

(3) 

(4) 

Answer: (2)

9. The figure shows the position – time (x – t) graph of one-dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is

(1)  0.4 Ns

(2)  0.8 Ns

(3)  1.6 Ns

(4)  0.2 Ns

Answer: (2)

Directions: Questions number 10 – 11 are based on the following paragraph.

A nucleus of mass M + ∆m is at rest and decays into two daughter nuclei of equal mass M/2 each. Speed of light is c.

10. The binding energy per nucleon for the parent nucleus is E₁ and that for the daughter nuclei is E2. Then

(1)  E2 = 2E1

(2)  E1 > E2

(3)  E2 > E1

(4)  E­1 = 2E2

Answer: (3)

11. The speed of daughter nuclei is

(1) 

(2) 

(3) 

(4) 

Answer: (2)

12. A radioactive nucleus (initial mass number A and atomic number Z) emits 3 α-particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be

(1) 

(2) 

(3) 

(4) 

Answer: (2)

13. A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it. The net field  at the centre O is

(1) 

(2) 

(3) 

(4) 

Answer: (3)

14. The combination of gates shown below yields

(1)  OR gate

(2)  NOT gate

(3)  XOR gate

(4)  NAND gate

Answer: (1)

15. A diatomic ideal gas is used in a Car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from V to 32V the efficiency of the engine is

(1)  0.5

(2)  0.75

(3)  0.99

(4)  0.25

Answer: (2)

16. If a source of power 4 kW produces 1020 photons/second, the radiation belong to a part of the spectrum called

(1)  X-rays

(2)  ultraviolet rays

(3)  microwaves

(4)  γ-rays

Answer: (1)

17. The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 × 103 are

(1)  5, 1, 2

(2)  5, 1, 5

(3)  5, 5, 2

(4)  4, 4, 2

Answer: (1)

18. In a series LCR circuit R = 200 Ω and the voltage and the frequency of the main supply is 220 V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by 30°. On taking out the inductor from the circuit the current leads the voltage by 30°. The power dissipated in the LCR circuit is

(1)  305 W

(2)  210 W

(3)  0 W

(4)  242 W

Answer: (4)

19. Let there be a spherically symmetric charge distribution with charge density varying as  up to r = R, and ρ(r) = 0 for r > R, where r is the distance from the origin. The electric field at a distance r(r < R) from the origin is given by

(1) 

(2) 

(3) 

(4) 

Answer: (2)

20. The potential energy function for the force between two atoms in a diatomic molecule is approximately given by , where a and b are constants and x is the distance between the atoms. If the dissociation energy of the molecule is D = [U(x = ∞) – Uat equilibrium], D is

(1)  b2/2a

(2)  b2/12a

(3)  b2/4a

(4)  b2/6a

Answer: (3)

21. Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30° with each other. When suspended in a liquid of density 0.8 g cm3, the angle remains the same. If density of the material of the sphere is 16 g cm3, the dielectric constant of the liquid is

(1)  4

(2)  3

(3)  2

(4)  1

Answer: (3)

22. Two conductors have the same resistance at 0°C but their temperature coefficients of resistance are α1 and α2. The respective temperature coefficients of their series and parallel combinations are nearly

(1) 

(2) 

(3) 

(4) 

Answer: (4)

23. A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of ‘P’ is such that it sweeps out a length s = t3 + 5, where s is in metres and t is in seconds. The radius of the path is 20 m. The acceleration of ‘P’ when t = 2 s is nearly

(1)  13 m/s2

(2)  12 m/s2

(3)  7.2 m/s2

(4)  14 m/s2

Answer: (4)

24. Two fixed frictionless inclined plane making an angle 30° and 60° with the vertical are shown in the figure. Two block A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B?

(1)  4.9 ms2 in horizontal direction

(2)  9.8 ms2 in vertical direction

(3)  Zero

(4)  4.9 ms2 in vertical direction

Answer: (4)

25. For a particle in uniform circular motion the acceleration  at a point P(R,θ) on the circle of radius R is (here θ is measured from the x–axis)

(1) 

(2) 

(3) 

(4) 

Answer: (3)

Directions: Questions number 2628 are based on the following paragraph.

An initially parallel cylindrical beam travels in a medium of refractive index μ(I) = μ0+ μ2I , where μ0 and μ2 are positive constants and I is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius.

26. As the beam enters the medium, it will

(1)  diverge

(2)  converge

(3)  diverge near the axis and converge near the periphery

(4)  travel as a cylindrical beam

Answer: (2)

27. The initial shape of the wave front of the beam is

(1)  convex

(2)  concave

(3)  convex near the axis and concave near the periphery

(4)  planar

Answer: (4)

28. The speed of light in the medium is

(1)  minimum on the axis of the beam

(2)  the same everywhere in the beam

(3)  directly proportional to the intensity I

(4)  maximum on the axis of the beam

Answer: (1)

29. A small particle of mass m is projected at an angle θ with the x-axis with an initial velocity v0 in the x-y plane as shown in the figure. At a time , the angular momentum of the particle is

(1) 

(2) 

(3) 

(4) 

where  are unit vectors along x, y and z-axis respectively.

Answer: ()

30. The equation of a wave on a string of linear mass density 0.04 kg m−1 is given by . The tension in the string is

(1)  4.0 N

(2)  12.5 N

(3)  0.5 N

(4)  6.25 N

Answer: (4)

Chemistry

31. The standard enthalpy of formation of NH₃ is –46.0 kJ mol–1. If the enthalpy of formation of H₂ from its atoms is –436 kJ mol–1 and that of N2 is –712 kJ mol–1, the average bond enthalpy of N–H bond in NH3 is

(1)  –964 kJ mol–1

(2)  +352 kJ mol–1

(3)  +1056 kJ mol–1

(4)  –1102 kJ mol–1

Answer: (2)

32. The time for half life period of a certain reaction A → products is 1 hour. When the initial concentration of the reactant ‘A’, is 2.0 mol L1, how much time does it take for its concentration to come from 0.50 to 0.25 mol L1 if it is a zero order reaction?

(1)  4 h

(2)  0.5 h

(3)  0.25 h

(4)  1 h

Answer: (3)

33. A solution containing 2.675 g of CoCl3 . 6 NH3 (molar mass = 267.5 g mol−1) is passed through a cation exchanger. The chloride ions obtained in solution were treated with excess of AgNO3 to give 4.78 g of AgCl (molar mass = 143.5 g mol−1). The formula of the complex is (At. Mass of Ag=108u)

(1)  [Co(NH3)6]Cl3

(2)  [CoCl2(NH3)4]Cl

(3)  [CoCl3(NH3)3]

(4)  [CoCl(NH3)5]Cl2

Answer: (1)

34. Consider the reaction:

Cl2(aq) + H2S(aq) → S(s) + 2H+(aq) + 2Cl (aq)

The rate equation for this reaction is rate = k [Cl2] [H2S]

Which of these mechanisms is/are consistent with this rate equation?

(A)  Cl2 + H2 → H+ + Cl + Cl+ + HS                 (slow)

Cl+ + HS → H+ + Cl + S                             (fast)

(B) H2S ⇔ H+ + HS                                            (fast equilibrium)

Cl2 + HS → 2Cl + H+ + S                           (slow)

(1)  B only

(2)  Both A and B

(3)  Neither A nor B

(4)  A only

Answer: (4)

35. If 10−4 dm3 of water is introduced into a 1.0 dm3 flask to 300 K, how many moles of water are in the vapour phase when equilibrium is established?

(Given: Vapour pressure of H2O at 300 K is 3170 Pa; R = 8.314 J K−1 mol−1)

(1)  5.56 × 10−3 mol

(2)  1.53 × 10−2 mol

(3)  4.46 × 10−2 mol

(4)  1.27 × 10−3 mol

Answer: (4)

36. One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular mass of 44 u. The alkene is

(1)  propene

(2)  1–butene

(3)  2–butene

(4)  ethene

Answer: (3)

37. If sodium sulphate is considered to be completely dissociated into cations and anions in aqueous solution, the change in freezing point of water (∆Tf), when 0.01 mol of sodium sulphate is dissolved in 1 kg of water, is (Kf = 1.86 K kg mol−1)

(1)  0.0372 K

(2)  0.0558 K

(3)  0.0744 K

(4)  0.0186 K

Answer: (2)

38. From amongst the following alcohols the one that would react fastest with conc. HCl and anhydrous ZnCl2, is

(1)  2–Butanol

(2)  2–Methylpropan–2–ol

(3)  2–Methylpropanol

(4)  1–Butanol

Answer: (2)

39. In the chemical reactions,

(1)  nitrobenzene and fluorobenzene

(2)  phenol and benzene

(3)  benzene diazonium chloride and fluorobenzene

(4)  nitrobenzene and chlorobenzene

Answer: (3)

40. 29.5 mg of an organic compound containing nitrogen was digested according to Kjeldahl’s method and the evolved ammonia was absorbed in 20 mL of 0.1 M HCl solution. The excess of the acid required 15 mL of 0.1 M NaOH solution for complete neutralization. The percentage of nitrogen in the compound is

(1)  59.0

(2)  47.4

(3)  23.7

(4)  29.5

Answer: (3)

41. The energy required to break one mole of Cl–Cl bonds in Cl2 is 242 kJ mol−1. The longest wavelength of light capable of breaking a single Cl – Cl bond is

(c = 3 x 108 ms−1 and NA = 6.02 x 1023 mol−1)

(1)  594 nm

(2)  640 nm

(3)  700 nm

(4)  494 nm

Answer: (4)

42. Ionization energy of He+ is 19.6 x 10−18 J atom−1. The energy of the first stationary state (n = 1) of Li2+is

(1)  4.41 × 1016 J atom1

(2)  −4.41 × 1017 J atom1

(3)  −2.2 × 1015 J atom1

(4)  8.82 × 1017 J atom1

Answer: (2)

43. Consider the following bromides:

Consider the following bromides:

(1)  B > C > A

(2)  B > A > C

(3)  C > B > A

(4)  A > B > C

Answer: (1)

44. Which one of the following has an optical isomer?

(1)  [Zn(en) (NH­32]2+

(2)  [Co(en)3]3+

(3)  [Co(H2O)4(en)]3+

(4)  [Zn(en)2]2+

Answer: (2)

45. On mixing, heptane and octane form an ideal solution. At 373 K, the vapour pressures of the two liquid components (heptane and octane) are 105 kPa and 45 kPa respectively. Vapour pressure of the solution obtained by mixing 25.0g of heptane and 35 g of octane will be (molar mass of heptane = 100 g mol−1 an dof octane = 114 g mol−1).

(1)  72.0 k Pa

(2)  36.1 k Pa

(3)  96.2 k Pa

(4)  144.5 k Pa

Answer: (1)

46. The main product of the following reaction is

(1) 

(2)

(3) 

(4) 

Answer: (1)

47. Three reactions involving H2PO4 are given below:

In which of the above does H2PO4 act as an acid?

(1)  (ii) only

(2)  (i) and (ii)

(3)  (iii) only

(4)  (i) only

Answer: (1)

48. In aqueous solution the ionization constants for carbonic acid are

K1 = 4.2 × 10−7 and K2 = 4.8 × 10−11

(1)  The concentration of CO32 is 0.034 M

(2)  The concentration of CO32 is greater than that of HCO3

(3)  The concentration of H+ and HCO3 are approximately equal

(4)  The concentration of H+ is double that of CO32

Answer: (3)

49. The edge length of a face centered cubic cell of an ionic substance is 508 pm. If the radius of the cation is 110 pm, the radius of the anion is

(1)  288 pm

(2)  398 pm

(3)  618 pm

(4)  144 pm

Answer: (4)

50. The correct order of increasing basicity of the given conjugate bases (R = CH3) is

(1) 

(2) 

(3) 

(4) 

Answer: (4)

51. The correct sequence which shows decreasing order of the ionic radii of the elements is

(1)  Al3+ > Mg2+ < Na+ < F < O2

(2)  Na+ > Mg2+ > Al3+ > O2 > F

(3)  Na+ > F > Mg2+ > O2 > Al3+

(4)  O2 > F > Na+ > Mg2+ > Al3+

Answer: (4)

52. Solubility product of silver bromide is 5.0 × 10−13. The quantity of potassium bromide (molar mass taken as 120 g of mol−1) to be added to 1 litre of 0.05 M solution of silver nitrate to start the precipitation of AgBr is

(1)  1.2 × 10−10 g

(2)  1.2 × 10−9 g

(3)  6.2 × 10−5 g

(4)  5.0 × 10−8 g

Answer: (2)

53. The Gibbs energy for the decomposition of Al2O3 at 500°C is as follows:

The potential difference needed for electrolytic reduction of Al2O3 at 500°C is at least

(1)  4.5 V

(2)  3.0 V

(3)  2.5 V

(4)  5.0 V

Answer: (3)

54. At 25°C, the solubility product of Mg(OH)₂ is 1.0 × 10−11. At which pH, will Mg2+ ions start precipitating in the form of Mg(OH)2 from a solution of 0.001 M Mg2+ ions?

(1)  9

(2)  10

(3)  11

(4)  8

Answer: (2)

55. Percentage of free space in cubic close packed structure and in body centred packed structure are respectively

(1)  30% and 26%

(2)  26% and 32%

(3)  32% and 48%

(4)  48% and 26%

Answer: (2)

56. Out of the following, the alkene that exhibits optical isomerism is

(1)  3–methyl–2–pentene

(2)  4–methyl–1–pentene

(3)  3–methyl–1–pentene

(4)  2–methyl–2–pentene

Answer: (3)

57. Biuret test is not given by

(1)  carbohydrates

(2)  polypeptides

(3)  urea

(4)  proteins

Answer: (1)

58. The correct order of  values with negative sign for the four successive elements Cr, Mn, Fe and Co is

(1)  Mn > Cr > Fe > Co

(2)  Cr > Fe > Mn > Co

(3)  Fe > Mn > Cr > Co

(4)  Cr > Mn > Fe > Co

Answer: (1)

59. The polymer containing strong intermolecular forces e.g. hydrogen bonding, is

(1)  teflon

(2)  nylon 6, 6

(3)  polystyrene

(4)  natural rubber

Answer: (2)

60. For a particular reversible reaction at temperature T, ∆H and ∆S were found to be both +ve. If Te is the temperature at equilibrium, the reaction would be spontaneous when

(1)  Te > T

(2)  T > Te

(3)  Te is 5 times T

(4)  T = Te

Answer: (1)

Mathematics

61. Let cos (α + β) = 4/5 and let sin (α- β) = 5/13, where 0 ≤α, β≤π/4, then tan 2α =

(1)  56/33

(2)  19/12

(3)  20/7

(4)  25/16

Answer: (1)

62. Let S be a non-empty subset of R. Consider the following statement:

P: There is a rational number x ∈ S such that x > 0.

Which of the following statements is the negation of the statement P?

(1)  There is no rational number x ∈S such that x ≤ 0

(2)  Every rational number x ∈S satisfies x ≤ 0

(3)  x ∈S and x ≤ 0 ⇒x is not rational

(4)  There is a rational number x ∈S such that x ≤ 0

Answer: (2)

63. Let  Then vector  is

(1) 

(2) 

(3) 

(4) 

Answer: (4)

64. The equation of the tangent to the curve  that is parallel to the x-axis, is

(1)  y = 1

(2)  y = 2

(3)  y = 3

(4)  y = 0

Answer: (3)

65. Solution of the differential equation cos x dy = y (sin x – y) dx,  is

(1)  y sec x = tan x + c

(2)  y tan x = sec x + c

(3)  tan x = (sec x + c)y

(4)  sec x = (tan x + c)y

Answer: (4)

66. The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and x =3π/2 is

(1)  4√2 + 2

(2)  4√2 – 1

(3)  4√2 + 1

(4)  4√2 – 2

Answer: (4)

67. If two tangents drawn from a point P to the parabola y2 = 4x are at right angles, then the locus of P is

(1)  2x + 1 = 0

(2)  x = −1

(3)  2x – 1 = 0

(4)  x = 1

Answer: (2)

68. If the vectors  are mutually orthogonal, the (λ, μ) =

(1)  (2, –3)

(2)  (–2, 3)

(3)  (3, –2)

(4)  (–3, 2)

Answer: (4)

69. Consider the following relations:

R = {(x, y) | x, y are real numbers and x = wy for some rational number w};

Then

(1)  Neither R nor S is an equivalence relation

(2)  S is an equivalence relation but R is not an equivalence relation

(3)  R and S both are equivalence relations

(4)  R is an equivalence relation but S is not an equivalence relation

Answer: (2)

70. Let f: R → R be defined by  If f has a local minimum at x = –1, then a possible value of k is

(1)  0

(2)  −1/2

(3)  −1

(4)  1

Answer: (3)

71. The number of 3×3 non-singular matrices, with four entries as 1 and all other entries as 0, is

(1)  5

(2)  6

(3)  at least 7

(4)  less than 4

Answer: (3)

Directions: Questions Number 72 to 76 are Assertion – Reason type questions. Each of these questions contains two statements.

Statement1: (Assertion) and Statement2: (Reason)

Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

72. Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ….., 20}.

Statement-1: The probability that the chosen numbers when arranged in some order will form an AP is 1/ 85.

Statement-2: If the four chosen numbers from an AP, then the set of all possible values of common difference is {±1, ±2, ±3, ±4, ±5}.

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

Answer: (2)

73. Statement1: The point A (3, 1, 6) is the mirror image of the point B (1, 3, 4) in the plane x – y + z = 5.

Statement-2: The plane x – y + z = 5 bisects the line segment joining A (3, 1, 6) and B (1, 3, 4).

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

Answer: (1)

74. 

Statement-1: S3 = 55 × 29

Statement-2: S1 = 90 × 28 and S2 = 10 × 28

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

Answer: (4)

75. Let A be a 2 × 2 matrix with non-zero entries and let A2 = I, where I is 2 × 2 identity matrix. Define Tr(A) = sum of diagonal elements of A and |A| = determinant of matrix A.

Statement-1: Tr(A) = 0

Statement-2: |A| = 1

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

Answer: (2)

76. Let f: R → R be a continuous function defined by 

Statement-1: f(c) = 1/3, for some c ∈ R.

Statement-2:  for all x ∈ R

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

Answer: (4)

77. For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is

(1)  There is a regular polygon with 

(2)  There is a regular polygon with 

(3)  There is a regular polygon with 

(4)  There is a regular polygon with 

Answer: (2)

78. If α and β are the roots of the equation x2 – x + 1 = 0, then α2009 + β2009 =

(1)  −1

(2)  1

(3)  2

(4)  −2

Answer: (2)

79. The number of complex numbers z such that |z – 1| = |z + 1| = |z – i| equals

(1)  1

(2)  2

(3)  ∞

(4)  0

Answer: (1)

80. A line AB in three-dimensional space makes angles 45° and 120° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive z-axis, then θ equals

(1)  45°

(2)  60°

(3)  75°

(4)  30°

Answer: (2)

81. The line L given by  passes through the point (13, 32). The line K is parallel to L and has the equation  Then the distance between L and K is

(1)  √17

(2)  17/√15

(3)  23/√17

(4)  23/√15

Answer: (3)

82. A person is to count 4500 currency notes. Let an denote the number of notes he counts in the nth minute. If a1 = a2 = …… = a10 = 150 and a10, a11, …… are in A.P. with common difference –2, then the time taken by him to count all notes is

(1)  34 minutes

(2)  125 minutes

(3)  135 minutes

(4)  24 minutes

Answer: (1)

83. Let f: R →R be a positive increasing function with

(1)  2/3

(2)  3/2

(3)  3

(4)  1

Answer: (1)

84. Let p(x) be a function defined on R such that p'(x) = p'(1 – x), for all x ∈ [0, 1], p (0) = 1 and p (1) = 41.

(1)  21

(2)  41

(3)  42

(4)  √41

Answer: (1)

85. Let f: (–1, 1) →R be a differentiable function with f(0) = –1 and f'(0) = 1. Let g(x) = [f(2f(x) + 2)]2. Then g'(0) =

(1)  –4

(2)  0

(3)  –2

(4)  4

Answer: (1)

86. There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

(1)  36

(2)  66

(3)  108

(4)  3

Answer: (3)

87. Consider the system of linear equations:

x1 + 2x2 + x3 = 3

2x1 + 3x2 + x3 = 3

3x1 + 5x2 + 2x3 = 1

The system has

(1)  exactly 3 solutions

(2)  a unique solution

(3)  no solution

(4)  infinite number of solutions

Answer: (3)

88. An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colour is

(1)  2/7

(2)  1/21

(3)  2/23

(4)  1/3

Answer: (1)

89. For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

(1)  11/2

(2)  6

(3)  13/2

(4)  5/2

Answer: (1)

90. The circle x2 + y2 = 4x + 8y + 5 intersects the line 3x – 4y = m at two distinct points if

(1)  –35 < m < 15

(2)  15 < m < 65

(3)  35 < m < 85

(4)  –85 < m < –35

Answer: (1)

Yoga Classes in J K Puri (Kanpur) The Memory Guru of India-Treatment of Colour Blindness

Name: The Memory Guru of India-Treatment of Colour Blindness

Area: J K Puri

Pincode: 208007

Address: The Memory Guru of India-Treatment of Colour Blindness, 123D, Pardevanpur,, Lalbunglow, Chandar Nagar, J K Puri, Near Siddhanath Park, Kanpur, Uttar Pradesh 208007

Contact Number: 099844 20572

Website: http://colourvision.in/

Map: