SAMPLE PAPER Note: (i)The medium of Test is English only. (ii) The test consists of 60 questions of 4 marks each. (iii) There is No Negative Marking (iii) The test is of 60 minutes duration. Stream- Mathematics 1. Let cos(α + β) = 4/ 5 and sin(α – β) = 5/ 13 where 0 ≤ α, β ≤π/4, then tan 2α = a) 56 /33 b) 19/ 12 c) 20/7 d) 25 /16 2. Let vector a = jˆ− kˆ and vector c = ˆi − ˆj − kˆ. Then vector b satisfying a ×b + c = 0 and a ⋅b= 3 is a) 2ˆi − ˆj + 2kˆ b) ˆi − ˆj − 2kˆ c) ˆi + ˆj − 2kˆ d) −ˆi + ˆj − 2kˆ 3. The equation of the tangent to the curve y = x +4/ x2 , that is parallel to the x-axis, is a) y = 1 b) y = 2 c) y = 3 d) y = 0 4. Solution of the differential equation cos x dy = y(sin x – y) dx, 0 < x < π/2 is a) y sec x = tan x + c b) y tan x = sec x + c c) tan x = (sec x + c)y d) sec x = (tan x + c)y 5. The number of 3 × 3 non-singular matrices, with four entries as 1 and all other entries as 0, is a) 5 b) 6 c) at least 7 d) less than 4 6. If α and β are the roots of the equation x2 – x + 1 = 0, then α2009 + β2009 = a) –1 b) 1 c) 2 d) –2 7. The number of complex numbers z such that |z – 1| = |z + 1| = |z – i| equals a) 1 b) 2 c) ∞ d) 0 8. 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 a) 34 minutes b) 125 minutes c) 135 minutes d) 24 minutes 9. Let f: R → R be a positive increasing function with lim x →∞ ( ) ( ) = 1. Then lim x →∞ ( ) ( ) = a) 2/3 b) 3/2 c) 3 d) 1 10. Consider the system of linear equations: x1 + 2x2 + x3 = 3 2 x1 + 3 x2 + x3= 3 3 x1 + 5 x2+ 2 x3 = 1 The system has a) exactly 3 solutions b) a unique solution c) no solution d) infinite number of solutions 11. 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 a) 11/2 b) 6 c) 13/ 2 d) 5/2 12. The circle x2 + y2 = 4x + 8y + 5 intersects the line 3x – 4y = m at two distinct points if a) –35 < m < 15 b) 15 < m < 65 c) 35 < m < 85 d) –85 < m < –35 13. The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b? a) a = 0, b = 7 b) a = 5, b = 2 c) a = 1, b = 6 d) a = 3, b = 4 14. It is given that the events A and B are such that P (A) = 1/4 , P(A /B) =1/2,P(B/A)= 2/3 , Then P (B) is a) 1/6 b) 1/3 c) 2/3 d) 1/2 15. The perpendicular bisector of the line segment joining P (1, 4) and Q (k, 3) has y−intercept − 4. Then a possible value of k is a) 1 b) 2 c) −2 d) −4 16. The area of the plane region bounded by the curves x + 2y2 = 0 and x + 3y2 = 1 is equal to a) 5 /3 b) 1/3 c) 2/ 3 d) 4/3 17. The value of [8log(1 + )] / 1+x2 dx a) π/8 log2 b) π/2 log2 c) log2 d) πlog2 18. A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P (A ∪ B) is a) 3/5 b) 0 c) 1 d) 2/5 Stream – Physics 19. For a body in uniform motion in one dimension, which of the following statements is not true? a) The body has constant speed. b) The body has constant velocity. c) The body has constant acceleration. d) The body moves equal distance in equal time intervals. 20. A jet engine works on the principle of conservation of a) Mass. b) Energy. c) Linear momentum. d) Angular momentum. 21. Two bodies of masses m and 4m, respectively, are moving with equal kinetic energies. The ratio of their linear momenta is a) ¼. b) ½. c) 1. d) 4. 22. A shell fired from a gun at an angle to the horizontal explodes in mid air. The centre of mass of the shell fragments will move a) vertically down. b) horizontally. c) along the same parabolic path of the unexploded shell. d) along the tangent to the parabolic path of the unexploded shell. 23. For a body in the gravitation field of the earth (mass M and radius R) the ratio of the gravitationa acceleration to the gravitational constant is a) R2/M. b) MR2. c) M/R2. d) M/R. 24. Consider the following two statements A: If heat is added to a system, its temperature must increase. B: If positive work is done by a system in a thermodynamic process, its volume must increase. a) Both A and B are correct. b) A is correct but B is wrong. c) A is wrong but B is correct. d) Both A and B are wrong. 25. An ideal gas at room temperature has 105 molecules per cubic centimeter. Its pressure is of the order of (atmosphere) a) 10-15. b) 10-10. c) 10-5. d) 1. 26. A particle executes simple harmonic motion with frequency f. The frequency with which its kinetic energy oscillates is a) zero. b) f/2. c) f. d) 2f. 27. If a glass sheet is placed between two charged bodies, the force between them will a) become zero. b) decrease. c) increase. d) remain unchanged. 28. A long conductor having charge q with charge density is moving with velocity 2v parallel to its own axis. The conventional current due to the motion of the conductor is a) zero. b) v/2. c) v. d) 2 v. 29. A charged particle enters the region of uniform magnetic field at an angle of 450.to the field. Its subsequent motion in the region of field will be a) undeflected. b) straight line at angle 450 to the initial direction. c) helical. d) circular. 30. Two sources of light are said to be coherent if they produce light beams a) in the same direction. b) of same amplitude. c) in the same phase . d) with constant phase difference. 31. Which of the following does not change when a light wave travels from air to water? a) Velocity. b) Wavelength. c) Frequency. d) Amplitude. 32. An observer moves towards a stationery plane mirror at a speed of 4ms-1. His image will move towards him with speed a) 8ms-1. b) 4ms-1. c) 2ms-1. d) Zero. 33. According to the radioactive decay law in one average life, the number of nuclei that decay are a) less than half. b) half c) more than half. d) All will decay. 34. In the Bohr model of atom, if the value of h increases by factor of 2, the size of the atom would a) decrease by a factor of 4. b) decreases by a factor of 2. c) increases by a factor of 2. d) increases by a factor of 4. 35. While performing a photoelectric effect experiment with a source of light no photons are emitted. To eject the electrons the source of light should be changed to one of a) higher frequency. b) higher intensity. c) higher wave length. d) lower intensity. 36. A photon, a beta particle and a proton all have same momentum. Which of these particles has the smallest wave length? a) Photon. b) Beta particle. c) Proton. d) All have same wave length. Stream-Chemistry 37. The distance between the first and the second Bohr Orbit of hydrogen atom is: a) b) c) d) 0.53*10-8 cm 2.11*10-8 cm 1.58*10-8 cm 2.64*10-8 cm 38. The standard e.m.f. for the cell reaction: Zn+Cu2+→Cu+Zn2+ is 1.10 volt at 25◦ c, The e.m.f. for the cell reaction when 0.1 M Cu2+ and 0.1 M Zn2+ solution are used at 25◦ is a) 1.10 V b) 0.110 V c) -1.10 V d) -0.110 V 39. Which are among the following is an example of ferroelectric substance: a) Quartz b) Lead Chromate c) Barium Titanate d) Lead Chloride 40. If the Ionic radii of K+ and F- are about 1.34°A each,the expected values of atomic radii of K and F should be respectively: a) 1.34 and 1.34°A b) 2.31 and 0.64° A c) 0.64 and 2.31°A d) 2.31 and 1.34° A 41. Which of the following has fractional bond order: a) O22+ b) O22c) F22d) H242. If a gas is exanded at constant temperature: a) No.of molecules of the gas decreases b) The K.E.of the molecule decreases c) The K.E.of the molecules remains the same d) The K.E.of molecules increases 43. The electron affinity of halogens shows the order: a) I>Cl>F<Br b) CI>Br>F>I c) F>Cl>Br>I d) F>I>Cl>Br 44. For the hypothetical reaction: 2A→3C,the reaction rate ( r ) is given by: a) r=− [ ] [ ] b) r=− [ ] c) r=− d) r= [ ] 45. The co-ordination numbers of CsCl structure & Fluorite structure respectively are: a) 8:8 & 8:4 b) 8:8 & 4:8 c) 4:8 & 8:8 d) 8:4 & 4:8 46. α-D- glucose contains which of the following functional group? a) Acetal b) Acetate c) Lactone d) Hemiacetal 47. The basicities of the acids H3PO2,H3PO3,H3PO4 and H4P2O7 are respectively: a) 1,2,3,7 b) 2,3,4,7 c) 1,2,3,4 d) 1,2,3,5 48. The general order of reactivity of carbonyl compounds for nucleophilic addition reaction is : a) H2C=0>RCHO>ArCHO>R2C=0>Ar2C=0 b) ArCHO>Ar2C=0>RCHO>R2C=0>H2C=0 c) Ar2C=0>R2C=0>ArCHO>RCHO>H2C=0 d) H2C=0>R2C=0>Ar2C=0>RCHO>ArCHO 49. Which of the following undergoes dehydration most readily: a) 1-phenyl-butan-1-ol b) 1-phenyl-butan-2-ol c) 2-phenyl-butan-2-ol d) 2-phenyl-butan-1-ol 50. In the following sequence the product D is: CH≡CH A B ! C " " ₂ ₂D a) Ethanol b) Ethane c) Ethyne d) Ethanal 51. The hybridization of Cr in [Cr(H2O)6]3t is a) d2sp3 b) sp3d2 c) dsp2 d) sp3d 52. Bond angle is maximum in which of the following hydrides. a) H2O b) H2S c) H2Te d) H2Se 53. Which of the following can possibly be used as analgesic without causing addiction and any modification. a) Morphine b) N-acetylpara aminophenol c) Diazepam d) Tetrahydrocatenol 54. In Lassaigne’s test for Sulphur in the organic compound with sodium nitroprusside solution,the purple color formed is due to a) Na4[Fe(CN)5NOS] b) Na3[Fe(CN)5S] c) Na2[Fe(CN)5NOS] d) Na3[Fe(CN)6] Stream – English Tick the option that is close in meaning to the given expression 55. Trivial a) several attempts b) bad intentions c) dark shadow d) Something unimportant 56. Child’s play a) a comic story b) something foolish c) an easy task d) a favorite pastime Read the passage below and answer the questions that follow: Mass production, however, was meaningless without parallel changes in the distribution system. In earlier societies, goods were normally made by handcraft methods. Products were created one at a time on a custom basis. The same was largely true of distribution. 57. Which of the following is not true of the industry of old times? a) simple machinery was used for production b) the product was produced according to the demands of the consumer c) products were dispatched manually one at a time d) the products were largely produced by hand. 58. Which of the following options the passage suggests a) mass production is not a very profitable activity b) distribution of small number of goods is convenient c) production in large numbers cannot be made by hands d) mass production requires large distribution methods Choose the option that will complete the sentence 59. My uncle told me that ___________ leaving for the US in the first week of July. a) he is b) he would be c) I was d) I will be 60. He has stated that he belongs_________ a village near Chandigarh a) in b) to c) from d) with