NRT INDIA (Code I015/JEE/01) COACHING INSTITUTE IIT-JEE-2015 Paper Code: I015/JEE/01 Time : 3.00 Hrs Unit Test-1 Sub :PCM Answer Sheet Code: …… Max. Marks :360 Date:…………………… TO BE COMPLETED BY THE CANDIDATE Name ..…………………………………….………..…………………….……………….……. SID. No …………………………………Signature of the candidate……..…….……………… DIRECTION TO CANDIDATES 1. 2. Attempt all questions . There are 45 questions each subject (PCBZ). . Each question carry +4 & −1 marks. 3. 4. All questions are Multiple Choice Question (carrying only one option is correct), darken the corresponding answer on OMR sheet provided separately. Do not write any thing on answer sheet other than information asked. 5. Blank papers, clipboard. Log tables slide rules, calculators, cellular phones, pagers, and electronic gadgets in any form are not allowed to be carried inside the examination hall. 6. Use black and blue ball point pen only in examination hall. 7. First of all fulfill the formalities in answer sheet and question paper properly before commencement. Examination Superintendent Signature of Guardian (Seal & Signature) OUR STUDY CENTRES IN LUCKNOW 1. 14/32, SEC-14 , RLB ROAD, NEAR MUNSI PULIA, INDIRA NAGAR , LUCKNOW. 2. L-2/610, VINEET KHAND, NEAR JAIPURIA SCHOOL, GOMTI NAGAR, LUCKNOW 3. 2nd FLOOR, LEELA MENSION, BEHIND LEELA CINEMA, HAZRATGANJ, LUCKNOW Call : 0522-3293158, 2714802, 9415905513, 8090510938, 7275924637, 7275924537 Website : www.nrtindia.com/.in/.org, E-mail: [email protected] , [email protected] NRT India , 14/32, RLB Road Near Munshi Pulia, Indira Nagar, Lucknow. Call: 0522-2714802, 9415905513, 8090510938 Branches : Indira Nagar, Gomti Nagar, Hazratganj 1 NRT INDIA 1. (Code I015/JEE/01) 2 The vector sum of two forces is perpendicular (a) BA sin θ to their vector differences. In that case, the (b) BA2 cos θ (c) BA2 sinθ cos θ forces (a) are equal to each other in magnitude (b) are not equal to each other in (d) Zero magnitude 6. 2. (c) cannot be predicted (d) are equal to each other If A and B are non-zero vectors which obey the relation A + B = A − B , then the angle between them is : A truck travelling due north at 20 ms −1 (a) turns 00 (c) 900 west and travels with same speed. What is (b) 600 (d) 1200 the change in velocity? (a) (b) 40 ms (c) 10 ms (d) 7. 20 ms−1 south –west −1 −1 A car travels 6 km towards north at an angle of 450 to the east and then travels distance of 4 south west km towards north at an angle 1350 to east. How north west far is the point from starting point? What angle 1 40 ms− north-west does the straight line joining its initial and final position makes with the east? 3. 50 km and tan−1 (5) Two forces P and Q have a resultant (a) perpendicular to P. The angle between the (b) 10 km and tan−1( 5 ) forces is : −1 (a) tan (−P/Q) (b) tan−1 (P/Q) (c) sin−1 (P/Q) (d) Cos−1 (−P/Q) 8. (c) 52 km and tan−1 (5) (d) 52 km and tan−1 ( 5 ) An object moves at a constant speed along a circular path in a horizontal XY plane, with the center at the origin,. When the object is at x= 4. If A × B = 3A. B, , then the value of A × B is (a) (b) A2 + B 2 + object’s acceleration when it is y= 2m? AB 1/2 3 (a) A+B −(8m/s2)j (b) (8m/s2)j 2 2 2 2 (c) (A +B + 3 AB) (d) (A +B +AB) 5. −2m, its velocity is –(4m/s)j. What is the 1/2 (c) −(4m/s2)j 1/2 (d) (4m/s2)j If the angle between the vectors A and B is θ, then value of the product B × A . A is equal to 9. The motion of a particle along a straight line is described by equation x=8+12t−t3 where x is in NRT India , 14/32, RLB Road Near Munshi Pulia, Indira Nagar, Lucknow. Call: 0522-2714802, 9415905513, 8090510938 Branches : Indira Nagar, Gomti Nagar, Hazratganj 2 NRT INDIA (Code I015/JEE/01) meter and t in second. The retardation of the (b) particle when its velocity becomes zero is (c) 4 times the original (a) 24 ms −2 (b) zero (c) 6 ms−2 10. A particle (d) (d) 12 ms−2 has initial velocity (2+3) and order of : (a) 1011 kg m−3 of velocity after 10 seconds will be : 9 2units (b) 5 2units (c) 5 units (d) 8 times the original 16. Density of matter inside atomic nuclei is of the acceleration (0.3+0.2). The magnitude (a) 1/2 times the original 9 units (c) 1017 kg m−3 (b) 1014kg m−3 (d) 1020 kg m−3 17. The universal gravitational constant G is of the order of : 11. Which of the following is the unit of latent heat? (a) 10−8 Nm2 Kg−2 (a) J (b) J Kg mol−1 (b) 10−10 Nm2 Kg−2 (c) J kg−1 (d) J Kg−1 mol−1 (c) 10−12 Nm2 Kg−2 (d) 10−14 Nm2 Kg−2 12. The unit of force as well as distance are doubled. How many times will the unit of 18. The order of Avogadro’ s number is kinetic energy be ? 1 2 (b) 2 (c) 4 (d) 8 (a) 1022 (b) 1023 (c) 1024 (d) 1025 (a) 19. The angle 10 54’ equal to : (a) 2.91×10−4 radian 13. Unit of Stefan’s constant is : (a) watt m2K4 (b) watt m2/K4 (b) 3.32×10−2 radian (c) watt /m2K (d) watt /m2K4 (c) 1.21× 10−6 radian (d) None of these 14. The unit of permittivity of free space , ∈0, is : (a) newton meter2/coulomb2 (b) coulomb2/newton meter2 20. The cgs unit of viscosity is poise (F) and the SI unit of viscosity is poiseuille (PI). Which of (c) coulomb2/(newton meter)2 the following relations is correct? (d) coulomb/newton meter (a) P=PI (b) 10P=PI (c) P= 10PI (d) None of these 15. If the unit of force and length are doubled, the unit of energy will be (a) 1/4 times the original 21. A man is throwing balls in air. He throws next ball when previous one is at highest point. If NRT India , 14/32, RLB Road Near Munshi Pulia, Indira Nagar, Lucknow. Call: 0522-2714802, 9415905513, 8090510938 Branches : Indira Nagar, Gomti Nagar, Hazratganj 3 NRT INDIA (Code I015/JEE/01) the throws each ball after 2 seconds, then 26. A particle is thrown vertically upwards. Its height to which ball rises is (Take g= 10 m/s2) velocity at half of the height is 10 m/s, then (a) the maximum height attained by it is (g= 10 10 m (b) 20 m (c) 30 m (d) 15m m/s2) 22. The average velocity of a body moving with uniform acceleration after travelling a distance (a) 8m (c) 10 m (b) 20 m (d) 16 m of 3.06 m is 0.34 ms−1. If the change in velocity of the body is 0.18 ms−1 during this time, its uniform accelerations is ; 27. If a body loses half of its velocity on penetrating 3 cm in a wooden block, then how (a) 0.01 ms−2 (b) 0.02 ms−2 much will it penetrate more before coming to (c) 0.03 ms−2 (d) 0.04 ms−2 rest? 23. A man throws a ball vertically upward and it (a) 1 cm (b) 2cm (c) 3 cm (d) 4 cm rises through 20 m and return to his hands. What was the initial velocity (u) of the ball and 28. A body dropped from a height ‘h’ with an initial for how much time (T) it remained in the air? speed zero reaches the ground with a velocity (a) u= 10 m/s, T= 2s of 3 km/hour. Another body of the same mass (b) u=10 m/s, T=4s was dropped from the same height ‘h’ with an initial speed 4 km/hour , will reach the ground (c) u=20 m/s, T= 2s with a velocity of : (d) u= 20 m/s, T= 4s (a) 24. A stone is dropped from rest from the top of a 3km/hour (c) 5km/hour (b) 4km/hour (d) 12 km/hour tower 19.6 m high. The distance travelled during the last second of its fall is : (Given g= other in magnitude , is perpendicular to the 9.8 m/s2) (a) 9.8 m (c) 4.9 m 29. The resultant of two forces, one double the (b) smaller of the two forces. The angle between 14.7 m the two forces is : (d) 19.6 m (a) 2 25. If for a particle position x ∝ t then 1200 (c) 900 (b) 600 (d) 1500 (a) velocity is constant (b) acceleration is constant (c) acceleration is variable (d) None of these 30. A body released from a great height freely towards the earth. Another falls body is released from the same height exactly one second later. The separation between the two NRT India , 14/32, RLB Road Near Munshi Pulia, Indira Nagar, Lucknow. Call: 0522-2714802, 9415905513, 8090510938 Branches : Indira Nagar, Gomti Nagar, Hazratganj 4 NRT INDIA (Code I015/JEE/01) bodies two seconds after the release of the (a) 0.52 second body is (g= 9.8 ms−2) (b) 2.5 (a) (b) 19.6 m (c) 0.25 (d) 4.9 m (d) 0.50 24.5 m (c) 9.8 m 31. limx→0 tan [−π2 ]x 2 −x 2 tan [−π2 ] sin 2 x equals where [ ] 37. 1−cos 2x sin 5x x 2 sin 3x limx‒0 denotes the greatest integer function (a) 10/3 (a) 0 (b) 3/10 (b) 1 (c) 6/5 (c) tan 10 − 10 (d) 5/6 (d) ∞ 38. limx→0 32. If un = 1 3 .5 + 1 5 .7 + ⋯…..+ 1 2n+1 2n+3 then limn→∞ un = 33. (a) 1 (b) 0 (c) 1/6 (d) ∞ 39. limn→∞ 4n 31/n − 1 = (a) 0 (b) 1 (c) ∞ (d) none of these 40. 34. = If [x] denotes the greatest integer less than or equal to x, then the value of limx→1 1 − x + x−1+[1−x] is (a) 0 sin x+log 1−x x2 (a) 0 (b) ‒½ (c) ½ (d) not defined limx→0 sin −1 x−tan −1 x x2 (c) ‒ 1 (d) none of these = (a) ‒ 1 (b) 0 (c) 1 (d) none of these The value of x 3 +2x 2 +x+1 limx→1 2 +2+3 1−cos (x −1) −1 2 (a) e (b) e1/2 (c) 1 (d) none of these (b) 1 41. is Let f(x) =limn→∞ x 2n −1 , x 2n +1 is then (a) f(x) = 1, for x > 1 35. 36. limx→∞ 2x 0 (b) f(x) is not defined for any value of x 2 x e x dx e 4x 2 equals (c) f(x) = ‒1, for x = 1 (a) 0 (b) ∞ (c) 2 (d) ½ limx→0 x 0 sin 3 x.cos x4 x dx (d) None of these 42. = 1 limx→∞ 1 + a+bx c+dx =( where a, b, c, d > 0) NRT India , 14/32, RLB Road Near Munshi Pulia, Indira Nagar, Lucknow. Call: 0522-2714802, 9415905513, 8090510938 Branches : Indira Nagar, Gomti Nagar, Hazratganj 5 NRT INDIA (Code I015/JEE/01) a/b (b) e (c) ec/b (d) ed/b (a) e b/c 49. If f(x)=x3 sgn x, then (a) f is derivable at x=0 43. limx→0 1 6 sin x−x+ x 3 x5 (b) f is continuous but not derivable at x=0 = (c) LHD at x=0 is 1 (a) 1/60 (d) None of these (b) 1/120 (c) 1/30 1+cos 4x x2 (d) 1/180 50. x<0 x=0 a If f(x)= x 16+ 4−4 44. 45. limx→0 1co sec 2x + 2cosec 2x + ⋯ + ncosec 2 2 x sin x x>0 is continuous at x=0, the value of a is : = (a) 0 (b) ∞ (a) 8 (b) −8 (c) n (d) none of these (c) 4 (d) None of these If a>b then f(x)= x−a b−x If f(x) = 2 ,g x−3 x = x−3 x+4 2(2x+1) , x 2 +x−12 and h(x) = then 51. limx→3 f x + g x + h(x) is (a) ‒ 2 (b) ‒1 (c) ‒ 2/7 (d) 0 is continuous on (a) (b, a) (b) [b, a] (c) [b, a) (d) (b, a] 1 46. sin hx 2 limx→ x = (a) e−1/6 (b) e1/6 (c) e (d) e−1 52. If f(x)= a+x 2 sin a+x −a 2 sin a x , x≠0 Is continuous at x=0 then f(0) (a) a2 cos a +a sin a 47. limx→∞ (a) x+cos α +sin cos t (c) 1 48. (b) a2 cos a+2a sin a = (c) 2a2 cos a +a sin a (b) ∞ (d) none of these If f(x)= log10 x , then at x=1 (d) None of these 53. (a) f(x) is continuous and f’ (1+)= log10 e If f (x)= x− x x 2 x≠0 x=0 (a) f(x) is continuous at x=0 + (b) f(x) is continuous and f’(1 ) =loge10 (c) f(x) is continuous and f’(1−) = loge10 (b) f(x) is discontinuous at x=0 (c) limx→0 f(x)=2 (d) None of these NRT India , 14/32, RLB Road Near Munshi Pulia, Indira Nagar, Lucknow. Call: 0522-2714802, 9415905513, 8090510938 Branches : Indira Nagar, Gomti Nagar, Hazratganj 6 NRT INDIA (Code I015/JEE/01) (d) None of these 58. If f(x)= x 1 x≠0 and f(0)=0then at x=0 1+e x (a) f is continuous 54. The function (b) f is discontinuous F(x)= max { (1−x), (1+x), 2}, (c) f is left continuous only x∈ (−∞, ∞) is (d) f is right continuous only (a) continuous at all points (b) differentiable at all points 59. If f(x)= [ x sin πx], then f(x) is : (c) Continuous at all points except at x=1 and x=−1, where it is discontinuous (a) continuous at x=0 (d) none of these (b) differentiable at x=1 (c) Both a and b 55. (d) None of these Let f(x)= x and g(x)= x 3 , then (a) f(x) and g(x) both are continuous at x=0 (b) f(x) and g(x) both are differentiable at x=0 (c) f(x) is differentiable but g(x) is not differentiable at x=0 (d) f(x) and g(x) both are not differentiable at x=0 56. 1 60. Let f(x)= x + x x . Then for all x (a) f is continuous (b) f’ is differentiable for same x (c) f’ is continuous (d) f” is continuous 2 The function f(x)=x − e 2x −1 , x≠0 is continuous at x=0. Then OH O (a) f(0)=1 61. The IUPAC name of (b) f(x) is not differentiable at x=0 (c) f’(0)= 1 3 4-hydroxy-2-pentanone (c) 2-oxo-4-pentanol (d) sin a+1 x+sin x x If f(x)= (a) 2-hydroxy-4-pentanone (b) (d) None of these 57. is : c 1 1 (x+bx 2 )2 −x 2 3 x<0 x=0 x>0 bx 2 is continuous at x=0 then c= (a) −3/2 (b) 1/2 (c) a (d) b 2-keto-2-pentanol 62. The IUPAC name of CH3CH2OCH(CH3)2 is : (a) isopropoxy ethane (b) 2-methoxy butane (c) 1- methyl-1-methoxy ethane (d) 2-ethoxy propane 63. The IUPC name of H3C −CH−CH2−CH−CH2Cl C2H5 OH (a) 1-chloro-4-methylhexan-2-ol (b) 1-chloro-4-methylhexan -2-al (c) 1-chlroor-4-ethylpentan-2-ol NRT India , 14/32, RLB Road Near Munshi Pulia, Indira Nagar, Lucknow. Call: 0522-2714802, 9415905513, 8090510938 Branches : Indira Nagar, Gomti Nagar, Hazratganj 7 NRT INDIA (d) (Code I015/JEE/01) 1-chloro-2-hydroxy-4-methylhexane (d) none of these 64. The IUPAC name of CH3−CH=C−CH2CH3 69. The IUPAC name of the following is : 7 CH2 CH2CH3 (a) 3-prophylhex-2-en (b) 6 5 4 3 2 1 CH3CH=CH−CH2−CH−CH2COOH NH2 3-propylhex-3-ene (a) 3- amino hept-5 enoic acid (c) 4-ethylhex-4-ene (b) 5-amino hex-2-ene-carboxylic acid (d) 3-ethylhex-2-ene (c) 3-amino-δ-heptenoic acid 65. The IUPAC nomenclature of (CH3)3 C−CH=C(CH3)2 is 70. The IUPAC name of CH3−C≡CCH(CH3)2 is : (a) 4-methylpent-2-yne (a) 2, 4, 4-trimethyl pent-3-ene (b) 4,4’-dimethylpent-2-yne (b) 2,4,4,-trimethyl pent-2-ene (c) 2,2,4-trimethyl pent-3-ene (c) methyl isopropyl acetylene (d) 2,2,4-trimethyl pent-2-ene (d) 2-methylpent-4-yne O C2H5−O 66. The IUPAC name of 71. The IUPAC name of C=O is : OH is (a) prop-2-enoic acid CH3−CH (b) but-1-enoic acid CH3 (a) ethoxy methanone (c) but-3-enoic acid (b) ethyl-2-methyl propanoate (d) pent-4-enoic acid (c) ethoxypropanone (d) 2-methyl ethoxy propanone 72. The IUPAC name of the compound shown below is : Cl 67. The correct IUPAC name of the compound Br CH3 (a) 2-bromo-6-chlorocyclohex-1-ene CH3CH2 − C = CH − CH − CH2 − CH3 6 7 6 9 (b) 10 CH3 CH2−CH−CH2−CH2−CH2−CH3 is (a) 5, 6-diethyl-3-methyl-dec-4-ene 6-bromo-2-chlorocyclohexene (c) 3-bromo-1-chlorocylohexene (d) 1-bromo-3-chlororcylohexene (b) 5,6-diethyl-8-methyl-dec-6-ene (c) 6-butyl-5-ethyl-3-methyl-oct-4-ene 73. How many structures are possible for following formula C6H14 (d) 2,4,5-triethyl-3-nonene O (a) 3 (b) 4 (c) 5 (d) 6 C2H5 − C 68. The IUPAC name of the compound is O CH3−C O (a) Propionic acetic anhydride 74. How many 20 amines are possible for following formula C6H15N (a) 12 (b) 16 (c) 15 (d) 24 (b) ethanoic propanoic anhydride (c) aceto ethanoate NRT India , 14/32, RLB Road Near Munshi Pulia, Indira Nagar, Lucknow. Call: 0522-2714802, 9415905513, 8090510938 Branches : Indira Nagar, Gomti Nagar, Hazratganj 8 NRT INDIA (Code I015/JEE/01) 75. How many Ald. and Ketones are possible for following formula C6H12O. (only structures) (a) 8 8 (d) 3 81. How many positional isomers all possible for following formula C4H8Cl2[only having Butane as a parent chain] (b) 8 6 (c) 16 18 (d) (c) 1 16 16 76. Which Isomeric Relation is present in following molecules CH3−CH2−CH2−COOH & CH3 − CH − CH3 COOH (a) Chain isomerism (b) Position Isomerism (c) Functional group. Isomerism (d) Geometrical Isomerism (a) 3 (b) 4 (c) 5 (d) 6 82. How many easters are possible for following formula C5H10O2 (Only structures). (a) 5 (b) 3 (c) 9 (d) 6 83. What is degree of unsaturation for given molecules C10H20N2Br2Cl2, C17H27NBr2Cl2, C10H10Cl10 77. How many total alcohol & ethers are possible (structure only) for following formula : C6H14O (a) 0 3 6 (b) 0 3 1 (c) 2 4 6 (d) 2 4 4 (a) 17 15 84. The presence of unsaturation (olefinic or acetylinic bond) in an organic compound can be tested with (b) 16 12 (c) 16 16 (d) 16 8 (a) Schiff’s reagent (b) Tollen’s reagent 78. What is degree of unsaturation for following formula : CN COOH CN (a) 8 8 (b) 8 7 (c) 2 7 (d) 8 6 (c) Fehling’s solution (d) Baeyer’s reagent 85. Which of following compound will give Iodop test positive (a) CH3OH (b) CH3−CH2−C−H O 79. What isomeric relation is in following compound CH3 CH3−CH2−CH2−CH2−OH & CH3−C−CH3 (c) CH3−C−CH2−C−CH3 O (d) O CH3CH2OH OH (a) Only Position isomerism 86. Which of the following compound will give carbyl Amine test positive (b) Only chain isomerism (c) Chain and position both (a) CH3CH2NH2 (b) CH3CH2NHCH3 (d) None of these (c) CH3−N− CH3 (d) All CH3 80. How many structure are possible having benzene ring only C7H14. (a) 0 (b) 2 87. Which of the following test will give fastest Lucas test with (HCl+ZnCl2) NRT India , 14/32, RLB Road Near Munshi Pulia, Indira Nagar, Lucknow. Call: 0522-2714802, 9415905513, 8090510938 Branches : Indira Nagar, Gomti Nagar, Hazratganj 9 NRT INDIA (Code I015/JEE/01) (a) CH3OH (b) CH3CH2OH OH OH (c) CH3−C−CH3 (d) CH3 88. Which of the following compound will produce white ppt with (AgNO3+NH4OH) (a) CH4 (b) C2H4 (c) C2H2 (d) CH3−C≡C−CH3 89. Which of following compound will give test of unsaturation as well as Iodopharm test (a) CH3−C−CH2−CH=CH2 O O (b) CH3−CH2−C−CH2−CH=CH2 O (c) CH= CH2 O (d) O 90. How many Ring structures are possible for C6H12 (a) 8 (b) 10 (c) 12 (d) 14 NRT India , 14/32, RLB Road Near Munshi Pulia, Indira Nagar, Lucknow. Call: 0522-2714802, 9415905513, 8090510938 Branches : Indira Nagar, Gomti Nagar, Hazratganj 10

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