FIITJEE PET V (EXTENDED)

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1 FIITJEE PET V (EXTENDED) MAINS DATE: Time: 3 hours Maimum Marks: 360 INSTRUCTIONS: Instructions to the Candidates 1. This Test Booklet consists of 90 questions. Use Blue/Black ball Point Pen only for writing particulars and bubbling of OMR.. For each correct answer 4 Marks will awarded and for each wrong answer 1 Mark will be deducted. 3. Attempt all questions. 4. In case you have not darkened any bubble you will be awarded 0 mark for that question. 5. Use of calculator/logarithmic table is not permitted. Don t write / mark your answers in this question booklet. If you mark the answers in question booklet, you will not be allowed to continue the eam. NAME: ENROLLMENT NO.: FIITJEE (Hyderabad Classes) Limited /B, Saifabad, (Opp. Secretariat) Hyderabad Ph: Fa: FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

2 PET-V (EXTENDED)-018-MPC Range of the function f defined by f() = sin (where [.] and {.} respectively denotes the greatest integer and the fractional part function) is (A) I, the set of integers (B) N, the set of natural numbers (C) W, the set of whole numbers (D) Q, the set of rational numbers. Let f() = [ ] (, 1), then range of f() is (where [.] denotes the greatest integer function) (A) {0, 1,, 3, 4, 5, 6} (B) {0, 1,, 3, 4, 5, 6, 7} (C) {1,, 3, 4, 5, 6} (D) {1,, 3, 4, 5, 6, 7} 3. If f() is an even function and satisfies the relation 1 f() f = g(), where g() is an odd function, then the value of f(5) is (A) 0 (B) 37 (C) 4 (D) f() = 5sgn 9 7 sin e is (A) an even function (C) neither even nor odd (B) an odd function (D) none of these 5. Let f() = sin cos be (where [.] denotes the greatest integer function) then range of f() will (A) {0} (B) {1} (C) {0, 1} (D) 0,1, 6. If f( + 3y, 7y) = 0, then f(, y) equals (A) 7 3y (B) 7 + 3y (C) 3 7y (D) 3 + 7y 7. If f() = 1, then f 1 () equals (A) 1 (B) Sgn 1 (C) 1 (D) none of these 000 r 8. If [] and {} represent integral and fractional part of, then the value of is r1 000 (A) (B) [] (C) {} (D) FIITJEE (Hyderabad Classes) Limited /B, Saifabad, (Opp. Secretariat) Hyderabad Ph: Fa: FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

3 PET-V (EXTENDED)-018-MPC-3 9. Which of the following function is even function a 1 (A) f() = (B) f() = a 1 a 1 a 1 (C) f() = a a a a (D) f() = sin The domain of the function f() = log10 1 is (A) [ 3, ], ecluding (B) [0, 1] ecluding 0.5 (C) [, 1], ecluding 0 (D) none of these 11. If f: X Y defined by f() = 3 sin + cos + 4 is one-one and onto, then Y is (A) [1, 4] (B) [, 5] (C) [1, 5] (D) [, 6] 1. If f() = sin 1 {4 ( 7) 3 } 1/5, then its inverse is (A) (4 sin 5 ) 1/3 (B) 7 (4 sin 5 ) 1/3 (C) (4 sin 5 ) /3 (D) 7 + (4 sin 5 ) 1/3 13. The inverse of the function y = log a 1 ; (a > 0, a 1) is (A) 1 (a a ) (C) defined for only positive (B) not defined for all (D) none of these The domain of the function f() = sin log cos sin sin (A) { : 1 } (B) {1} (C) not defined for any value of (D) { 1, 1} 15. Let f: R R be a function defined by f() = (A) one-one and into (C) many one and onto 5 is (B) one-one and onto (D) many one and into Which of the following statement is correct? (A) 1 > 1 C (B) 1 = 1 C (C) 1 < 1 C (D) C = sec cot 1 = (A) tan (B) cot (C) sec (D) cosec 18. If sin cos = 1, then the value of sin 4 + cos 4 is (A) 0 (B) 1 (C) 1 (D) none of these FIITJEE (Hyderabad Classes) Limited /B, Saifabad, (Opp. Secretariat) Hyderabad Ph: Fa: FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

4 PET-V (EXTENDED)-018-MPC If tan + cot = 3, then the value of sec + cosec is (A) 6 (B) 9 (C) 1 (D) 3 0. If sec = 5 sec tan 1sin tan is 3 sin (A) 0 (B) 1 (C) 1 (D), then the value of 1. Which of the following statement is correct? (A) sin = 1 + p ; (p > 0) (B) cos = t 1, (t > ) (C) tan = 1 q, (q > ) (D) sec = 4 m, (0 < m < 1) sin tan. If = 780, then the value of cos (A) 3 (B) 6 (C) 3 (D) 6 3. cot cos cot cos = (A) 1 (B) 1 (C) 0 (D) 4. cos 6 + sin cos 3 cos 4 = (A) 0 (B) 1 (C) 1 (D) tan140tan If tan 40 =, then value of 1tan140tan130 is 1 1 (A) (B) (C) 6. cos 16 + sin 34 = 1 (D) 1 (A) 0 (B) 1 (C) 1 (D) 1 7. If a sin + b cos = c, then the value of tan is (A) b c (B) c b (C) a c a c a c b c (D) a c c b FIITJEE (Hyderabad Classes) Limited /B, Saifabad, (Opp. Secretariat) Hyderabad Ph: Fa: FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

5 PET-V (EXTENDED)-018-MPC-5 8. If 0, and sin = 1, then the value of cos 4 sin 6 is (A) 3 4 (B) 1 4 (C) 1 (D) 0 9. If cos + sec =, find the value of sin + tan (A) 1 (B) (C) 0 (D) If , then cannot take the value of (A) 0 (B) (C) 3 3 (D) A uniform chain has mass M and length L. It is lying on a smooth horizontal table with half its length hanging vertically downward. The work done in pulling the chain up the table is (A) MgL / (B) MgL / 4 (C) MgL /8 (D) MgL/16 3. If the block in the shown arrangement is acted upon by a constant force F for t 0, its maimum speed will be (A) F/ mk (B) F / mk (C) F/ mk (D) F / mk 33. A self propelled vehicle of mass m, whose engine delivers a constant power P, has an acceleration a = (P/mv). (Assume that there is no friction). In order to increase its velocity from v 1 to v, the distance it has to travel will be. 3P (A) v v 1 (B) m v 3 3 v 1 m 3P m (C) v v 1 (D) m v 3 v 1 3P 3P 34. A stone tied to string of length is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time the stone is at its lowest position and has a speed u. The magnitude of the change in velocity as it reaches a position, where the string is horizontal is (A) (C) u u g (B) g g (D) u g FIITJEE (Hyderabad Classes) Limited /B, Saifabad, (Opp. Secretariat) Hyderabad Ph: Fa: FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

6 PET-V (EXTENDED)-018-MPC An elastic string of unstretched length L and force constant k is stretched by a small length. it is further stretched by small length y. The work done in the second stretching is 1 (A) ky 1 (B) k y (C) 1 k y 1 (D) ky y 36. A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to k where k is a positive constant. Then if kinetic energy, potential energy and mechanical energy r of the particle are KE, PE and ME respectively. which one is correct? k k k (A) KE,PE,ME r r r k k (B) KE,PE,ME zero r r (C) KE zero,pe zero,me zero k k k (D) KE,PE,ME r r r 37. A 10 kg block is pulled along a frictionless surface in the form of an arc of a circle of radius 10m. The applied force F is 00 N as shown. IF the block started from rest at point P, then its velocity at Q will be? (take g=10 m/s ) (A) 14.7 m/s (C) 16.7 m/s (B) 15.7 m/s (D) 17.3 m/s 38. A block of mass m released from rest from point O as shown below. The velocity of the block at the lowest points are v D,v E,v F respectively. Assume coefficient of kinetic friction between surface and the block is same in all cases. Then, (A) vd ve vf (B) vf ve vd (C) vd ve vf (D) vd ve vf 0 FIITJEE (Hyderabad Classes) Limited /B, Saifabad, (Opp. Secretariat) Hyderabad Ph: Fa: FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

7 PET-V (EXTENDED)-018-MPC The mass m slides down the track and completes the vertical circle on the smooth curved surface. The minimum value of h will be (A) R (B) R (C).5 R (D) 3 R 40. A body of mass m is moving in a circle of radius r with a constant speed v. The force on the body is mv and is directed towards the center. If work done by this force in moving the body over half the r circumference and complete circumference is W and W', then mv (A) W, r,w ' zero (B) r (C) mv W,r,W' zero r mv mv W,W'. r r r (D) W zero,w' zero 41. In the shown figure, a small mass m starts sliding down a smooth and stationary circular track. Which of the following graph best represents the variation of magnitude of the force applied by the track on the mass and the angle? (A) (B) (C) (D) FIITJEE (Hyderabad Classes) Limited /B, Saifabad, (Opp. Secretariat) Hyderabad Ph: Fa: FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

8 PET-V (EXTENDED)-018-MPC-8 4. A particle of mass m is located in a one dimensional potential field where potential energy of the a b particle has the form U where a and b are positive constants. The position of equilibrium is (A) b (B) b (C) a (D) a a a b b 43. Two cylindrical vessels of equal cross sectional area. A contain water upto height h1 andh. The vessels are interconnected so that the levels in them become equal. The work done by the force of gravity during the process is (A) zero (B) h1 h A g h1 h (C) A g 44. Two springs A and Bk k ends. If the energy stored in A is E, that in B is A B Ah1h (D) g are stretched by applying forces of equal magnitudes at the four (A) E (B) E (C) E (D) E In the shown diagram mass of A is m and that of B is m. All the surfaces are smooth. System is released from rest with spring unstretched. Then, the maimum etension be m in spring will (A) mg k (B) mg k (C) 3mg k (D) 4mg k FIITJEE (Hyderabad Classes) Limited /B, Saifabad, (Opp. Secretariat) Hyderabad Ph: Fa: FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

9 PET-V (EXTENDED)-018-MPC A chain of length L and mass M is arranged as shown in following four cases. The correct decreasing order of potential energy (assumed zero at horizontal surface) is (A) i ii iii iv v (B) i ii iii iv v (C) i ii iv iii v (D) i ii iv v iii 47. A particle free to move along ais has potential energy given by U K1ep, where K is a positive constant of appropriate dimensions. Then. (A) At point away from the origin, the particle is in unstable equilibrium (B) For any finite non zero value of, there is force directed away from the origin (C) If its total mechanical energy if K/, it has its minimum KE at the origin (D) For small displacements from =0, the motion is simple harmonic. 48. A 1.0 kg block collides with a horizontal weightless spring of force constant.75 1 Nm as shown in figure. The block compresses the spring 4.0 m from the rest position. If the coefficient of kinetic friction between the block and horizontal surface is 0.5, the speed of the block at the instant of collision is 1 (A) 0.4ms 1 (B) 4ms 1 (C) 0.8ms (D) 8ms In the figure shown all the surfaces are frictionless, and mass of the block, m = 1 kg. The block and wedge are held initially at rest. Now wedge is given a horizontal acceleration of 10m/ s by applying a force on the wedge, so that the block does not slip on the wedge. Then work done by the normal force in ground frame on the block in 3 seconds is (A) 30 J (B) 60 J (C) 150 J (D) 100 3J for FIITJEE (Hyderabad Classes) Limited /B, Saifabad, (Opp. Secretariat) Hyderabad Ph: Fa: FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

10 PET-V (EXTENDED)-018-MPC When a conservative force does positive work on a body. (A) the potential energy increases (B) the potential energy decreases (C) total energy increases (D) total energy decreases 51. A particle is released from rest at origin. It moves under influence of potential field U 3, kinetic energy at = is (A) J (B) 1 J (C) 1.5 J (D) 0 J 5. Water is pumped from a depth of 10m and delivered through a pipe of cross section 1 3 needed to deliver a volume of 10 m per second the power required will be (A) 10 kw (B) 9.8 kw (C) 15 kw (D) 4.9 kw 10 m. If it is 53. A body with mass kg moves in one direction in the presence of a force which is described by the potential energy graph. If the body is released from rest at =m, then its speed when it crosses =5 m is U(J) X(meter) (A) zero (B) 1 1ms (C) -1 ms (D) 3ms A body is moving uni directionally under the influence of a source of constant power. Its displacement in time t is proportional to (A) t 1/ (B) t (C) 3/ t (D) t FIITJEE (Hyderabad Classes) Limited /B, Saifabad, (Opp. Secretariat) Hyderabad Ph: Fa: FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

11 PET-V (EXTENDED)-018-MPC A simple pendulum consisting of a mass M attached in a string of length L is released from rest at an angle. A pin is located at a distance ' ' below the pivot point. When the pendulum swings down, the string hits the pin as shown in the figure. The maimum angle which string makes with the vertical after hitting the pin is 1 Lcos 1 Lcos (A) cos L (B) cos L 1 Lcos 1 Lcos (C) cos L (D) cos L 56. A particle mass is tied to an ideal string and whirled in a vertical circle of radius L, Where L is off course the length of the string. If the ratio of the maimum to minimum tension in the string throughout the motion is :1, then the maimum possible speed of the particle will be (A) 11gL (B) 5gL (C) 10gL (D) 3gL 57. Under the action of force, kg body moves such that its position as a function of time t is given by 3 t, is in mere and t in second. Calculate the work done by the force in the first second. 3 (A) 14 J (B) 16 J (C) 18 J (D) zero 3i ˆ 1.5j ˆ N i ˆ 3j ˆ m and is travelling at 58. A force of acts on 5 kg body. The body is at a position of 1 4ms. The force acts on the body until it is at the position ˆ i ˆ work on the body, the final speed of the body. 5j m. Assuming no other force does (A) 5m / s (B) 10m / s (C) 15m / s (D) None FIITJEE (Hyderabad Classes) Limited /B, Saifabad, (Opp. Secretariat) Hyderabad Ph: Fa: FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

12 PET-V (EXTENDED)-018-MPC A block of mass m is hung vertically from an elastic thread of force constant mg. Initially the thread a was as its natural length and the block is allowed to fall freely. The kinetic energy of the block when it passes through the equilibrium position will be (A) mga (B) mga (C) zero (D) mga 60. The total work done on a particle is equal to the change in its kinetic energy (A) always (B) only if the force acting on it are conservative (C) only if gravitational force along acts on it (D) only if elastic force along acts on it 61. Compare the stability of N, N, N,N in increasing order N N N N (B) N N N N (A) (C) N N N N (D) N N N N 6. The paramagnetic behaviour of B is due to the presence of (A) unpaired electron in b MO (B) unpaired electron in *MO (C) unpaired electron in *MO (D) unpaired electron in b MO 63. The polarizing power of the following anion N 3, O, and F follows the order : (A) N 3 > F > O (B) O > N 3 > F (C) O > F > N 3 (D) N 3 > O > F 64. Calculate the formal charge on all N in N = N = N from left to right (A) 1, 1, +1 (B) 1, +1, 1 (C) +1, 1, 1 (D) +1, 1, The hybridization of orbitals on N atom in NO 3,NO,MH 4 are (A) sp, sp, sp 3 (B) sp, sp, sp 3 (C) sp, sp 3, sp (D) sp, sp 3, sp FIITJEE (Hyderabad Classes) Limited /B, Saifabad, (Opp. Secretariat) Hyderabad Ph: Fa: FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

13 PET-V (EXTENDED)-018-MPC The correct order of increasing bond length of C H, C O, C C, C=C (A) C H < C=C < C O < C C (B) C C < C=C < C O < C H (C) C IO < C H < C C < C=C (D) C H < C O < C C < C=C 67. Which of the following compounds has the lowest mpt. (A) CaCl (B) CaBr (C) CaI (D) CaF 68. For which element the inertness of the electron pair will not be observed? (A) Sn (B) Fe (C) Pb (D) In 69. A neutral molecule XF 3 has a zero dipolemoment. The element X is most likely (A) Cl (B) Boron (C) Nitrogen (D) Carbon 70. Cl O bond order in HClO 4 ion is (A) 1.33 (B) 1.50 (C) 1.75 (D) Choose the right statement (A) NO and N O 4 both are paramagnetic (B) NO is diamagnetic and N O 4 paramagnetic (C) NO is paramagnetic and N O 4 diamagnetic (D) None of these 7. NO. of bond in H S O 6, H SO 3, H S O 5 are respectively (A) 1, 4, 3 (B) 4, 3, 1 (C) 4, 1, 3 (D) 1, 3, The relative stabilities of CN, CN +, CN. (A) CN CN CN (B) CN CN CN (C) CN CN CN (D) CN CN CN 74. Which of the following will have higher solubility in ether. (A) NaCl (B) LiCl (C) KCl (D) None 75. The molecule having smallest bond angle is (A) AsCl 3 (B) SbCl 3 (C) PCl 3 (D) NCl 3 FIITJEE (Hyderabad Classes) Limited /B, Saifabad, (Opp. Secretariat) Hyderabad Ph: Fa: FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

14 PET-V (EXTENDED)-018-MPC The ON O bond angle is maimum in (A) NO 3 (B) NO (C) NO (D) NO 77. In an octahedral structure, the pair of d orbitals involved in d sp 3 hybridisation is : (A) d,d (B) d y,d (C) dz,d z (D) d y,d yz y z y 78. Which of the following bond is strongest? (A) C C (B) C H (C) H H (D) None of these 79. Which of the following represents the Lewis structure of N molecule? (A) N N (B) N N (C) N N (D) N N 80. Atomic number of the four elements A, B, C & D are respectively Z-1, Z, z + 1, Z +. If Z = 9, what is types of bonding between B and D. (A) ionic (B) covalent (C) dative (D) none of these 81. Which one has more ionic character. (A) NaCl (B) KCl (C) RbCl (D) CsCl 8. Which one has more ionic character? (A) NaCl (B) MgCl (C) AlCl 3 (D) All having same 83. Which shows the highest lattice energy? (A) RbF (B) CsF (C) NaF (D) KF 84. Knowing that size of Na + > Mg + and S - > CI -, predict which compound will be least soluble in polar solvent (A) MgS (B) Na S (C) MgCI (D) NaCI FIITJEE (Hyderabad Classes) Limited /B, Saifabad, (Opp. Secretariat) Hyderabad Ph: Fa: FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

15 PET-V (EXTENDED)-018-MPC Molecular shape of SF 4, CF 4 and XeF 4 are (A) the same, with, 0 and 1 lone pair of electrons respectively (B) the same, with 1, 1 and 1 lone pair of electron respectively (C) different, with 0, 1, and lone pair of electrons respectively (D) different, with 1, 0 and lone pair of electrons respectively 86. Which of the following molecules is covalent and shows epanded octet in its formation? (A) HF (B) NF 3 (C) BF 3 (D) ClF The orbital involved in sp 3 d hybridization. (Assuming z ais as the internuclear ais) (A) d (B) d (C) d (D) z yz d y z 88. Hybridization state of I in ICl is : (A) dsp (B) sp (C) sp (D) sp Covalent bond eists in : (A) Na S (B) AlCl 3 (C) NaH (D) MgCl 90. The above potential energy curve is given for the formation of H molecule as a function of inter nuclear distance of H atoms. At what point in the curve H is found in the most unstable state? (A) A (B) B (C) C (D) D FIITJEE (Hyderabad Classes) Limited /B, Saifabad, (Opp. Secretariat) Hyderabad Ph: Fa: FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

16 PET-V (EXTENDED)-018-MPC-16 MATHEMATICS FIITJEE PET V (EXTENDED) MAINS_ANSWERS DATE: B. A 3. A 4. B 5. C 6. B 7. D 8. C 9. B 10. D 11. D 1. D 13. A 14. B 15. D 16. C 17. B 18. C 19. B 0. B 1. D. C 3. C 4. B 5. B 6. B 7. B 8. D 9. C 30. C PHYSICS 31. C 3. A 33. B 34. D 35. D 36. A 37. D 38. C 39. C 40. D 41. B 4. D 43. C 44. B 45. D 46. C 47. BONUS 48. D 49. C 50. B 51. A 5. C 53. BONUS 54. C 55. C 56. A 57. B 58. B 59. B 60. A CHEMISTRY 61. D 6. A 63. D 64. B 65. B 66. A 67. C 68. B 69. B 70. BONUS 71. C 7. C 73. BONUS 74. B 75. B 76. B 77. A 78. C 79. A 80. A 81. D 8. A 83. C 84. A 85. D 86. D 87. D 88. D 89. B 90. A FIITJEE (Hyderabad Classes) Limited /B, Saifabad, (Opp. Secretariat) Hyderabad Ph: Fa: FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :