FIITJEE PET III (EXTENDED)

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1 FIITJEE PET III (EXTENDED) MAINS DATE: Time: 3 hours Maximum 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 exam. NAME: ENROLLMENT NO.:

2 PET-III (EXTENDED)-018-MPC- 1. The coordinates of two consecutive vertices A and B of a regular hexagon ABCDEF are (1, 0) and (, 0) respectively. The equation of the diagonal CE is 3x y 4 (B) x 3y4 0 (C) x 3y 4 (D) none of these. The distance between the lines 3x + 4y = 9 and 6x + 8y + 15 = 0 is 3 (B) 33 (C) (D) none of these 3. The equations of the three sides of a triangle are x =, y + 1 = 0 and x + y = 4. The coordinates of the circumcentre of the triangle of are (4, 0) (B) (, 1) (C) (0, 4) (D) none of these t t 4. If P1, be any point on a line then the range of values of t for which the point P lies between the parallel lines x + y = 1 and x + 4y = 15 is t (B) 0 t (C) t 0 (D) none of these If the intercept made on the line y = mx by lines y = and y = 6 is less than 5, then the range of values of m is 4 4,, (B), 3 3 (C), 4 4 (D) none of these 6. If the point (a, a) falls between the lines x + y =, then a = (B) a = 1 (C) a < 1 (D) a < If A sin, and B 1,cos,, are two points on the same side of the line x y = 0, then belongs to the interval 3,, (B), 4 4 (C), 4 4 (D) none of these 8. Let P = (1, 1) and Q = (3, ). The point R on the x-axis such that PR + RQ is the minimum is 5 1,0 3 (B),0 3 (C) (3, 0) (D) none of these

3 PET-III (EXTENDED)-018-MPC-3 9. Three vertices of a quadrilateral in order are (6, 1), (7, ) and ( 1, 0). If the area of the quadrilateral is 4 unit, then the locus of the fourth vertex has the equation x 7y = 1 (B) x 7y + 15 = 0 (C) (x 7y) + 14(x 7y) 15 = 0 (D) none of these 10. A line passing through the point (, ) and the axes enclose an area. The intercepts on the axes made by the line are given by the two roots of x x + = 0 (B) x + x + = 0 (C) x x + = 0 (D) none of these 11. If a f(x) + b a a b 1 f x = x 1, x 0 and a b, then f() is equal to a b a b (B) (C) a b a b (D) a b a b 1. If f(x) = x n + a, if f() = 6 and f(4) = 138, then f(3) is equal to 56 (B) 8 (C) 64 (D) The period of the function f(x) = 4sin 3 4 (B) x 3 4x 3 cos 6 3 is 4 (C) 3 4 (D) Range of function f defined by f(x) = sinx integer and the fractional part function) is I, the set of integers (C) W, the set of whole numbers (where [.] and {.} respectively denotes the greatest (B) N, the set of natural numbers (D) Q, the set of rational numbers 15. The range of the function f(x) = 3 sin x cos x is, 13 (B) [, 3] (C) 3, 13 (D) [ 3, ] 16. The domain of definition of f(x) = 1 x x is (, ) [, ] (B) (, ) [ 1, 1] (C) [ 1, 1] (, ) (, ) (D) none of these

4 PET-III (EXTENDED)-018-MPC If S is the set of all real x for which 1 e (1/x) 1 > 0, then S is equal to (, 0) (1, ) (B) (, ) (C) (, 0] [1, ) (D) none of these The domain of the function f(x) = log10 1 x x is [ 3, ], excluding (.5) (B) [0, 1], excluding 0.5 (C) [, 1], excluding 0 (D) none of these x 19. The domain of the function f(x) = sin log x cos sin x sin x {x : 1 x } (B) {1} (C) not defined for any value of x (D) { 1, 1} 1 0. The domain of f(x) = is cos x cos x [ n, n]; n I (B) (n, n 1 ); n I 4n 14n 3 4n 1 4n 1 (C), ; n I (D), ; n I 1. The domain of f(x) is (0, 1), therefore domain of f(e x ) + f(ln x ) is ( 1, e) (B) (1, e) (C) ( e, 1) (D) ( e, 1). If [.] denotes the greatest integer function, then the domain of the real value function log [x + ½] x x is 3 3 1, (B),, (C),, (D) none of these x x x The domain of the function f(x) = sin cos tan is [0, 3] (B) [ 6, 6] (C) [ 1, 1] (D) [ 3, 3] 4. The domain of the function f(x) = x 1 x [, 6] (B) (, 6] (C) [8, 1] (D) none of these

$] denotes the fractional part function) (0, ) I (B) (1, ) I (C) R I (D) (, ) I 7. Number of ordered pair (x, y) satisfying x + 1 = y and y + 1 = x, is 0 (B) 1 (C) (D) 3 8.$ Roots of the equation x 5 x 19 = 0 are real, equal and rational (C) real, unequal and irrational (B) real, unequal and rational (D) complex number 9.

Roots of the equation x 5 x 19 = 0 are real, equal and rational (C) real, unequal and irrational (B) real, unequal and rational (D) complex number 9.

5 PET-III (EXTENDED)-018-MPC-5 5. Let f(x) = (x 1 x 9 + x 4 x + 1) 1/. The domain of the function is (, 1) (B) ( 1, 1) (C) (1, ) (D) (, ) x 6. The domain of the function f(x) = ln ln is x (where [.] denotes the fractional part function) (0, ) I (B) (1, ) I (C) R I (D) (, ) I 7. Number of ordered pair (x, y) satisfying x + 1 = y and y + 1 = x, is 0 (B) 1 (C) (D) 3 8. Roots of the equation x 5 x 19 = 0 are real, equal and rational (C) real, unequal and irrational (B) real, unequal and rational (D) complex number 9. The number of values of a for which (a 3a + )x + (a 5a + 6)x + a 4 = 0 is an identity in x is 0 (B) 1 (C) (D) 3 log x 4x The real roots of the equation 5 = x 1 are 1 and (B) and 3 (C) 3 and 4 (D) 4 and In the figure a rope of mass m and length is such that its one end is fixed to a rigid wall and the other is applied with a horizontal force F as shown below, then tension at the middle of the string is F (B) F (C) zero (D) F/ 3. Figure shows a light spring balance connected to two blocks of mass 0 kg each. The graduations in the balance measure the tension in the spring. The reading of the balance is 40 kg (C) 0 kg (B) zero kg (D) Depends on mass of spring balance

PET-III (EXTENDED)-018-MPC-6 33. A block of mass 10 kg is suspended through two light spring balance as shown below.

6 PET-III (EXTENDED)-018-MPC A block of mass 10 kg is suspended through two light spring balance as shown below. Both the scales will read 5 kg (B) The upper scale will read 10 kg and the lower zero (C) Both the scales will read 10 kg (D) The readings may be anything but their sum will be 10kg 34. In an imaginary atmosphere, the air exerts a small force F on any particle in the direction of the particle s motion. A particle of mass m projected upward takes a time t 1 in reaching the maximum height and t in the return journey to the original point. Then. t 1 t (B) t 1 t (C) t1 t (D) The relation between t 1 &t depends on the mass of the particle. 35. A steel ball is placed on the surface of water in a deep tank. Water exerts a resistive force which is proportional to the velocity of the ball. The steel sinks into the water : With decreasing acceleration and finally attains a constant velocity (B) with constant acceleration equal to the gravitational acceleration (C) with constant acceleration less than the gravitational acceleration (D) with acceleration decreasing initially and reversing after a finite time 36. A force F va is exerted on a particle in addition to the force of gravity, where v is the velocity of the particle and A is a constant vector in the horizontal direction. The minimum speed of projection for a particle of mass m so that it continues to move with a constant velocity is given by mg (B) mg (C) mg (D) mg 3A A A

PET-III (EXTENDED)-018-MPC-7 37. Blocks A and C starts from rest & moves to the right with acceleration aa 4t m/s and ac 3m/s. Here t is in seconds.

7 PET-III (EXTENDED)-018-MPC Blocks A and C starts from rest & moves to the right with acceleration aa 4t m/s and ac 3m/s. Here t is in seconds. The time when block B again comes to res is : 1 s (B) 3 s (C) 1 4 s (D) 1 s 38. A body of mass M is kept on a rough horizontal surface (friction coefficient =). A person is trying to pull the body by applying a horizontal force but the body is not moving. The force by the surface on the body is F where. F= mg (B) Mg F Mg 1 (C) F=Mg (D) Mg F Mg In the arrangement shown in figure the wall is smooth and friction coefficient between the blocks is =0.1 A horizontal force F= 1000 N is applied on the kg block. The wrong statement is The normal interaction force between the blocks is 1000 N (B) The friction force between the blocks is non zero (C) The friction force between the blocks is zero (D) Both the blocks accelerate downward with acceleration gm/ s 40. The force F 1 required to just moving a body up an inclined plane is double the force F required to just prevent the body from sliding down the plane. The coefficient of friction is. The inclination of the plane is 1 tan (B) 1 tan 1 (C) tan 1 (D) tan 3

The coefficient of friction between the block A of mass m and block B of mass m is. There is no friction between block B and the inclined plane.

8 PET-III (EXTENDED)-018-MPC Given ma 30kg, mb 10kg,m c 0kg. Between A and B 1 0.3, between B and C 0. and between C and ground The least horizontal force F to start motion of any part of the system of three blocks resting upon one another as shown below is (Take g 10m/s ) 90 N (B) 80 N (C) 60 N (D) 150 N 4. The coefficient of friction between the block A of mass m and block B of mass m is. There is no friction between block B and the inclined plane. If the system of blocks A and B is released from rest and there is no slipping between A and B then. 1 sin tan (B) (C) sin (D) tan / 43. A block A is placed over a long rough plank B same mass as shown in fig. The plank is placed over a smooth horizontal surface. At time t=0, block A is given a velocity v 0 in horizontal direction. Let v 1 and v be the velocity of A and B at time t. Then choose the correct graph between v1 and v and t : (B) (C) (D)

PET-III (EXTENDED)-018-MPC-9 44. Two particles of mass m each are tied at the ends of a light string of length a.

9 PET-III (EXTENDED)-018-MPC Two particles of mass m each are tied at the ends of a light string of length a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance a from the centre P (as shown in the figure). Now, the mid point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes x, is : F a m a x (C) F x m a 45. A small particles of mass m is released from rest from point A inside a smooth hemispherical bowl as shown. The ratio of magnitude of centripetal force and normal reaction on the particle at any point B varies with as (B) (D) F x m a x F a x m x (B) (C) (D)

10 PET-III (EXTENDED)-018-MPC A particle of mass m oscillates along the horizontal diameter AB inside a smooth spherical shell of radius R. At any instant K.E. of the particle is K. Then force applied by particle on the shell at this instant is B K R (B) K R (C) 3K R (D) K R 47. A long horizontal rod has a bead which can slide along its length and is initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with a constant angular acceleration,. If the coefficient of friction between the rod and bead is, and gravity is neglected, then the time after which the bead starts slipping is 1 (B) (C) (D) Infinitesimal 48. A particle travels along the arc of a circle of radius r. Its speed depends on the distance travelled as v a, where a is a constant. The angle between the vectors of total acceleration and the velocity of the particle is 1 1 tan /r (B) cos / r 1 1 sin / r cot / r (C) (D) 49. The narrow tube AC forms a quarter circles in a vertical plane. A ball B has an area of cross section slightly smaller than that of the tube and can move without friction through it. B is placed at A and displaced slightly. During the motion from A to C it wall: Always be in contact with the inner wall of the tube (B) Always be in contact with the outer wall of the tube (C) Initially be in contact with the inner wall and later with outer wall (D) Initially be in contact with the outer wall and later with the inner wall

11 PET-III (EXTENDED)-018-MPC A particle is moving in a circle of radius R in such a way that at any instant the normal and tangential components of the acceleration are equal. If its speed at t=0 is u 0, the time taken to complete the first revolution is R R /u 0 (B) u 0 /R (C) 1 e R (D) e u u 51. A small body of mass m can slide without friction along a trough bent which is in the form of a semi circular arc of radius R. At what height h will the body be at rest with respect to the trough, if the trough rotates with uniform angular velocity about a vertical axis. g g g R (B) R (C) R (D) R 5. A smooth hollow cone whose vertical angle is with its axis vertical and vertex downwards revolves about its axis time per seconds. A particle is placed on the inner surface of cone so that it rotates with same speed. The radius of rotation for the particle is gcot /4 (B) gsin /4 (C) 4 /g (D) g/4 sin 53. A particle of mass m is suspended from a fixed point O by a string of length. At t=0, it is displaced from its equilibrium position and released. The graph which shows the variation of the tension T in the string with time t is 0 0 (B) (C) (D)

PET-III (EXTENDED)-018-MPC-1 54. A particle is resting on an inverted cone as shown. It is attached to cone by a thread of length 0cm. String remains parallel to slope of cone.

12 PET-III (EXTENDED)-018-MPC A particle is resting on an inverted cone as shown. It is attached to cone by a thread of length 0cm. String remains parallel to slope of cone. The cone is given angular acceleration of 0.5 rad / sec then at what time does mass leave contact with surface (assuming sufficient friction) 0 sec (B) 10 sec (C) 40 sec (D) 5 sec 55. A particle initially at rest is released from A as shown in figure. The approximate variation of direction of resultant acceleration as particle moves from A to B is clockwise (C) direction does not changes (B) anticlockwise (D) none of these 56. A particle P of mass m attached to a vertical axis by two strings AP and BP length L each. The separation AB = L, P rotates around the axis with an angular velocity ' '. The tension in the strings AP and BP are T1 and T respectively, then which of the following is incorrect T1 T (B) T1 T m L (C) T1 T mg (D) BP will remain taut only if g/l

13 PET-III (EXTENDED)-018-MPC A simple pendulum has a bob of mass m and swings with an angular amplitude. The tension in thread is T. At a certain time the string makes an angle with the vertical ( ), incorrect statement is 1 1 T mg for cos cos1 3 (B) T mg cos for only (C) T=mg cos for all values of (D) T will be larger for smaller values of 58. A particle of mass m moves along a circle of radius R The modulus of the average vector of force acting on the particle over the distance equal to a quarter of the circle is zero is the particle moves with uniform speed v mv (B) if the particle moves with uniform speed v R mv (C) if the particle moves with uniform speed v R (D) ma if particle moves with constant tangential acceleration a, the initial velocity being equal to zero 59. Consider a pendulum, consisting of a massless string with a mass on the end. The mass is held with the string horizontal, and then released. The mass swings down, and then on its way back up, the string is cut at point P when it makes an angle of with the vertical. Find the angle for which the range of the particle is maximum tan 3 (B) tan 3 (C) tan 1 1 (D) 1 tan A particle of mass m moves along a circle of constant radius R with radial acceleration changing with n time as a kt where k is constant and n>1. The tangential force on the particle varies with time as. mn mn (C) r n mn Rk t (B) n 1 Rk t (D) None Rk t n

14 PET-III (EXTENDED)-018-MPC Calculate number of electrons present in 9.5 g of PO 4 : 6 (B) 5 N A (C) 0.1 N A (D) 4.7 N A 6. What is the number of moles of O atom in 16 amu of HNO 3? (B) (C) 6 N A (D) 6 N A 63. What is the charge of 96 amu of S? C (B) 3. x C (C) 9.6 x C (D) 6C 64. 0g of an ideal gas contains only atoms of S and O occupies 5.6 L at 1 atm and 73 K. What is the mol. wt. of gas? 64 (B) 80 (C) 96 (D) None of these x 10 atoms of an element weight 1.15 gm. The atomic mass of the element is : 10 (B).3 (C) 35.5 (D) The number of neutrons in a drop of water (0 drops = 1mL) at 4C 6.03 x 10 (B) x 10 (C) 6.03 x 10 0 (D) x Total number of electrons present in 18 ml of water (d= 1g/ml) 6.03 x 10 3 (B) 6.03 x 10 (C) 6.03 x 10 1 (D) 6.03 x How many grams of CaWO 4 would contain the same mass of tungsten that is present in 570 gr of FeWO 4? (W = 184) 55 (B) 540 (C) 555 (D) g of CaCO 3 contains 10 moles of CaCO 3 (C) 6 x 10 3 atoms of Ca (B) 0.1 g atom of Ca (D) 50% of a Ca in by weight 70. The mole fraction of NaCl in a solution containing 1 mole of NaCl in 1000g of water is : (B) (C) 0.5 (D) The amount of H SO 4 present in 400 ml of.1 M solution of the acid is :.45g (B) 3.9g (C) 9.80g (D) 4.9g

15 PET-III (EXTENDED)-018-MPC A mixture containing 100g H and 100g O is ignited so that water is formed according to the reaction, H + O H O; How much water will be formed? 11.5g (B) 50g (C) 5 g (D) 00 g 73. Amount of oxygen required for complete combustion of 7g Al is : 4g (B) 1g (C) 0g (D) 6g M solution of aqueous KOH has 30% by weight of KOH. Calculate density of solution g/ml (B) 1.88 g/ml (C) g/ml (D) 1.6 g/ml w% HCl has density equal to 1.0 g ml 1. The molarity (M) and molality (m), respectively, are 15.7, 15.7 (B) 1, 1 (C) 15.7, 1 (D) 1, H O (l) H O(l) + O (g) 100 ml of X molar H O gives 3 L of O gas under the condition when 1 mol occupies 4 L. The value of X is.5 (B) 1.0 (C) 0.5 (D) Mole fraction of a solute in an aqueous solution is 0.. The molality of the solution will be (B) (C) (D) The largest number of molecules is in 36g of water (C) 46g of ethyl alcohol (B) 8g of carbon monoxide (D) 54g of nitrogen pentoxide 79. P 4 + x OH + yh O ZPH 3 + m H PO. The ratio of x and y in the above reaction is 1 : 1 (B) : 3 (C) 1 : (D) 3 : 80. What is the empirical formula of a vanadium oxide if.74 g of metal oxide contains 1.53g of a metal? V O 3 (B) VO (C) V O 5 (D) V O The EW of H 3 PO 4 in the reaction is Ca(OH) + H 3 PO 4 CaHPO 4 + H O 49 (B) 98 (C) 3.66 (D) In a gaseous mixture containing 7g of N, 8g of O and g of CO. The mole fraction of N in the mixture is 0.5 (B) 0.5 (C) 0.1 (D) 0.9

16 PET-III (EXTENDED)-018-MPC-16 w 83. The molality of 40% W aqueous NaOH solution is (B) (C) (D) Metal X forms two oxides. Formula of the first oxide is XO. The first oxide contains 50% of oxygen. If the second oxide contains 60% of oxygen, the formula of the second oxide is X O (B) XO 3 (C) X O 3 (D) X 3 O 85. Arrange the following in the increasing order of oxidation state of Mn : (I) Mn + (II) MnO (III) KMnO 4 (IV) K MnO 4 I > II > III > IV (B) I < II < IV < III (C) II < III < I < IV (D) III < I < IV < II xaso ymno zh O aaso bmno coh x, y, z, a, b, c are stoichiometric coefficient x + y =? 5 (B) 7 (C) 3 (D) In the reaction Na S O 3 + I Na S 4 O 6 + NaI ; Na S O 3 acts as oxydising agent (B) precipitating agent (C) reducing agent (D) both oxydising and reducing agent 88. A compound contains atoms A, B and C. The oxidation number of A is +, of B is +5 and of C is. The possible formula of the compound is : ABC (B) B (AC 3 ) (C) A 3 (BC 4 ) (D) A 3 (B 4 C) 89. Which of the following is not redox reaction? BaO + H SO 4 BaSO 4 + H O (B) BaO + O BaO (C) KClO 3 + KCl + 3O (D) SO + H S H O + 3S 90. When KMnO 4 acts as oxidizing agent and ultimately forms MnO 4, MnO, Mn O 3 and Mn + then the number of electrons transferred in each case respectively is 4, 3, 1, 5 (B) 1, 5, 3, 7 (C) 1, 3, 4, 5 (D) 3, 5, 7, 1

17 PET-III (EXTENDED)-018-MPC-17 MATHEMATICS FIITJEE PET III (EXTENDED) MAINS_ANSWERS DATE: C. B 3. A 4. A 5. A 6. C 7. A 8. A 9. C 10. C 11. D 1. C 13. B 14. B 15. D 16. C 17. A 18. D 19. B 0. D 1. C. B 3. B 4. D 5. D 6. B 7. A 8. C 9. B 30. B PHYSICS 31. A 3. C 33. C 34. A 35. A 36. B 37. C 38. B 39. B 40. D 41. C 4. B 43. B 44. B 45. A 46. C 47. A 48. A 49. C 50. C 51. D 5. A 53. D 54. A 55. A 56. A 57. C 58. C 59. C 60. C CHEMISTRY 61. B 6. D 63. C 64. B 65. D 66. B 67. D 68. B 69. B 70. A 71. B 7. A 73. A 74. B 75. D 76. A 77. A 78. A 79. A 80. C 81. A 8. B 83. B 84. B 85. B 86. BONUS 87. C 88. C 89. A 90. C

FIITJEE PET VI (REG_1 ST YEAR)

FIITJEE PET VI (REG_1 ST YEAR) MAINS_SET A DATE: 8.07.018 Time: 3 hours Maximum Marks: 360 INSTRUCTIONS: Instructions to the Candidates 1. This Test Booklet consists of 90 questions. Use Blue/Black ball