FIITJEE PET I (EXTENDED-) MAINS DATE: 9.07.017 Time: hours Maximum Marks: 60 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.. 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.:
PET-I (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 (A) x y 4 (B) x y4 0 (C) x y 4. The distance between the lines x + 4y = 9 and 6x + 8y + 15 = 0 is (A) (B) (C) 10 10 5. 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 (A) (4, 0) (B) (, 1) (C) (0, 4) 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 4 5 5 4 (A) t (B) 0 t (C) t 0 5 6 6 5 5. 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 (A),, 4 4 (B), (C), 4 4 6. If the point (a, a) falls between the lines x + y =, then (A) a = (B) a = 1 (C) a < 1 (D) a < 1 1 7. 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 (A),, 4 4 4 4 (B), 4 4 (C), 4 4
PET-I (EXTENDED-)-018-MPC- 8. Let P = (1, 1) and Q = (, ). The point R on the x-axis such that PR + RQ is the minimum is 5 1 (A),0 (B),0 (C) (, 0) 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 (A) x 7y = 1 (B) x 7y + 15 = 0 (C) (x 7y) + 14(x 7y) 15 = 0 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 (A) x x + = 0 (B) x + x + = 0 (C) x x + = 0 11. If a f(x) + b a (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) = 18, then f() is equal to (A) 56 (B) 8 (C) 64 (D) 1 1. The period of the function f(x) = 4sin (A) 4 (B) 4 4x 4x 4 6 cos is (C) 4 (D) 4 1 14. Range of function f defined by f(x) = sinx integer and the fractional part function) is (A) 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) = sin x cos x is (A), 1 (B) [, ] (C), 1 (D) [, ]
PET-I (EXTENDED-)-018-MPC-4 16. The domain of definition of f(x) = 1 x x is (A) (, ) [, ] (B) (, ) [ 1, 1] (C) [ 1, 1] (, ) (, ) 17. If S is the set of all real x for which 1 e (1/x) 1 > 0, then S is equal to (A) (, 0) (1, ) (B) (, ) (C) (, 0] [1, ) 18. 1 The domain of the function f(x) = log10 1 x x is (A) [, ], excluding (.5) (B) [0, 1], excluding 0.5 (C) [, 1], excluding 0 1 1 1 x 19. The domain of the function f(x) = sin log x cos sin x sin x (A) {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 (A) [ n, n]; n I (B) (n, n 1 ); n I 4n 14n 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 (A) ( 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 1 (A), (B),, (C),, x x x 1 1 1. The domain of the function f(x) = sin cos tan 4 4 4 is (A) [0, ] (B) [ 6, 6] (C) [ 1, 1] (D) [, ]
PET-I (EXTENDED-)-018-MPC-5 4. The domain of the function f(x) = x 1 x (A) [, 6] (B) (, 6] (C) [8, 1] 5. Let f(x) = (x 1 x 9 + x 4 x + 1) 1/. The domain of the function is (A) (, 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) (A) (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 (A) 0 (B) 1 (C) (D) 8. Roots of the equation x 5 x 19 = 0 are (A) 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 a + )x + (a 5a + 6)x + a 4 = 0 is an identity in x is (A) 0 (B) 1 (C) (D) log x 4x5 5 0. The real roots of the equation 5 = x 1 are (A) 1 and (B) and (C) and 4 (D) 4 and 5 1. A particle is projected vertically upwards from a points A on the ground. It takes time t 1 to reach a point B, but it still continues to move up. If it takes further t time to reach the ground from point B. Then height of point B from the ground is 1 1 (A) g(t 1 t ) 1 (B) g t 1 t (C) g(t 1 t ) (D) gt 1 t 8. A particle is released from rest from a tower of height h. The ratio of times to fall equal heights h, i.e., t 1 : t : t is (A) : :1 (B) : : 1 (C) 9 : 4 : 1 (D) 1: ( 1): ( )
PET-I (EXTENDED-)-018-MPC-6. In a car race car A takes t 0 time less to finish than car B and passes the finishing point with a velocity v 0 more than car B. The cars start from rest and travel with constant accelerations a 1 and a. Then the v0 ratio is equal to t0 a1 a1 a a (A) (B) (C) aa 1 (D) a a1 4. From the top of a tower, a stone is thrown up and reaches the ground in time t 1. A second stone is thrown down with the same speed and reaches the ground in time t. A third stone is released from rest and reaches the ground in time t. 1 1 1 1 (A) t (t1 t ) (B) t t1t (C) (D) t t1 t t t t 1 5. At a height 0.4m from the ground, the velocity of a projectile in vector form is v 6ijm/s (the x- axis is horizontal and y-axis is vertically upwards). Find the angle of projection (A) 75 (B) 60 (C) 0 6. Time taken by the projectile to reach from A to B is t. Then the distance AB is (A) ut (B) 4ut (C) ut (D) ut 7. With what minimum speed must a particle be projected from origin so that it is able to pass through a given point (0m, 40m). Take g = 10 m/s (A) 100 m/s (B) 1000 m/s (C) 500 m/s 8. A projectile is projected at an angle (>45 ) with an initial velocity u. The time t, at which its horizontal velocity will equal the vertical velocity. (A) t = g u (cos sin ) (B) t = g u (cos + sin ) (C) t = g u (sin cos ) (D) t = g u (sin cos )
PET-I (EXTENDED-)-018-MPC-7 9. A body is thrown horizontally from a tower, 100 m high with a velocity 10 ms -1. It is moving at an angle 45 0 with horizontal after: (A) sec (B) 4 sec (C) 1 sec (D) sec 40. A ball is projected from ground with a speed of 0 m/s at an angle of 45 o with horizontal. There is a wall of 5 m height at a distance of 10 m from the projection point. The ball will hit the wall at a height of (A) 5 m (B) 7.5 m (C) 10 m (D) 1.5 m 41. The x and y coordinates of a particle at any time t are given by x = 7t + 4t and y = 5t, where x and y are in m and t in s. The acceleration of the particle at 5 s is (A) zero (B) 8 m/s (C) 0 m/s (D) 40 m/s 4. There are two values of time for which a projectile is at the same height. The sum of these two times is equal to (T = time of flight of the projectile) (A) T/ (B) 4T/ (C) T/4 (D) T 4. A body is projected at an angle 60 with the horizontal with kinetic energy K. When the velocity makes an angle 0 with the horizontal, the kinetic energy of the body will be (A) K (B) K (C) K (D) K 4 44. A body freely falling from the rest has a velocity v after it falls through a height h. The distance it has to fall down for its velocity to become double, is (A) h (B) 4h (C) 6h (D) 8h 45. A ball is projected from point A with velocity 10 ms 1 perpendicular to the inclined plane as shown in figure. Range of the ball on the inclined plane is (A) 40 m (B) 0 m (C) 1 m (D) 60 m 46. A ball is thrown from the top of a tower in vertically upward direction. Velocity at a point h m below the point of projection is twice of the velocity at a point h m above the point of projection. Find the maximum height reached by the ball above the top of tower. 5 4 (A) h (B) h (C) h (D) h
PET-I (EXTENDED-)-018-MPC-8 47. A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at m/s. He reaches the ground with a speed of m/s. At what height did he bail out? (A) 111 m (B) 9 m (C) 18 m (D) 91 m 48. Adjacent graph shows the variation of velocity of a rocket with time. Find the time of burning of fuel from the graph (A) 10 sec (B) 110 sec (C) 10 sec (D) cannot be estimated from the graph 10 49. The following shows the time-velocity graph for a moving object. The maximum acceleration will be (A) 1 m/sec (B) m/sec (C) m/sec (D) 4 m/sec 50. A rocket is projected vertically upwards and its timevelocity graph is shown in the figure. The maximum height attained by the rocket is (A) 1 km (B) 10 km (C) 100 km (D) 60 km 51. A grasshopper can jump maximum distance 1.6 m. It spends negligible time on the ground. How far can it go in 10 seconds? (A) 5 m (B) 10 m (C) 0 m (D) 40 m 5. A particle is projected with a certain velocity at an angle above the horizontal from the foot of an inclined plane of inclination 0. If the particle strikes the plane normally then is equal to (A) 0 + tan 1 (B) 45 (C) 60 (D) 0 + tan 1 ( ) 5. A person can thrown a stone a maximum height of h meter. The maximum distance to which he can throw the stone is (A) h (B) h/ (C) h (D) h
PET-I (EXTENDED-)-018-MPC-9 54. A particle starts from rest and accelerates as shown in the graph (figure). Determine the distance travelled in the first 0s. (A) 4.5 m (B) 6.5 m (C) 16.5 m a x (m/s ).0 1.0 0 1.0.0.0 5.0 10.0 15.0 0.0 t(s) 55. A car moving on a straight road with a speed 0m/s. At t = 0, the driver of the car applies the brakes after watching an obstacle 150m ahead. After application of brakes the car retards with m/s. Find the position of the car from the obstacle at t =1s. (A) 96 m (B) 54 m (C) 50 m (D) none 56. From a point on the ground a particle is projected with initial velocity u, such that its horizontal range is maximum. Find the magnitude of average velocity during its descent. 5 u (A) (B) 5 u 5 u 5 u (C) (D) 57. A point moves in the plane x y according to the law x = 4 sin t and y = 4(1 cos t) where k and are positive constants. Find the distance s traversed by the particle during time 5 s. (A) 10 m (B) 0 m (C) 40 m (D) 10 m 58. The sum, difference and cross product of two vectors A and B are mutually perpendicular if (A) A and B are perpendicular to each other and A=B (B) A and B are perpendicular to each other (C) A and B are perpendicular but their magnitudes are arbitrary (D) A=B and their directions are arbitrary 59. A boy throws a ball upwards with velocity v 0 as shown in fig. The wind imparts a horizontal acceleration of 4 m/s to the left. The angle at which the ball must be thrown so that the ball returns to the boy s hand is (g = 10 m/s ) (A) tan 1 5 (B) tan 5 1 (C) tan 4 1 (D) tan 1 4
PET-I (EXTENDED-)-018-MPC-10 60. A rifle shoots a bullet with a muzzle velocity of 400 m/sec at a small target 400 metre away. The height above the target at which the bullet must be aimed to hit the target is: (g = 10 m/s ) (A) 1 metre (B) 5 metre (C) 10 metre (D) 0.5 metre 61. The ratio of the speed of electron in first Bohr orbit of H-atom to speed of light in vacuum is (A) 17 (B) 7.0 x 10 - (C) 100 (D) 10-6. If the speed of electron in the Bohr s first orbit of hydrogen atom is x, the speed of the electron in the Bohr s third orbit is (A) x/9 (B) x/ (C) x (D) 9x 6. In the Bohr s model of the hydrogen atom, the ratio of the kinetic energy to the total energy of the electron in a quantum state n is (A) 1 (B) (C) -1 (D) - 64. The ratio of E E to E E 1 4 for H-atom is approximately (A) 10. (B) 15.4 (C) 5.6 (D) 1.4 65. The time period for revolution of electron in Bohr orbit of ground state (n 1 ) is T 1 and time period for T1 1 revolution of electron in higher orbit (n ) is T. Which values of n 1 and n are not correct if? T 8 (A) n1 1,n (B) n1,n 4 (C) n1,n (D) n 1,n 6 66. Increasing order (lowest first) for the values of e/m (charge/mass) for electron (e) proton (p), neutron (n) and -particle () is (A) e, p, n, (B) n, p, e, (C) n, p,, e (D) n,, p, e 0 0 67. The ratio of energy of radiations of wavelengths 000 A and 4000 A is (A) (B) 4 (C) ½ (D) ¼ 68. A 100 watt bulb emits monochromatic light of wavelength 400nm. The number of photons emitted per second by the bulb are (A).01 x 10 19 (B).01 x 10 0 (C).01 x 10 1 (D).01 x 10
PET-I (EXTENDED-)-018-MPC-11 69. Which transition of electron in the hydrogen atom emits maximum energy? (A) 1 (B) 1 4 (C) 4 (D) 70. Among the following species in which case Bohr theory can be applicable (A) He (B) He + (C) Li 1+ (D) Be + 71. The highest excited state that an unexcited hydrogen atom can reach when they are bombarded with 1.08 ev photon is (A) n = 1 (B) n = (C) n = (D)n = 4 7. The threshold frequency of a metal is 4 x 10 14 s 1. The minimum energy of photon to cause photoelectric effect is : (A).06 x 10 1 J (B) 1.4 x 10 18 J (C).4 x 10 19 J (D).64 x 10 19 J 7. The work function for a metal is 4 ev. To emit a photo electron of zero velocity from the surface of the metal, the wavelength of incident light should be : (A) 700 A (B) 1700 A (C) 5900 A (D) 100 A 74. According to Bohr s atomic theory, which of the following is/are correct: Z (I) Kinetic energy of electron n (II) The product of velocity of electron and principle quantum number n Z Z (III) Frequency of revolution of electron in an orbit n Z (IV) Coulombic force of attraction on the electron 4 n (A) I, III, IV (B) I, IV (C) II (D) I 75. Electromagnetic radiation with maximum wavelength is (A) radiowave (B) X ray (C) infrared (D) ultraviolet 76. In hydrogen atom, energy of first exicited state is.4 ev. The kinetic energy of the same orbit of Hydrogen atom would be (A) +.4 ev (B) +6.8 ev (C) 1.6 ev (D) +1.6 ev
PET-I (EXTENDED-)-018-MPC-1 77. The ionization energy of Hydrogen atom is 1.6 ev. What will be the ionization energy of He +? (A) 1.6 ev (B) 54.4 ev (C) 1.4 ev (D) zero 78. The photo electric current decreases if (A) The frequencies of incident radiation decreases below threshold frequency (B) The exposure time is decreased (C) The intensity of the source of light is decreased 79. An electron in an atom jumps in such a way that its kinetic energy changes from x to x. The change 4 in potential energy will be : (A) x (B) x (C) x (D) x 8 4 4 80. The potential energy of an electron in the hydrogen atom is 6.8 ev. Indicate in which excited state, the electron is present? (A) first (B) second (C) third (D) fourth 81. What is the potential energy of an electron present in N shell of the Be + ion? (A).4 ev (B) 6.8 ev (C) 1.6 ev (D) 7. ev 8. What is the ratio of time periods (T 1 / T ) in second orbit of hydrogen atom to third orbit of He + ion? (A) 8/7 (B) /7 (C) 7/ (D) None of these 8. Electromagnetic radiation having = 10 A 0 is subjected to a metal sheet having work function = 1.8 ev. What will be the velocity of photo electrons having maximum kinetic energy. (A) 0, no emission will occur (B) 4.5 x 10 6 m/s (C).09 x 10 6 m/s (D) 8.7 x 10 6 m/s 84. The ratio of slopes of K max vs. v and V 0 vs. v curves in the photoelectric effect gives (v = frequency, K max = maximum kinetic energy, V 0 = stopping potential) : (A) Charge of electron (B) Planck s constant (C) work function (D) the ratio of Planck s constant of electronic charge 85. The number of photons of light having wave number x in 10 J of energy source is : (A) 10 hcx (B) hc (C) 10 10x hcx
PET-I (EXTENDED-)-018-MPC-1 86. Identify the incorrect expression 4 nh ze me (A) V (B) V (C) E (D) mr nh nh nh r 4 me z 87. The correct increasing order of wavelength among the following (A) rays < x ray < UV < visible < IR (B) X ray < UV < visible < rays < IR (C) UV < visible < IR < ray < X ray (D) ray < UV < visible < IR < X ray 88. In Photoelectric effect, the KE of photo electron increases linearly with the (A) Wave length of incident light (B) frequency of incident light (C) velocity of incident light (D) atomic mass of an element 89. A light source of wavelength.. illuminates a metal and ejects photo electron with (K.E) max = 1eV. Another light source of wavelength x/, ejects photo electrons from same metal surface with (K.E) max = 4eV. Find the value of work function. (A) 1eV (B) ev (C) 0.5 ev (D) None of these 90. The photo electric emission from a surface starts only when the light incident upon the surface has certain minimum. (A) intensity (B) wavelength (C) frequency (D) velocity
PET-I (EXTENDED-)-018-MPC-14 MATHEMATICS FIITJEE PET I (EXTENDED-) MAINS_ANSWERS DATE: 9.07.017 1. C. B. A 4. A 5. A 6. C 7. A 8. A 9. C 10. C 11. D 1. C 1. B 14. B 15. D 16. C 17. A 18. D 19. B 0. D 1. C. B. B 4. D 5. D 6. B 7. A 8. C 9. B 0. B PHYSICS 1. D. D. C 4. B 5. C 6. C 7. D 8. C 9. C 40. B 41. B 4. D 4. B 44. B 45. A 46. C 47. B 48. A 49. D 50. D 51. C 5. A 5. C 54. B 55. C 56. D 57. C 58. D 59. B 60. B CHEMISTRY 61. B 6. B 6. C 64. B 65. C 66. D 67. A 68. B 69. A 70. B 71. C 7. D 7. D 74. A 75. A 76. A 77. B 78. C 79. A 80. A 81. D 8. B 8. C 84. A 85. C 86. C 87. A 88. B 89. C 90. C