TWT. TEST DATE :- 16 Aug 2015 BATCH : SA57R3 USE ONLY BALL PEN TO DARKEN YOUR ANSWERS.

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1 TWT TEST DATE :- 6 Aug 05 BATCH : SA57R3 Instructions : This booklet is your question paper. Answers hae to be marked on the proided OMR sheets. Blank sheets are proided for rough work alongwith the question paper. Log tables, Slide rule, Calculators, Cellular phones and other Electronic deices in any form are NOT allowed in the examination hall. If a student is caught copying, he/ she will not be allowed to write the exam. On the OMR sheet, write your name, Registration No using ball-pen only. USE ONLY BALL PEN TO DARKEN YOUR ANSWERS. There are total 50 questions in this paper. Only one choice is correct. Each question carries + 4 for correct answer. There is - marking for incorrect answer. Head Office 40, 4th floor, Shopper s point, S.V. Road, Andheri (West), Mumbai : Tel. : / 53 / 5357 / 5657 / : Pune Office Sahakar Nagar : PMC s Raji Gandhi Academy of e-learning School & Jr. College of Science, Shidarshan, Shahu College Road, Sahakar Nagar, Pune Tel. : / F.C. Road : st Floor, Office No. 0, Nandadeep, F.C. Road, Shiaji Nagar, Pune Tel. : / Tel. : / 53 / 5357 / 5657 / :

2 Class XI TWT - (6.8.5) Batch : N3, N, R3, FC XI, Normal Physics. A stone is thrown ertically upward with an initial elocity 0. The distance traelled in time 5 0 9g (D) 8g 8g g 5 0 is 3g. A pebble dropped from the top of a tower reaches the ground in 8 second. In what time the pebble coers the first quarter of the height of the tower? s 3 s 4 s (D) 5 s 3. A, B, C and D are the points in a ertical line such that AB = BC = CD. If a body falls freely from A, then the times of descent through AB, BC and CD are in the ratio : : 3 : : 3 : : 3 (D) : 4 : 9 4. Two bodies begin a free fall from the same height at a time interal of N s. If ertical separation between the two bodies is after n second from the start of the first body, then n is equal to gn gn 5. If a particle moes a long two semicircular paths from point A to B of radius R as shown in the figure, the numerical ratio of displacement to distance is N (D) N gn gn A B 4 6 (D) 3 6. A car is moing along a straight road with uniform acceleration. It passes two points P and Q separated by a distance with elocities 30 km h and 40 km h respectiely. The elocity of car midway between P and Q is 33.3 km h 0 3 km h 5 km h (D) km h 7. A particle moing in a straight line with uniform acceleration is obsered to be at a distance a from a fixed point initially. It is at distance b, c, d from the same point after n, n, 3n second. The acceleration of the particle is c b a c b a c b a (D) c b a n 9n 4n n

3 8. A drier applies the brakes on seeing traffic signal 400 m ahead. At the time of applying the brakes ehicle was moing with 5 ms and retarding with 0.3 ms. The distance of ehiclee after minute from the traffic light is 5 m 3.75 m 360 m (D) 40 m 9. The acceleration time graph of a particle moing in a straight line is as shown in figure. The elocity of the particle at time t = 0 is m/s. The elocity after seconds will be 6 m/s 4 m/s m/s (D) 8 m/s 0. Which of the following figures represents the motion of a body started from rest moing in a straight line under constant acceleration? t t t (D) t. A body starts from rest moes along a straight line with constant acceleration. The ariation of speed with distance s is gien by graph O s O s O s (D) O s. A particle s position as a function of time is described as y(t) = t + 3t + 4. What is the aerage elocity of the particle from t = 0 to t = 3 sec? 3 m/s 6 m/s 9 m/s (D) m/s

4 3. A point moes such that its displacement as a function of time is gien by; x = t +. Its acceleration at time t is t (D) t 4 3 x x x x x x 4. Which of the following statement is false? A body can hae a constant elocity and still a arying speed A body can hae a constant elocity and a constant speed. A body can hae a constant speed and still hae a arying elocity. (D) the direction of elocity of a body can change when its acceleration is constant. 5. The displacement of a particle is represented by the following equations. X = 3t 3 + 7t + 5t + 8. where s is in metre and t in second. The acceleration of the particle at t = s is 4 m/s 8 m/s 3 m/s (D) zero 6. If the ratio of aerage elocity of the particle from first 4 sec to first 0 sec is n 4 then find n. (m/s) 4 0 t (s) (D) 0 7. A stone is dropped from the top of the tower and reaches the ground in 3 s. Then the height of the tower is 8.6 m 39. m 44. m (D) 98 m 8. A particle has an initial elocity of 3î 4ĵ and an acceleration of 0.4î 0.8ĵ. Its speed after 0 sec is 0 units 7 units 3.89 units (D) 7 units 9. A boy sitting on the topmost berth in the compartment of a train which is just going to stop on a railway station, drops an apple aiming at the open hand of his brother situated ertically below his hands at a distance of about m. The apple will fall: in the hands of his brother slightly away from the hands of his brother in the direction of motion of train. slightly away from the hands of his brother in the direction opposite to the motion of the train (D) none of the aboe.

5 0. Three ectors a, b and c each haing a magnitudes of 5 units add to gie a null ector. What is the angle between ectors a and b? (D) If ector A î 3ĵ and B 3î 4ĵ. Then the component of ector A along B is 3î 4ĵ 3î 3. 4 ĵ 5 8 3î 4 ĵ (D) 3î 4 ĵ If three ectors along co ordinate axes represent the adjacent sides of a cube of side b, then the unit ector along its diagonal passing through the origin will be î Ĵ kˆ î Ĵ kˆ î Ĵ kˆ 3b î Ĵ kˆ (D) 3. A ector of magnitude a rotated through an angle. What is the magnitude of the change in the ector? a sin a cos a sin (D) a cos. x t 4. A particle moes along the positie branch of the cure y = where x =, x and y are measured in metres and t in seconds. At t = s, the elocity of the particle is î 4 ĵ m/s 4î ĵ m/s î 4ĵ m/s (D) 4î ĵ m/s 5. A particle moes in xy plane. The position ector of particle at any time t is 3 ˆ r {(t)i (t ) j}m ˆ. The rate of change of at time t = second. (where is the angle which its elocity ector makes with positie x-axis) is 7 rad/s 4 rad/s 4 7 rad/s (D) 6 5 rad/s

6 6.. A particle has initial elo 3i ˆ kˆ ms. Find angle made by displacement after sec with XY plane 3 7 (a) cos (b) cos (c) sin ABCD is a square of side a. A body starts from A and reaches C through the indicated path. The ratio of elocity and speed is D (D) a C 8. A stone is released from the top of a tower. It coers 4.5 m distance in the last second of its journey. What is the height of the tower? (D) 9. The magnitude of the resultant of A B and A B 40 is A B iˆ 3 ˆj ms when it was at origin and has constant acceleration ocity A B (D) (d) a A A B 3 sin 7 a B a 30. The motion of a body on a straight line is gien by the equation. speed in m/sec and t in sec. The body was at rest at, The final constant speed(after infinite time) is.0 m/sec The magnitude of the initial acceleration is The speed aries with time as where is the (D) all the aboe.

7 Class - XI (SA57R3, R4, Mains) TWT - 5 (6.8.5) Chemistry. The waelength associated with a golf ball weighing 00 gm and moing at a speed of 5 m/h is of the order of : 0 0 m 0 0 m 0 30 m (D) 0 40 m. A bulb emits ligth of = 4500Å. The bulb is rated 50 watt and 8% energy is emitted as light. The number of photons emitted per second is : (D) Three isotopes of an element hae atomic masses M, (M + ) and (M + ). If the aerage atomic mass of the element is (M + 0.5), then the ratio of % occurrence of M, (M + ) and (M + ) is: : : 4 : : 3 : : (D) : : 4. Number of waes produced by an electron in one complete reolution in n th orbit is : n n (n + ) (D) (n + ) 5. The mass of a particle is 0 0 g and its diametre is 0 4 cm. If its elocity is 0 8 cm sec with 0.000% uncertainty in measurement. The uncertainty in its position is : m m m (D) m 6. The mass of an electron is m, charge is e and it is accelerated from rest through a potential difference of V olts. The elocity acquired by electron will be : V m ev m ev m (D) Zero Space for rough work

8 7. When an electron makes a transition from (n + l) state to n state, the frequency of emitted radiations is related to n according to (n >> ) n 3 n n 3 (D) n /3 8. The first use of quantum theory to explain the structure of an atom was made by : Heisenberg Rutherford Bohr (D) Einstein 9. If, m and KE be the waelength, mass and kinetic energy of a particle. Then the kinetic energy in the terms of and mass m is gien by : KE = h m KE = h m KE = h m (D) KE = 0. The waelength of a special line for an electronic transition is inersely related to : number of electrons undergoing transitions. the nuclear charge of the atom. the elocity of an electron undergoing transition. (D) the difference in energy leels inoled in the transition. h m. The positions of both an electron and a helium atom are known with nm. Further, the momentum of electron is known within kgms. The minimum ucertainty in the measurement of momentum of He atom is : 50 kgms kgms 80 kgms (D) kgms. The principle quantum number n corresponding to the excited state of He + ion, if on transition to the ground state that ion emits two photons in succession with waelength of 08.5 nm and 30.4 nm is : 5 3 (D) 4 3. When an electron is transited from E to E energy leel, the waelength of photon produced is. In making electronic transition from 4 3 E to E leel, the waelength is : = = 3 4 = 3 (D) = 4 3 Space for rough work

9 4. An electron is allowed to moe freely in a closed cubic box of length of side 0 cm. The maximum uncertainty in its elocity will be obsered as : m sec m sec m sec (D) m sec 5. An energy of 4.6 ev is required to remoe one of the electrons from a neutral He atom. The energy required to remoe both the electrons from the neutral atom is : 4.6 ev 49. ev 5.8 ev (D) 79.0 ev 6. When an electron come close to the nucleus : its kinetic energy increases, potential energy and total energy decrease kinetic energy and total energy increase, potential energy decreases kinetic energy and total energy decrease, potential energy increases (D) kinetic energy, potential energy and total energy increase. 7. An atom has x energy leels, then the total number of lines in the emission spectrum will be : ( x + ) x x (D) (x ) 8. If the shortest waelength of H atom in Lyman series is x, then longest waelength in Balmer series of He + is : 9x 5 36x 5 9. The radius of which of the following orbit is same as that of the first Bohr's orbit of atom? He + (n = ) Li + (n = ) Li + (n = 3) (D) Be 3+ (n = ) x 4 (D) 5x 9 0. When particles are sent through a thin metal foil, most of them go straight through the foil because: particles are lighter than electrons particles are positiely charged Most part of the atom is empty space (D) particles moe with high elocity. The wae number of first line of Balmer series of hydorgen is 500 cm. The wae number of the first Balmer line of Li + ion is : 500 cm cm cm (D) 36,800 cm Space for rough work

10 . The wae number of first line in the Balmer series of hydrogen is 500 cm. The wae number of the first line in the Balmer series of Be 3+ would be : cm cm 3800 cm (D) 950 cm 3. The ratio of the radii of first orbits of H, He + and Li + is : : : 3 6 : 3 : : 4 : 9 (D) 9 : 4 : 4. If Kinetic energy of a proton is increased nine times the waelength of the de Broglie wae associated with it would become : 3 times 9 times /3 times (D) /9 times 5. The uncertainty in the position of an electron moing with a elocity of cm s (accurate up to 0.0%) will be :.9 cm 7.68 cm 0.58 cm (D) 3.8 cm 6. The uncertainty in momentum of moing particle is kg m s, the minimum uncertainty in its position would be : m m m (D) m 7. A dye absorbs a photon of waelength and re emits the same energy into two photons of waelength and respectiely. The waelength with and is related as : = = = (D) = ( ) 8. The energy of a photon is gien as : E = J atom then, the waelength () of the photon is: 6.56 nm 65.6 nm 656 nm (D) nm Gien, h(planck s constant) = J-s c (elocity of light) = ms 9. In hydrogen atom, energy of first excited state is -3.4 ev. Then K.E. of same orbit of hydrogen atom +3.4eV +6.8eV 3.6eV (D) +3.6eV 30. de-broglie relationship can be expressed by: m p h P m h m (D) h mp Space for rough work

11 Class - XI TWT - 6 (6.8.5) Batch : SA57R, R3, P, PN, FC, NE, N3 + N4 (MATHS). The maximum alue of sin cos, R is (a) 3 (b) (c) (d). If x 3x 4, where x is an integer, then the number of possible alues of x is/are (a) 3 (b) 4 (c) (d) Infinite 3. If sin sin, then cos cos is equal to (a) 3 (b) (c) (d) 0 x 4. The number of integral solutions of, is x (a) 4 (b) 5 (c) 3 (d) none 5. The expression tan.tan.tan, simplifies to R (a) tan (b) tan (c) tan3 (d) None 6. If p a cos bsin, then for all real alues of, (a) (c) p a b (b) a b p a b (c) None p a b

12 7. The number of real solutions of the equation sin x cos x are (a) Infinite (b) (c) 0 (d) None 8. If, the alue of tan A tan B? o A B 5 (a) (b) 3 x 6x 0 sin y 0, y 0,, then 9. If (c) A, B n,n I (d) none (a) x (b) x (c) x 3 (d) none of these 0. Which of the following is a rational number? (a) sin5 o (b) cos5 o o o (c) sin5 cos5 o o (d) sin5 cos 75 x 0 x R, then belongs to interal. If (a), 5. If, are roots of (b), (c) x x 0, is equal to then (d) none (a) 0 (b) (c) - (d) 3. If p,q, r R such that p q r 0 and p is not equal to r, then roots of q r p x r p q x p q r 0are (a) can t say (b) real (c) imaginary (d) none of these The alue of expression cos cos cos cos is (a) (b) 0 (c) (d) None of these 5. Roots of the equation (a) sin 36,sin5 4x 5x 0 are (b) cos 36,sin8 (c) sin 36,cos8 (d) None

13 If x is a factor of x ax 3x b, then (a) a 3, b (b) a 3, b (c) a 3, b (d) None 7. If a, b,c R and ax bx 5 0 does not hae any real root roots, then (a) a b 5 0 (b) a b 5 0 (c) a b 0 (d)none of these 8. If, are roots of equation (a) x 4x 0 (b) x x 0 find the equation whose roots are x 3x 0 (c),? x x 0 (d)none of these 9. For all real alues of,cot cot is equal to 0 (a) tan (b) tan (c) cot 3 (d)none 0. If, are roots of ax bx c 0 ; and h, h are roots of respectie determinants of these equations, then D (a) D (b) c a (c) a p? b 4ac p px qx r 0and D,D are q (d) b 4pr 4ac. The alue of cos 73º + cos 47º - sin 43º + sin 07º is equal to : (a) (b) (c) 3 (d)none of these. The expression 4 cos 4 x - cos x cos 4 x when simplified reduces to : (a) /3 (b) 3/ (c) -/3 (d)-3/ 3. If the roots of the quadratic equation x + px + q = 0 are tan 30º and tan 5º respectiely, then the alue of + q p is : (a) 3 (b) 0 (c) (d)

14 4. If cot ( ) = 0, then sin ( ) is equal to (a) sin (b) cos (c) sin (d)cos 5. 0 sin 0. sec 0º = (a) (b) (c) (d) 6. The alue of 4 8 cos cos cos cos will be (a) 6 (b) (c) 0 (d) 6 7. If X R, then range of x x x 7 x 7 is (a) 9 7, (b) 9 7, (c) 9 5, (d) 7, 8. A = cos + sin 4 has atleast one solution then (a) < A < (b) 3 6 < A < (c) 3 4 < A < 3 6 (d) 3 4 < A < 9. If the expression cos 3 x + sin 3 x + sin (3 + x) 8 cos(9 x) + cos (56 + x) 9 sin(x + 7 ) is expressed in the form of a sinx + b cosx, then (a + b) is equal to (a) 7 (b) 7 (c) 3 (d)3 30. cos (00) + cot (00) + sec (00) + tan (00) + cosec (00) equals to (a) 0 (b) (c) - (d) not defined

15 TWT SA57R3 Answer Key Physics Answer Key (6.8.05) R3 Qus. Ans. Qus. Ans. Qus. Ans. C D Bouns C C D 3 A 3 C 3 A 4 C 4 A 4 C 5 B 5 C 5 A 6 C 6 C 6 Bouns 7 A 7 C 7 A 8 A 8 C 8 B 9 A 9 B 9 A 0 D 0 B 30 A Chemistry Answer Key (6.8.05) SA57PN, SA57NE Qus. Ans. Qus. Ans. Qus. Ans. C B D A B B 3 B 3 C 3 B 4 A 4 B 4 C 5 A 5 D 5 C 6 C 6 A 6 A 7 A 7 D 7 B 8 C 8 A 8 C 9 A 9 BONUS 9 A 0 D 0 C 30 C Chemistry Answer Key (6.8.05) SA57PN, SA57NE C B A B B C 3 D 3 A 3 A 4 C 4 A 4 A 5 C 5 C 5 B 6 C 6 B 6 C 7 C 7 B 7 C 8 C 8 C 8 D 9 C 9 B 9 D 0 B 0 A 30 B

FIITJEE PET I (EXTENDED-2)

FIITJEE PET I (EXTENDED-2) 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