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AIEEE IIT-JEE SAMPLE PAPERS NARAYANA TUTORIALS TEST PAPER KEY SOLUTIONS ANSWERS QUESTIONS STUDY MATERIAL
CODE CHANCH NARAYANA I I T A C A D E M Y NARAYANA PART TEST – 04 PAPER – I –:– Date: 12–12–10 Ti m e : 3 ho ur s M a xi m um m ar ks : 2 4 0 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. 12. Section I contains 8 multiple choice questions. Each INSTRUCTIONS question has 4 choices (A), (B), (C) and (D), out of A. General: which only one is correct. 1. This booklet is your Question Paper containing 60 13. Section II contains 4 multiple correct answer type questions. The booklet has 20 pages. questions. Each questions has 4 choices (A), (B), (C) and (D), out of which one or more answers are 2. The question paper CODE is printed on the right hand correct. top corner of this booklet. 14. Section III contains 2 compression types (2 3. Blank papers, clipboards, log tables, slide rules, compressions each with 3 questions). calculators, cellular phones, pagers, and electronic gadgets in any form are not allowed to be carried inside 15. Section IV contains 2 Matrix Match Type Questions. the examination hall. D. Marking Scheme 4. The answer sheet, a machine–readable Objective 16. For each questions in Section I, you will be awarded 3 Response Sheet (ORS), is provided separately. marks if you have darkened only the bubble corresponding to the correct answer and zero mark if no 5. DO NOT TAMPER WITH / MUTILATE THE ORS OR bubble is darkened. In case of bubbling of incorrect THE BOOKLET. answer, minus one (–1) mark will be awarded B. Filling the ORS 17. For each question in Section II, you will be awarded 4 6. On the lower part of the ORS, write in ink, your name in marks if you have darkened all the bubble(s) box L1, your Registration No. in box L2 and Name of the corresponding to the correct choice(s) for the answer, Centre in box L3. Do not write these anywhere else. and zero mark if no bubble is darkened. In all other 7. Write your Registration No. in ink, in the box L4 provided cases, minus one (–1) mark will be awarded. in the lower part of the ORS and darken the appropriate 18. For each question in Section III, you will be awarded 4 bubble UNDER each digit of your Registration No. with a marks if you darken the bubble corresponding to the good quality Blue or Black ball pen. correct answer and zero mark if no bubble is darkened. In all other cases, minus one (–1) mark will be 8. The ORS has a CODE printed on its lower and upper awarded. parts. 19. For each question in Section IV, you will be awarded 2 9. Make sure the CODE on the ORS is the same as that on marks for each row in which you have darkened the this booklet and put your signature in ink in box L5 on bubble(s) corresponding to the correct answer. Thus, the ORS affirming that you have verified this. each question in this section carries a maximum of 8 10. IF THE CODES DO NOT MATCH, ASK FOR A marks. There is no negative marking for incorrect CHANGE OF THE BOOKLET. answer(s) for this section. C. Question paper format: 11. The question paper consists of 3 parts (Part I: Chemistry:, Part II: Mathematics, Part III: Physics). Each part has 4 sections. Name of the Student Roll Number I have read all the instructions and shall abide by them I have verified all the information filled in by the Candidate ……..……………………………………………………… ……………………………………………………….. Signature of the Candidate Signature of the Invigilator NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 PART I : CHEMISTRY PAPER – I SECTION – I Straight Objective Type This section contains 8 multiple choice questions. Each question has 4 choices ((A), ((B), (C)and ((D), out of which ONLY ONE is correct. 1. Which of the following bonds determines the secondary structure of proteins ? (A)Electrovalent bond (B)Covalent bond (C)Hydrogen bond (D)Coordinate bond 2. The odd one amongst these on basis of structure is (A)Glycogen (B) Amylopectin (C) Amylose (D Cellulose 3. Henry's law may be stated as (A)The mass of a gas dissolved per unit volume of a solvent is inversely proportional to the pressure of the gas in equilibrium with the solution at constant temperature. (B)The volume of a gas dissolved in a unit volume of solvent at a given temperature is independent of the pressure of the gas in equilibrium with the solution at constant temperature. (C)The mass of a gas dissolved per unit volume of a solvent is inversely proportional to the temperature of the gas in equilibrium with the solution at constant pressure. (D) The volume of a gas dissolved in solvent at a given pressure is independent of the temperature. 4. A mixture of water and toluene is distilled under equilibrium conditions at 1 atm pressure. If the vapour pressure of pure water at the equilibrium temperature is 570 torr, what is the mole fraction of toluene in the distillate. (A)0.5 (B)0.25 (C)0.75 (D)Insufficient data 5. How many unit cells are present in a cube– shaped ideal crystal of NaCl of mass 1.00 g [Atomic masses: Na = 23. Cl = 35.5] (A)2.57 x 1021 unit cells (B)5.14 x 1021 unit cells (C)1.28 x 1021 unit cells (D)1.71 x 1021 unit cells Space for Rough Work 2 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 6. 2C6H6 (l) + 15O2 (g) 12 CO2(g) + 6H2O (l) H – U = ? (at 298 K) (A)+ 7.43 kJ (B)+ 3.72 kJ (C) – 7.43 kJ (D)–3.72 kJ 7. The pyknometric density of sodium chloride crystal is 2.165 x 103 kg m–3 while its X–rays density is 2.178 x 103 kg m–3. The fraction of unoccupied sites in sodium chloride crystal is (A) 5.96 x 10–3 (B) 5.96 –2 (C) 5.96 x 10 (D) 5.96 x 10–1 8. The standard reduction potentials in acidic medium are 0.77V and 0.54V respectively for Fe3 / Fe2 and I 3 / I . The equilibrium constant for the reaction 2 Fe 3 3I 2 Fe 2 I 3 is (antilog of 7.7834= 6.25 107 , antilog of 9.9123= 8.168 109 , antilog of 4.5011= 3.171104 , antilog of 2.1602= 1.446 102 ) (A) 6.25 107 (B) 8.168 109 (C) 3.171104 (D) 1.446 102 SECTION – II Multiple Correct Answer Type This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices ((A), ((B), (C)and ((D), out of which ONE OR MORE is/are correct. 9. Protein is present in : (A)Nail (B)Hair (C)Wool (D)DNA 10. The base adenine occurs in : (A)DNA (B)RNA (C)GTP (D)ATP 11. Which of the following is a non branched polymer ? (A)Low density polythene (B)Polyester (C)Nylon (D)PVC 12. Example of plasticizer is (A)di–n–butyl phthalate (B)di–n–octylphthalate (C)cresyl triphosphates (D)Styrene Space for Rough Work 3 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 SECTION – III Linked Comprehension Type This section contains 2 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices ((A), ((B), (C)and (D)out of which ONLY ONE is correct. Paragraph for Questions Nos. 13 to 15 Redox reactions play a pivotal role in chemistry and biology. The values of SRP (E0) of two half–cell reactions decide which way the reaction is expected to proceed. A simple example is a Daniel cell in which zinc goes into solution and copper gets deposited. Given below are a set of half–cell reactions (acidic medium) along with their E0 (with respect to normal hydrogen electrode) values. Using this data. I 2 2e 2 I E 0 0.54 Cl2 2e 2Cl E 0 1.36 Mn3 e Mn 2 E 0 1.50 Fe3 e Fe 2 E 0 0.77 O2 4 H 4e 2 H 2O E 0 1.23 13. Among the following, identify the correct statement: (A) Chloride ion is oxidized by O2 (B) Fe2+ is oxidized by iodine (C) iodide ions is oxidized by chlorine (D) Mn2+ is oxidisied by chlorine 14. While Fe3+ is stable, Mn3+ is not stable in acid solution because: (A) O2 oxidises Mn2+ to Mn3+ (B) O2 oxidises both Mn2+ and Fe2+ (C) Fe3+ oxidises H2O to O2 (D) Mn3+ oxidises H2O to O2 15. The standard reduction potential values of three metallic cations, X, Y, Z are 0.52, – 3.03 and –1.18V respectively. The order of reducing power of the corresponding metal is : (A) Y > Z > X (B) X > Y > Z (C) Z > Y > X (D) Z > X > Y Space for Rough Work 4 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 Paragraph for Questions Nos. 16 to 18 2 liter of 1 molar solution of a complex salt CrCl3 .6H 2O (mol. wt 266.5) shows an osmotic pressure of 98.52 atm at 300K. The solution is now treated with 1 liter of 6 M AgNO3 16. Weight of AgCl precipitated is (A)861 gm (B)143.5 gm (C)287.0 gm (D)574.0 gm 17. Osmotic pressure of the clear solution that is obtained after removing precipitate is.. (A)54.28 atm (B)65.68 atm (C)75.45 atm (D)95.80 atm 18. The van't Hoff factor i is : (A)1 (B)2 (C) 3 (D)4 Space for Rough Work 5 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 SECTION – IV Matrix Match Type This section contains 2 questions. Each question contains statements given in p q r s t two columns, which have to be matched. The statements in Column I are A p q r s t labeled A, B, C and D, while the statements in Column II are labelled p, q, r, p q r s B t s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles C p q r s t corresponding to the answers to these questions have to be darkened as p q r s t D illustrated in the following example: If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s and t; then the correct darkening of bubbles will look like the following: 19. Match the column I and II Column – I Column – II (Solute) (Van’t Hoff factor, i) A AlCl3 if 0.8 P i = 3.4 B BaCl2 if 0.9 Q i = 2.8 C Na 3 PO 4 if 0.9 R i = 3.8 D K4 Fe CN 6 if 0.7 S i = 3.7 20. Consider the reduction reactions: i) Sn2 2e Sn; ESRP 0.14V 0 ii) Sn4 2e Sn2 ; ESRP 0.13V 0 Column I Column II 0 A Esn4 / sn P –0.005V B Standard oxidation potential of Sn to Sn4+ Q + 0.005V C Disproportionation of Sn2+ R Spontaneous D Oxidation of Sn to Sn4+ (1 M) S Non–spontaneous Space for Rough Work 6 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 PART II : MATHEMATICS Straight Objective Type This section contains 8 multiple choice questions. Each question has 4 choices ((A), ((B), (C)and ((D), out of which ONLY ONE is correct. BC BA BI 21. Let I be the incentre of the triangle ABC, where then the diameter BC BA k of the circumcircle of the triangle is (A) k(cos A/2 + cos C/2) (B) k(sin A/2 + sin C/2) (C) k(cot A/2 + cot C/2) (D) k (tan A/2 + tan C/2) 22. The reciprocal of the distance between two points, one on each of the lines x 2 y 4 z 5 x 1 y 2 z 3 and 3 2 5 2 3 4 (A) cannot be less than 9 (B) having minimum value 5 3 (C) cannot be greater than 78 (D) cannot be 2 19 x y z 23. and perpendicular to the Equation of the plane containing the straight line 2 3 4 x y z x y z plane containing the straight lines and is 3 4 2 4 2 3 (A) x + 2y – 2z = 0 (B) 3x + 2y – 2z = 0 (C) x – 2y + z = 0 (D) 5x + 2y – 4z = 0 24. The distance between the plane x – 2y + z –6 = 0 and the plane containing the sets of points (1 + 2, 2 + 3, 3 + 4) and (2 + 3, 3 + 4, 4 + 5), where , are parameters, is (A) 3/ 2 (B) 6 (C) 12 (D) 2 6 25. Three numbers a, b, c are choosen randomly from the set of natural numbers. The probability that 'a2 + b2 + c2' is divisible by 7 is (A) 1/3 (B) 1/4 (C) 1/5 (D) 1/7 Space for Rough Work 7 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 26. If the equation z2 + z + = 0 has a purely imaginary root and lies on the circle |z| = 1 then the imaginary part of that root, is (are) (A) 2 (B) 0 5 1 (C) 2 2 (D) 2 27. Let z (, ) = cos + ei sin (, R, i = 1 ) then the exaustive set of values of modulus of z(, 2), as varies, is (A) [0, 1] (B) [0, 2 ] (C) [1, 2] (D) [ 2 , 2] 28. If |z| = 1 and z 1 then one of the possible values of arg(z) – arg (z + 1) – arg (z – 1), is (A) –/6 (B) /3 (C) –/2 (D) /4 SECTION – II Multiple Correct Answer Type This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices ((A), ((B), (C)and ((D), out of which ONE OR MORE is/are correct. n Cr 2r 1 n Let for nN, f (n) 1 r 29. then r 0 r 1 r 2 (A)f(2n) = f(2n + 1) (B) f(n) = f(n + 1) (C) f(2n) = f(2n – 1) (D) f(2011) = f(2012) 30. Let k1, k2 be two integers such that (n – a)! = (n – b)!, 2a + b + 1 = k1n + k2 n where a b n and a, b, n N . Let P and Q be two points on the curve y log1/2 x k 2 / 2 log2 4x 4k x k k Point P also lies on the circle x 2 2 l 2 . 2 + y2 = k13 – 2k2, however Q lies inside the circle such that its abscissa is an integer then (A)The values of k1 and k2 are respectively 2 and –1 (B) maximum value of OP.OQ is 7 (C) minimum value of PQ is 1 (D) minimum value of OP . OQ is 3 Space for Rough Work 8 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 31. Let OABC be a tetrahedron whose four faces are equilateral triangles of unit side. Let OA a , OB b and OC c , then 1 3 (A) c a b 2 2 a b 1 (B) c a b 2 3 a b 2 1 1 (C) volume of the tetrahedron is (D) a b c 2 3 2 32. If a, b, c, d are unit vectors such that a b . c d 1 and a.c 1 2 then (A) a, b, c are non coplanar (B) b, d are non parallel (C) b, c, d are coplanar (D) a, d are parallel and b, c are parallel SECTION – III Linked Comprehension Type This section contains 2 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices ((A), ((B), (C)and (D)out of which ONLY ONE is correct. Paragraph for Questions Nos. 33 to 35 1 x Consider a G.P. with first term 1 x , x 1 , common ratio n and number 2 of terms (n+1). Let ‘S’ be sum of all the terms of the G.P., then 33. ‘S’ equals m 1 (A) n 2n 1 1 x 1 x . lim x n 2n 1 k 2 m k 0 m 1 n 1 2 1 x 1 x . lim x n 1 2n (B) n k 2 m k 0 m 1 n 2 1 x 1 x . lim x n 1 2n 1 (C) n k 2 m k 0 m 1 n 2 1 x 1 x . lim x n 2n (D) n k 2 m k 0 Space for Rough Work 9 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 34. The coefficient of xn in 'S' is (A) 2n (B) 2n+1 (C) 22n (D) 22n+1 r n 1 35. Cr 2 equals r 0 nr n (A) (3/4) (B) 1 (C) 2n (D) 3n Paragraph for Questions Nos. 36 to 38 All the 52 cards of a well shuffled pack of playing cards are distributed equally or unequally among 4 players named P1, P2, P3 & P4 . For i = 1, 2, 3, 4, let i = number of ace(s) given to Pi i = number of black card(s) given to Pi i = number of red card(s) given to Pi i = number of diamond(s) given to Pi 36. The probability that i 1 i = 1, 2, 3, 4, is 4! (A) 13C4 × 13 4 24 (B) [2 + 3 × 212 – 313 – 1]/224 (C) [134 – 4C1 124 + 4C2 114 – 4C3 104 + 4C4 94]/134 (D) 1 – 4(3/4)13 – 6 (1/2)13 – (1/4)12 37. If i + i = 13 i = 1, 2, 3, 4 then the probability that i = 1 i = 1, 2, 3, 4, is 133 (A) 54 72 /134 (B) 17 7 2 52 7 3 32 (C) 34 132 /174 27 (D) 134 38. If i + i = 13 i = 1, 2, 3, 4 then the probability that |i – i| = 1 i = 1, 2, 3, 4, is 2 2 26! 52! (26!) (4!) 52! (A) 2 2 4 (B) 2 2 2 4 (6!) (7!) (13!) (6!) (7!) (2!) (13!) 2 2 26! 52! 26! 52! (C) 4! 2 2 2 4 (D) 4! 2 2 4 (6!) (7!) (2!) (13!) (6!) (7!) (2!) (13!) Space for Rough Work 10 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 SECTION – IV Matrix Match Type This section contains 2 questions. Each question contains statements given in p q r s t two columns, which have to be matched. The statements in Column I are A p q r s t labeled A, B, C and D, while the statements in Column II are labelled p, q, r, p q r s B t s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles C p q r s t corresponding to the answers to these questions have to be darkened as p q r s D t illustrated in the following example: If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s and t; then the correct darkening of bubbles will look like the following: 39. Match the following n 2k n 1 2k Let f (n) n C k cos and g(n) n 1 Ck cos , then k 0 n k 0 n Column –I Column –II (A) f(n) is (p) A rational number (B) f(6) is (q) An irrational number (C) g(6) is (r) –27 (D) g(8) is (s) 2g(n + 2) (t) 2g(n) 40. Let n(P) represents the number of points P() lying on the rectangular hyperbola xy = 15!, under the conditions given in column I, match the value of n(P) given in column II. Column –I Column –II (A) , I (p) 32 (B) , I and HCF ( , ) 1 (q) 64 (C) , I and divides (r) 96 (D) , I and HCF ( , ) 35 (s) 4032 (t) 8064 Space for Rough Work 11 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 PART III : PHSICS SECTION – I Straight Objective Type This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C)and ((D), out of which ONLY ONE is correct. 41. ˆ In region x > 0, a uniform and constant magnetic field B1 2B0 k exists. ˆ Another uniform and constant magnetic field B2 B0 k exists in region x < 0. A positively charged particle of mass m and charge q i s crossing origin at time t = 0 with a velocity u u 0 ˆ . The particle comes back to i its initial position after a time : (B 0 , u 0 are positive constants) 3 m (A) 2 q B0 2 m (B) q B0 3m (C) q B0 (D) Particle does not come back to its initial position. 42. In the circuit shown the capacitor has charge Q. At t = 0 sec the key K is closed to complete the circuit. The charge on the capacitor at the instant potential difference across the inductor L1 is zero. Q (A) Q (B) 3 2Q (C) (D) 0. 3 Space for Rough Work 12 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 43. In the ideal oscillating circuit, the capacitance of the capacitor is 25 F and has initial charge of 30 C. The inductance of coil is 0.04 H. The maximum magnitude of current in the circuit, after closing the switch K is (A) 10 mA (B) 30 mA (C) 60 mA (D) 3 mA 44. A parallel beam of light of intensity I and cross section area S is incident on a plate at normal incidence. The photoelectric emission efficiency is 100%, the frequency of beam is and the work function of the plate is (h > ). Assuming all the electrons are ejected normal to the plane and with same maximum possible speed. The net force exerted on the plate only due to striking of photons and subsequent emission of electrons is S 2h 2S h (A) h 2m(h ) (B) h 2m(h ) S h 2S h (C) h 2m(h ) (D) h m(h ) 45. Electrons in a sample of gas containing hydrogen like atom (Z=3) are in fourth excited state. When photons emitted only due to transition from third excited state to second excited state are incide nt on a metal plate photoelectrons are ejected. The stopping potential for these photoelectrons is 3.95 eV. Now, if only photons emitted due to transition from fourth excited state to third excited state are incident on the same metal plate, the stopping potential for the emitted photoelectrons wil l be approximately equal to (A) 0.85 eV (B) 0.75 eV (C) 0.65 eV (D) None of these Space for Rough Work 13 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 46. A point object Q moves along line BA with velocity u towards focus F of the concave mirror. AD is line parallel to the principal axis OP and the shown angle is very small. If is the image of the point object Q at the shown instant, then the velocity vector of image is given by (A) v1 (B) v2 (C) v3 (D) v4 . 47. A pendulum of length ‘’ is free to oscillate in vertical plane about point O. An observer is viewing the bob of the pendulum directly from above. The pendulum is performing small oscillations in water (refractive index is µ) about its equilibrium position. The equation of trajectory of bob as seen by observer is : x2 y2 (A) µ 2 x 2 + y 2 = 2 (B) + =1 2 µ2 2 2 x2 y2 (C) + =1 (D) x 2 + y 2 = 2 2 µ 48. While measuring length of an object, it was observed that the zero of the vernier lies between 1.4 and 1.5 of the main scale and the fifth vernier division coincides with a main scale division. If the length of the object measured is , then the value of (– 1.4) in terms of the least count C of the instrument is (A) C (B) 1.45 C (C) 4 C (D) 5 C. Space for Rough Work 14 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 SECTION II Multiple Correct Choice Type This section contains 5 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE is/are correct. 49. A beam of light having frequency is incident on an initially neutral metal of work function (h > ). Then (A) all emitted photoelectrons have kinetic energy equal to (h – ). (B) all free electrons in the metal, that absorb photons of energy h completely, may not be ejected out of the metal. (C) after being emitted out of the metal, the kinetic energy of photoelectrons decreases continuously as long as they are at a finite distance from metal. (D) the emitted photo electrons move with constant speed after being ejected out of metal. 50. Pick up the correct statements : (A) Due to the time varying magnetic field in a certain region an induced electric field may be produced in a region where that magnetic field is not present. (B) A uniform magnetic field increasing at constant rate, induces an electric field which is constant and non conservative. (C) Non zero force exerted by uniform and constant magnetic field on a moving charged particle does no work but always changes momentum of the particle. (D) All the above statements are wrong. Space for Rough Work 15 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 51. A conducting rod of length is moved at constant velocity ‘v 0 ’ on two parallel, conducting, smooth, fixed rails, that are placed in a uniform constant magnetic field B perpendicular to the plane of t he rails as shown in figure. A resistance R is connected between the two ends of the rail. Then which of the following is/are correct : R XB V0 X x (A) The thermal power dissipated in the resistor is equal to rate of work done by external person pulling the rod. (B) If applied external force is doubled than a part of external power increases the velocity of rod. (C) Lenz’s Law is not satisfied if the rod is accelerated by external force (D) If resistance R is doubled then power required to maintain the constant velocity v 0 becomes half. 52. A point object 'O' is placed at focus of a diverging lens of focal length ' f '. When a converging lens of focal length (f/2) is placed in between object and lens at distance f/2 from diverging lens then: (A) The final image will be found at second focus of the converging lens (B) Final image will be formal on the object itself. (C) Final image is real. (D) Final image is virtual Space for Rough Work 16 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 Section III Comprehension Type This section contains 2 groups of questions. Each group has 3 multiple choice questions based on a paragraph. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Paragraph for Question Nos. 53 to 55 A particle (1) having positive charge q and mass m is moving along ˆ x–axis with a velocity v v 0 i in space having uniform and constant B B0 ˆ i magnetic field , where v 0 and B 0 are positive constants. At time t = 0 second, the moving particle (1) strikes another stationary uncharged particle (2) of mass m lying at origin, as shown in figu re (i). The collision is perfectly elastic and the uncharged particle (2) after collision moves along a straight line (in x –y plane) making an angle 45° with positive x–axis, as shown in figure (ii). Assume that there is no transfer of charge between the p articles during collision. 53. The time period of revolution of charged particle (after t = 0 second) is 2 m 2 2 m (A) (B) qB qB m (C) (D) None of these 2q B 54. The minimum time after t = 0, at which the charged particle touches x–axis is 2 2 m m qB (A) (B) 2q B 2 m (C) qB (D) After t = 0 charged particle does not touch x –axis. Space for Rough Work 17 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 55. The minimum time after t = 0, at which velocity of both particles are parallel is m 2 m (A) (B) qB qB m (C) 2 2q B (D) Velocities of both cannot be parallel. Paragraph for Question Nos. 56 to 58 The radionuclide 56 Mn is being produced in a cyclotron at a constant rate P by bombarding a maganese target with deutrons. 56 Mn has a half life of 2.5 hours and the target contains large number of only the stable maganese isotope 55 Mn. The reaction that produces 56 Mn is : 55 Mn + d 56 Mn + p After being bombarded for a long time, the activity of 56 Mn becomes constant equal to 13.86 × 10 10 s –1 . (Use ln2 = 0.693; Avogadro No = 6 × 10 23 ; atomic weight 56 Mn = 56 gm/mole) 56. At what constant rate P, 56 Mn nuclei are being produced in the cyclotron during the bombardment ? (A) 2 × 10 11 nuclei/s (B) 13.86 × 10 10 nuclei/s (C) 9.6 × 10 10 nuclei/s (D) 6.93 × 10 10 nuclei/s 57. After the activity of 56 Mn becomes constant, number of 56 Mn nuclei present in the target, is equal to (A) 5 × 10 11 (B) 20 × 10 11 (C) 1.2 × 10 14 (D) 1.8 × 10 15 58. After a long time bombardment, number of 56 Mn nuclei present in the target depends upon (a) the number of 56 Mn nuclei present at the start of the process. (b) half life of the 56 Mn (c) the constant rate of production P. (A) All (a), (b) and (c) are correct (B) only (a) and (b) are correct (C) only (b) and (c) are correct (D) only (a) and (c) are correct Space for Rough Work 18 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 SECTION – IV Matrix Match Type p q r s t This section contains 2 questions. Each question contains statements given in two A p q r s t columns, which have to be matched. The statements in Column I are labeled A, B, C B p q r s t and D, while the statements in Column II are labelled p, q, r, s and t. Any given C p q r s t statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles corresponding to the answers to D p q r s t these questions have to be darkened as illustrated in the following example: If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s and t; then the correct darkening of bubbles will look like the following: 59. Column–I gives certain situations regarding a point object and its image formed by an optical instrument. The possible optical instruments are concave and convex mirrors or lenses as given in Column–II. Same side of principal axis means both image and object should either be above the principal axis or both should be below the principal axis as shown in figure. Same side of optical instrument means both image and object should be either left of the optical instrument or both should be on right of the optical instrument as shown in figure. Match the statements in column–I with the corresponding statements in column–II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in OMR. Column A Column B (A) If point object and its image are on same side of (p) Concave mirror principal axis and opposite sides of the optical instrument then the optical instrument is (B) If point object and its image are on opposite side of (q) Convex mirror principal axis and same sides of the optical instrument then the optical instrument is (C) If point object and its image are on same side of (r) Concave lens principal axis and same sides of the optical instrument then the optical instrument is (D) If point object and its image are on opposite side of (s) Convex lens principal axis and opposite sides of the optical instrument then the optical instrument is (t) Both convex lens and concave mirror Space for Rough Work 19 NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10 60. Four different circuit components are given in each situation of column–I and all the components are connected across an ac source of same angular frequency = 200rad/sec. The information of phase difference between the current and source voltage in each situation of column–I is given in column–II. Match the circuit components in column–I with corresponding results in column –II. Column A Column B (A) (p) the magnitude of required phase difference is 2 (B) (q) the magnitude of required phase difference is 4 (C) (r) the current leads in phase to source voltage (D) (s) the current lags in phase to source voltage (t) Current and source voltage are in same phase Space for Rough Work 20