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Class 12 Exam 2011 : Chemistry

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Model With Solutions STD. XII Sci. Fourth Edition: September 2015 Salient Features A set of 4 Question Papers with solutions each for Physics, Chemistry, Maths & Biology (Total 16 Question Papers) Prepared as per the new board paper pattern. Includes Board Question Papers: March, October 2013, 2014 and March 2015. Complete answers to every question with relevant marking scheme. Graphs and diagrams provided wherever necessary. Simple and lucid language. Self-evaluative in nature. Solutions with relevant marking scheme to Board Question papers available in downloadable PDF format at www.targetpublications.org/tp952 Printed at: Dainik Saamana, Navi Mumbai No part of this book may be reproduced or transmitted in any form or by any means, C.D. ROM/Audio Video Cassettes or electronic, mechanical including photocopying; recording or by any information storage and retrieval system without permission in writing from the Publisher. TEID : 952 Preface HSC is the cornerstone of a student s career as it opens up the doors to turn their dreams into reality. It acts as a platform for students to specialize in a field that interests them the most. However, to achieve this it becomes imperative to get into the details of each subject and to clarify its fundamentals. Adequate knowledge base thus helps kids to boost their self confidence and pave their way up in the final examinations. It is rightly said, practice makes a man perfect . Keeping this adage in mind, we are proud to introduce Std XII Science Model Question Papers . This set of question papers provides students thorough practice for preparation of their final examinations. The book consists of 16 question papers in all based on Physics, Chemistry, Maths and Biology (a set of four question papers for each subject). Along with the question papers, we ve provided model answers with relevant marking schemes so as to make sure that students understand the importance of each question. These question papers reflect the latest changes in content and paper pattern as updated by the Board of Higher Secondary Education. Furthermore we have also included Board Question Papers of March, October 2013, 2014 and March 2015 examinations, solutions to which are available in downloadable PDF format at our website www. targetpublications.org. The purpose behind this is to make students familiar with the current question pattern and marking schemes. It also gives them a holistic understanding of the exact nature of the board question papers. We are sure that, these question papers would provide ample practice to students in a systematic manner and would boost their confidence to face the challenges posed in examinations. We welcome your valuable suggestions and feedback towards this book. We wish the students all the best for their examinations. Yours faithfully Publisher Index No. Subject Marking Scheme 1. Physics 2. Chemistry 3. Maths 4. Biology 5. Board Question Paper: March 2013 6. Board Question Paper: October 2013 6. Board Question Paper: March 2014 7. Board Question Paper: October 2014 8. Board Question Paper: March 2015 Test Physics Chemistry Maths Biology 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 Physics Chemistry Maths Biology Physics Chemistry Maths Biology Physics Chemistry Maths Biology Physics Chemistry Maths Biology Physics Chemistry Maths Biology Page No. Model Answers Question Papers 1 3 5 7 9 137 12 154 16 175 19 194 22 214 25 227 28 239 31 250 34 263 38 285 42 307 45 330 49 350 52 361 55 372 58 385 61 65 69 73 76 80 84 88 91 95 99 103 106 110 114 118 121 125 129 133 In this book, we have deliberately included the Board Question Papers for March 2013 and October 2013 for mathematics although it follows the old pattern. * marked questions in the above board papers are deleted from the new syllabus as compared to the earlier syllabus. Target Publications Pvt. Ltd. Physics Physics : Marking Scheme There will be one single paper of 70 marks in Physics. Duration of the paper will be 3 hours. Physics paper will consist of two parts viz: Section-I and Section-II. Each section will be of 35 marks. Same answer sheet will be used for both the sections. Each section will consist of 4 questions. The sequence of the 4 questions in each section may or may not remain same. The paper pattern for Section I and Section II will be as follows: Question 1: (7 Marks) This question will be based on Multiple Choice Questions. There will be 7 MCQs, each carrying one mark. One question will be based on calculations. Students will have to attempt all these questions. Question 2: (12 Marks) This question will contain 8 questions, each carrying 2 marks. Students will have to answer any 6 out of the given 8 questions. 4 questions will be theory-based and 4 will be numericals. Question 3: (9 Marks) This question will contain 4 questions, each carrying 3 marks. Students will have to answer any 3 out of the given 4 questions. 2 questions will be theory-based and 2 will be numericals. Question 4: (7 Marks) This question will contain 2 questions, each carrying 7 marks. Students will have to answer any 1 out of the given 2 questions. 4/5 marks are allocated for theory-based question and 3/2 marks for numerical. Distribution of Marks According to Type of Questions Type of Questions Objectives Short Answers Brief Answers Total Marks Marks with option Percentage (%) 14 42 14 70 14 56 28 98 20 60 20 100 1 Target Publications Pvt. Ltd. Sr. No. Making Scheme Unit Marks Without Marks with option option 1 Circular Motion 04 05 2 Gravitation 03 05 3 Rotational Motion 04 06 4 Oscillations 05 07 5 Elasticity 03 04 6 Surface Tension 04 05 7 Wave Motion 03 04 8 Stationary Waves 05 07 9 Kinetic Theory of Gases and Radiation 04 06 10 Wave Theory of light 03 04 11 Interference and Diffraction 04 06 12 Electrostatics 03 04 13 Current Electricity 03 04 14 Magnetic Effects of Electric Current 03 04 15 Magnetism 03 04 16 Electromagnetic Induction 04 06 17 Electrons and Photons 03 04 18 Atoms, Molecules and Nuclei 04 06 19 Semiconductors 03 04 20 Communication Systems 02 03 2 Target Publications Pvt. Ltd. Chemistry Chemistry : Marking Scheme There will be one written paper of 70 Marks in Chemistry. Duration of the paper will be 3 hours. Chemistry paper will have two parts viz: Part I of 35 marks and Part II of 35 marks Same Answer Sheet will be used for both the parts. In the question paper, for each part there will be 4 Questions. Students have freedom to decide the sequence of answers. The sequence of the 4 Questions in each part may or may not remain same. The paper pattern as per the marking scheme for Part I and Part II will be as follows: Question 1: (7 Marks) There will be 7 multiple choice Questions (MCQs), each carrying 1 mark. Total marks = 7 Question 2: (12 Marks) There will be 8 Questions out of which 6 Questions are to be answered, each carrying 2 marks. Total marks = 12 Question 3: (9 Marks) There will be 4 Questions out of which 3 Questions are to be answered, each carrying 3 marks. Total marks = 9 (There will be 3 Questions based on numericals from part I) Question 4: (7 Marks) There will be 2 Question out of which 1 Question has to be answered. It will carry 7 marks. Total Marks = 7 (There will be 2/3 marks Questions based on numericals from Part I) Distribution of Marks According to Type of Questions Type of Questions Marks Marks with option Percentage (%) Objectives 14 14 20 Short Answers 42 56 60 Brief Answers 14 28 20 Total 70 98 100 3 Target Publications Pvt. Ltd. No. Making Scheme Topic Name Marks Without Marks With Option Option 1 Solid State 04 06 2 Solutions and Colligative Properties 05 07 3 Chemical Thermodynamics and Energetics 06 08 4 Electrochemistry 05 07 5 Chemical Kinetics 04 06 6 General Principles and Processes of Isolation of Elements 03 05 7 p Block Elements 08 10 8 d and f Block Elements 05 06 9 Coordination Compounds 03 04 10 Halogen Derivatives of Alkanes and Arenes 04 06 11 Alcohols, Phenols and Ethers 04 06 12 Aldehydes, Ketones and Carboxylic Acids 05 07 13 Compounds Containing Nitrogen 04 06 14 Biomolecules 04 06 15 Polymers 03 04 16 Chemistry in Everyday Life 03 04 4 Target Publications Pvt. Ltd. Mathematics Mathematics : Marking Scheme There will be one single paper of 80 Marks in Mathematics. Duration of the paper will be 3 hours. Mathematics paper will consist of two parts viz: Part-I and Part-II. Each Part will be of 40 Marks. Same Answer Sheet will be used for both the parts. Each Part will consist of 3 Questions. The sequence of the Questions will be determined by the Moderator. The paper pattern for Part I and Part II will be as follows: Question 1: This Question will carry 12 marks and consist of two sections (A) and (B) as follows: (A) (12 Marks) This Question will be based on Multiple Choice Questions. There will be 3 MCQs, each carrying two marks. (B) This Question will have 5 sub-questions, each carrying two marks. Students will have to attempt any 3 out of the given 5 sub-questions. Question 2: This Question will carry 14 marks and consist of two sections (A) and (B) as follows: (A) (14 Marks) This Question will have 3 sub-questions, each carrying three marks. Students will have to attempt any 2 out of the given 3 sub-questions. (B) This Question will have 3 sub-questions, each carrying four marks. Students will have to attempt any 2 out of the given 3 sub-questions. Question 3: This Question will carry 14 marks and consist of two sections (A) and (B) as follows: (A) (14 Marks) This Question will have 3 sub-questions, each carrying three marks. Students will have to attempt any 2 out of the given 3 sub-questions. (B) This Question will have 3 sub-questions, each carrying four marks. Students will have to attempt any 2 out of the given 3 sub-questions. Distribution of Marks According to Type of Questions Type of Questions Short Answers Brief Answers Detailed Answers Total Marks Marks with option Percentage (%) 24 24 32 80 32 36 48 116 30 30 40 100 5 Target Publications Pvt. Ltd. Making Scheme Maths I Marks With Unit Sr. No. Option 1 Mathematical Logic 08 2 Matrices 06 3 Trigonometric Functions 10 4 Pair of Straight Lines 07 5 Vectors 08 6 Three Dimensional Geometry 04 7 Line 05 8 Plane 06 9 Linear Programming 04 Total 58 Maths II Marks With Unit Sr. No. Option 1 Continuity 06 2 Differentiation 08 3 Applications of Derivatives 08 4 Integration 09 5 Definite Integral 6 Applications of Definite Integral 7 Differential Equations 08 8 Probability Distribution 06 9 Binomial Distribution 05 08 Total 6 58 Target Publications Pvt. Ltd. Biology Biology : Marking Scheme There will be one written paper of 70 Marks in Biology. Duration of the paper will be 3 hours. Biology paper will have two parts viz: Part I of 35 marks and Part II of 35 marks There will be two separate answer sheets for both the parts. In the same question paper, each part will have 4 Questions. Sequence of answering the questions can be determined by the students. The paper pattern for Part I and Part II will be as follows: Question 1: There will be 7 multiple choice Questions (MCQs), each carrying one mark. Total marks = 7 (7 Marks) Question 2: This will have Questions as A , B and C . In that, Q.A will be based on : Answer in one sentence. There will be 6 Questions each carrying 1 mark Total marks = 6 Q.B will have one Question based on diagrams Total Marks = 2 Q.C will have 4 Questions, each carrying 2 marks Students will have to answer any 2 out of given 4 Questions Total marks = 4 Total Marks (A + B + C) = 12 (12 Marks) Question 3: This will have Questions as A and B Q.A will have 3 Questions each carrying 3 marks Students will have to answer any 2 out of given 3 Questions Total Marks = 6 Q.B will have one Question based on diagrams Total Marks = 3 Total Marks (A + B) = 9 (9 Marks) Question 4: In this Question, 2 Questions will be asked each carrying 7 marks. Students will have to answer any one out of given 2 Questions Total Marks = 7 (7 Marks) Distribution of Marks According to Type of Questions Type of Questions Objectives Short Answers Brief Answers Total Marks Marks with option Percentage (%) 14 42 14 70 14 56 28 98 20 60 20 100 7 Target Publications Pvt. Ltd. Making Scheme Marks With Option 12 07 09 03 05 07 1 Topic Name Marks Without Option 08 No. 09 Genetic Basis of Inheritance 2 Gene : It s Nature, Expression and Regulation 3 Biotechnology: Process and Application 4 Enhancement in Food Production 5 Microbes in Human Welfare 6 Photosynthesis 7 Respiration 8 Reproduction in Plants 07 09 9 Organisms and Environment I 03 05 10 Origin and Evolution of Life 07 09 03 05 05 07 10 14 11 Chromosomal Basis of Inheritance 12 Genetic Engineering and Genomics 13 Human Health and Diseases 14 Animal Husbandry 15 Circulation 16 Excretion and Osmoregulation 17 Control and Co-ordination 18 Human Reproduction 07 09 19 Organisms and Environment II 03 05 8 Target Publications Pvt. Ltd. Physics model question paper Set - I physics Time: 3 Hours Total Marks: 70 Note: i. ii. iii. iv. v. All questions are compulsory Neat diagrams must be drawn wherever necessary. Figure to the right indicate full marks. Use of logarithmic table is allowed. All symbols have their usual meaning unless otherwise stated. SECTION I Q.1. Select and write the most appropriate answer from the given alternatives for each sub-question: i. If a wave enters from air to water, then what remains unchanged? (A) Frequency (B) Amplitude (C) Velocity (D) Wavelength ii. If the earth stops rotating, the value of g at the equator will _______. (A) increase (B) decrease (C) remain same (D) become zero iii. On being churned the butter separates out of milk due to _______. (A) centrifugal force (B) adhesive force (C) cohesive force (D) frictional force iv. The average kinetic energy of a gas molecule is _______. (A) proportional to pressure of gas (B) inversely proportional to volume of gas (C) inversely proportional to absolute temperature of gas (D) proportional to absolute temperature of gas v. Speed of sound in air is 300 m/s. The distance between two successive nodes of a stationary wave of frequency 1000 Hz is _______. (A) 10 cm (B) 20 cm (C) 15 cm (D) 30 cm vi. The time period of a spring of force constant k loaded with mass m is _______. 1 (A) T m and T k (B) T m and T k 1 1 1 (C) T and T k (D) T and T m m k vii. [7] If a person, sitting on a rotating table, with his arms outstretched and holding heavy dumb bells in each hand, suddenly lowers his hands, then _______. (A) his angular velocity decreases (B) his angular velocity does not change (C) his angular momentum increases (D) his moment of inertia decreases Q.2. Attempt any SIX: i. Distinguish between deforming force and stress. ii. A simple harmonic progressive wave of frequency 5 Hz is travelling along the positive X direction with a velocity of 40 m/s. Calculate the phase difference between two points separated by a distance of 0.8 m. 9 [12] Target Publications Pvt. Ltd. H.S.C. Model Question Paper iii. iv. State Wien s displacement law. State its significance. Obtain an expression for time period of a satellite orbiting very close to earth s surface in terms of mean density. 3 Show that, T = , where = mean density of earth G v. Define frequency of S.H.M. Discuss its unit and dimension. vi. A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 9 kg. It rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds into it. vii. A uniform wire under tension is fixed at its ends. If the ratio of tensions in the wire to the square of its length is 320 dyne/cm2 and fundamental frequency of vibration of wire is 400 Hz, find its linear density. viii. A mass of 4 kg is tied at the end of a string 1.2 m long, revolving in a horizontal circle. If the breaking tension in the string is 200 N, find the maximum number of revolutions per minute the mass can make. Q.3. Attempt any THREE: i. A cyclist speeding at 18 km/hr on a level road takes a sharp circular turn of radius 4 m without reducing the speed. The coefficient of static friction between the tyres and the road is 0.2. Will the cyclist slip while taking the turn? Calculate maximum safety speed. Will it be constant always? ii. A brass wire of radius 2 mm is loaded by a mass of 32.8 kg. What would be the decrease in its radius? (Y = 9 1010 N/m2, Poisson s ratio = 0.36) iii. State and prove law of conservation of angular momentum. Give two examples. iv. What is a heat engine? Explain working and efficiency of heat engine. Q.4. Discuss analytically the composition of two S.H.M s of same period and parallel to each other. Obtain their resultant amplitude. Also find the resultant amplitude when phase difference of two S.H.M s is a. 0 b. Find the height of a geostationary satellite (communication satellite) from the surface of the earth. (Mass of the earth = 6 1024 kg, radius of the earth = 6400 km, G = 6.67 10 11 N.m2/kg2) OR Q.4. Derive an expression for the kinetic energy of a body rotating with uniform angular velocity. A body describes S.H.M in a path 0.16 m long. Its velocity at the centre of the line is 0.12 m/s. Find the period and magnitude of velocity at a distance 1.7 10 2 m from the mean position. [9] [7] [7] SECTION II Q.5. Select and write the most appropriate answer from the given alternatives for each subquestion: i. Velocity of light in air is c . Its velocity in a medium of refractive index 1.5 will be _______. c (A) c (B) (C) c 1.5 (D) c + 1.5 1.5 ii. For what value of velocity of electrons, the stopping potential will be able to stop them? (A) 103 m/s (B) Very high speeds (C) Very low speeds (D) All speeds iii. If the lengths of two wires of same material are in the ratio 2 : 1, then the ratio of their specific resistances will be _______. (A) 1 : 2 (B) 2 : 1 (C) 4 : 1 (D) 1 : 1 10 [7] Target Publications Pvt. Ltd. Physics iv. If R and L stand for the resistance and inductance respectively, then among the following the one having the dimensions of frequency is _______. R L R L (B) (C) (A) (D) L R L R v. The phenomenon of paramagnetism is a consequence of _______. (A) distortion effect (B) orientation effect (C) both (A) and (B) (D) neither (A) nor (B) vi. In an amplitude modulated wave, the power content of the carrier is maximum for which value of m ? (A) zero (B) 1 (C) 0.1 (D) 0.4 vii. In Boolean algebra, A B = _______. (A) A B (B) A + B (C) A B (D) A B Q.6. Attempt any SIX: i. A solenoid of 100 turns per unit length and cross-sectional area 2 10 4 m2 carries a current of 6 A. It is placed in horizontal axis at 30 with direction of uniform magnetic field of 0.3 T. Calculate magnetic moment of solenoid and torque experienced by solenoid due to the field. ii. Four resistances 5 , 5 , 5 and 15 form a Wheatstone s network. Find the resistance which when connected across the 15 resistance, will balance the network. iii. Define cut off potential. Show graphically variation of photoelectric current with collector plate potential for different intensity of incident radiation. iv. Explain why microscopes of high magnifying power have oil-immersion objectives. v. Explain I V characteristics of zener diode with suitable graph. vi. Calculate the de Broglie wavelength of proton if it is moving with speed of 8 106 m/s. (mp = 1.67 10 27 kg). vii. An alternating emf E = 250 sin t V is connected to a 1250 resistor. Calculate the rms current through the resistor and the average power dissipated in one cycle. viii. Write any two points of difference between amplitude modulation and frequency modulation. [12] Q.7. Attempt any THREE i. An alternating e.m.f is applied to a circuit containing resistance. Discuss the behaviour of current in the circuit. ii. With the help of a neat circuit diagram, explain working of P-N junction diode as a half-wave rectifier. iii. A resistance of 5 is connected in parallel to a galvanometer of resistance 495 . Find the fraction of the total current, passing through galvanometer. iv. Two parallel plate air capacitors have their plate areas 100 cm2 and 400 cm2 respectively. If they have the same charge and potential and the distance between the plates of the first capacitor is 0.4 mm, what is the distance between the plates of the second capacitor? [9] Q.8. Explain origin of spectral line and obtain Bohr s formula. If the difference in velocities of light in glass and water is 0.24 108 m/s, find the velocity of light 3 in air (Given : g = , w = 4/3) 2 OR Q.8. Explain principle, construction and working of transformer. Also, derive equation of transformer. When a surface is irradiated with light of wavelength 4950 , a photocurrent appears which vanishes if a retarding potential greater than 0.6 V is applied across the phototube. When different source of light is used, it is found that the critical retarding potential is changed to 1.1 V. Find the work function of the emitting surface and the wavelength of the second source. 11 [7] [7] Target Publications Pvt. Ltd. Physics Model ANSWER paper Set I Physics SECTION I Q.1. Select and write the most appropriate answer from the given alternatives for each sub-question: i. (A) ii. [1] (A) gE = g R 2 For = 0, g E = g. g E > gE. [1] iii. (A) [1] iv. (D) 1 3 mv 2 k B T 2 2 Kinetic energy of gas Temperature v. (C) Average kinetic energy of a gas Distance between two successive antinode = = [1] 2 v 300 = 3 = 15 10 2 m = 15 cm. 2n 10 2 [1] vi. (B) [1] vii. (D) When the man pulls his arms, the speed of rotation of the table increases but the distance R of the dumbells from the axis of rotation decreases. Hence, moment of inertia of the man decreases and angular velocity of turn table increases. [1] Q.2. Attempt any SIX: i. No. i. ii. iii. iv. v. Deforming force It is externally applied force. It tries to deform the body. S.I unit is N. Its dimension is [M1L1T 2]. It is a vector quantity. Stress It is internal restoring force per unit area. It opposes the deformation. S.I unit is N/m2. Its dimension is [M1L 1T 2]. It is a tensor quantity. (any two correct points of difference) ii. (1 2) [2] Given: To find: n = 5Hz, v = 40 m/s, x = 0.8 m, Phase difference ( ) 2 x Formulae: i. v = n ii. Calculation: From formula (i), v 40 = =8m = n 5 [1] 137 Target Publications Pvt. Ltd. H.S.C. Model Answer Paper From formula (ii), = 2 0.8 8 = 2 0.1 = rad 5 rad 5 Wien s displacement law: The wavelength ( m) emitted with maximum intensity by a black body is inversely proportional to its absolute temperature. Mathematically, 1 1 m i.e., m = b. T T where b = constant called Wien s constant. Significance: a. It can be used to estimate very high temperature such as surface temperature of stars, sun, moon, celestial bodies etc. b. It explains the common observation of the change of colour of a solid from dull red to yellow and then to white on heating. c. As the temperature increases, the maximum intensity of radiation shifts towards the shorter wavelength side. Thus Wien s law is also called displacement law. (any two points of significance) ( 2) Time period in terms of mean density: The phase difference between two points is iii. iv. (R h)3 GM Since T = 2 b. Mass of the earth, M = c. [1] where = mean density of the earth Substituting, the value of M in the equation (i), T = 2 R h 3 4 G R 3 3 3 R h = 4 R3 3 4 2 R h 4 R 3 G 3 [ ] 3 3 T = d. When satellite is orbiting very close to the earth, h 0. Equation (ii) becomes, GR 3 . (ii) T= T= 3 G a. The number of oscillations performed by a particle executing S.H.M. per unit time is called frequency of S.H.M. k 1 1 It is given by n = = = T 2 2 m Unit: Hz or c.p.s or r.p.s in SI system. Dimension: [M0L0T 1] [1] 3 R 3 GR 3 b. c. 138 [1] .(i) a. v. [1] [ ] [1] [ ] [ ] Target Publications Pvt. Ltd. Physics Given: To find: m = 10 g = 10 10 3 kg, v = 500 m/s, r = 0.5 m, l = 1 m, m = 9 kg, Angular speed ( ) Formulae: vi. i. L = mvr ii. I= ml 2 3 iii. L = I [1] Calculation: From formula (i), L = (10 10 3) 500 0.5 L = 2.5 kg m2/s From formula (ii), I= 9 12 = 3 kg m2 3 From formula (iii), = L 2.5 = = 0.83 rad/s 3 I Angular speed of the door is 0.83 rad/s. Given: T = 320 dyne/cm2, n = 400 Hz, l2 To find: Linear density (m) Formula: vii. n= [1] 1 2l T m [ ] Calculation: From formula, 1 T m= 4n 2 l 2 m= 1 320 4 (400) 2 m= 80 160000 [ ] m = 5 10 4 kg/m Linear density of the wire is 5 10 4 kg/m. viii. Given: To find: Formula: Calculation: [1] r = 1.2 m, m = 4 kg, T = 200 N, Maximum no of revolutions (nmax) Tmax = mr 2max = mr (2 nmax)2 From formula, n2max = [ ] 200 4 1.2 4 (3.14) 2 [ ] 1 2 200 nmax = 2 16 1.2 (3.14) 1 = antilog [log(200) log(16) log(1.2) 2 log (3.14)] 2 1 = antilog [2.3010 1.2041 0.0792 2 0.4969] 2 1 = antilog 0.0239 2 = antilog[0.0120] nmax = 1.028 r.p.s. nmax = 1.028 60 r.p.m. nmax = 61.68 Hz The maximum number of revolutions per minute is 61.68 Hz [1] 139 Target Publications Pvt. Ltd. H.S.C. Model Answer Paper Q.3. Attempt any THREE: 18000 i. v = 18 km/hr = m/s = 5 m/s, r = 4 m, s = 0.2 3600 v2 = 52 = 25 m2/s2 s rg = 0.2 4 9.8 = 7.84 m2/s2 Condition for safe turning is, v2 s rg Comparing values of v2 and ( s rg) 25 7.84 As condition for safe turning is not met, the cyclist will slip while taking circular turn. Max. Safe speed, vmax = s rg = 7.84 = 2.8 m/s This speed limit is not always constant. It depends upon friction between tyres and roads. For worn-out tyres or road wet with oil or water, magnitude of friction will change. Thus value of maximum safe speed will vary. ii. r = 2 mm = 2 10 3 m, m = 32.8 kg, Y = 9 1010 N/m2, Decrease in radius ( r) L r FL i. Y = ii. = 2 lr r l Given: To find: Formulae: [ ] [ ] [ ] [ ] [1] [1] Calculation: From formula (i), l F mg = = L AY ( r 2 )Y l 32.8 9.8 = L (2 10 3 ) 2 9 1010 32.8 9.8 = 3.14 4 9 104 = {antilog[log (32.8) + log (9.8) log (3.14) log (4) log (9)]} 10 4 = {antilog[1.5159 + 0.9912 0.4969 0.6021 0.9542]} 10 4 = {antilog [ 0.4539]} 10 4 = 2.844 10 4 From formula (ii), lr r = L = 2.842 10 4 2 10 3 0.36 r = {antilog[log (2.842) + log (2) + log (0.36)]} 10 7 = {antilog[0.4536 + 0.3010 + 1 .5563]} 10 7 = {antilog[0.3109]} 10 7 r = 2.046 10 7 m The decrease in radius of wire is 2.046 10 7 m. iii. Statement: The angular momentum of a body remains constant, if resultant external torque acting on the body is zero. Proof: a. Consider a particle of mass m, rotating about an axis with torque . Let p be the linear momentum of the particle and r be its position vector. b. 140 By definition, angular momentum is given by, L = r p ....(i) [1] [1] [ ] Target Publications Pvt. Ltd. c. Physics Differentiating equation (i) with respect to time t, d dL = (r p) dt dt d. dL dp dr = r + p dt dt dt .(ii) [ ] dp dr But, = v, = F and p = m v dt dt Equation (ii) becomes, dL = r F + 0 [ v v = v2 sin 0 = 0] dt e. Also, = r F dL = dt [ ] f. dL If resultant external torque ( ) acting on the particle is zero, then = 0. dt L = constant I = constant Hence, angular momentum remains conserved. Examples: 1. The angular velocity of revolution of a planet around the sun in an elliptical orbit increases, when the planet comes closer to the sun and vice-versa. 2. A person carrying heavy weights in his hands and standing on a rotating platform can change the speed of the platform. 3. A diver performs somersaults by jumping from a high diving board keeping his legs and arms out stretched first, and then curling his body. (Any 2 of the above examples) ( 2) iv. Heat engine: a. A heat engine is a device which converts heat energy into mechanical energy. b. This engine works in cyclic process. It takes heat from bodies at higher temperature, converts part of it to mechanical work and remaining to a body at lower temperature. c. The cycle is repeated again and again to get useful work for some purpose. Working: a. Suppose, Q1 = amount of heat absorbed by the working substance from the source at temperature in one complete cycle. Q2 = amount of heat rejected at temperature in the cycle. W = net amount of external work done by the working substance, on the environment in the cycle. b. Net amount of heat absorbed in one cycle, Q = Q1 Q2 c. As the working substance returns to its initial state, the change in its internal energy = 0 U = 0 According to the first law of thermodynamics, Q = U + W Q = W i.e., Net amount of heat absorbed = External work done by the engine Q1 Q2 = W 141 [ ] [1] [1] Target Publications Pvt. Ltd. At source T1 Q1 H.S.C. Model Answer Paper Working substance Q2 At sink T2 [1] W Thermal efficiency: a. Thermal efficiency of a heat engine is the ratio of net work done per cycle by the engine to the total amount of heat absorbed per cycle by the working substance from the source. Q Q2 Q W = 1 1 2 Q1 Q1 Q1 b. It is given by = c. where, Q1 = Heat absorbed by the system in one complete cycle, Q2 = Heat rejected to the environment. For Q2 = 0, = 1, i.e., the engine will have 100% efficiency in converting heat into work. It is not possible experimentally to construct such an ideal engine with = 1. d. [1] Q.4. Analytical treatment of composition of two S.H.M s: i. Let the two linear S.H.M s be given by equations, . (1) x1 = A1 sin ( t + 1) x2 = A2 sin ( t + 2) . (2) where A1, A2 are amplitudes, 1, 2 are initial phase angles and x1, x2 are the displacement of two S.H.M s in time t . is same for both S.H.M s. ii. iii. iv. v. The resultant displacement of the two S.H.M s is given by, x = x 1 + x2 ....(3) Using equations (1) and (2) , equation (3) can be written as, x = A1 sin ( t + 1) + A2 sin ( t + 2) = A1 [sin t cos 1 + cos t sin 1] + A2 [sin t cos 2 + cos t sin 2] = A1 sin t cos 1 + A1 cos t sin 1 +A2 sin t cos 2 + A2 cos t sin 2 = [A1 sin t cos 1 + A2 sin t cos 2] +[A1 cos t sin 1 + A2 cos t sin 2] x = sin t [A1 cos 1 + A2 cos 2] + cos t [A1 sin 1 + A2 sin 2] . (4) Let A1 cos 1+ A2 cos 2 = Rcos . (5) . (6) and A1 sin 1 + A2 sin 2 = R sin Using equations (5) and (6), equation (4) can be written as, x = sin t. R cos + cos t.R sin = R [sin t cos + cos t sin ] x = R sin ( t + ) . (7) Equation (vii) represents linear S.H.M. of amplitude R and initial phase angle with same period. Resultant amplitude (R): Squaring and adding, equations (v) and (vi),we get, (A1 cos 1 + A2 cos 2)2 + (A1 sin 1 + A2 sin 2)2 = R2cos2 + R2sin2 A12cos2 1+A22 cos2 2+2A1 A2 cos 1 cos 2+A12 sin2 1+A22sin2 2+2A1A2 sin 1 sin 2 = R2 (cos2 + sin2 ) A12 (cos2 1+sin2 1) + A22 (cos2 2+sin2 2) + 2A1A2 (cos 1 cos 2+sin 1 sin 2) = R2 A12 + A22 + 2A1 A2 cos ( 1 2) = R2 R= 142 2 A1 A2 2 2A1A 2 cos 1 2 ....(8) [1] [1] Target Publications Pvt. Ltd. Physics Equation (8) represents resultant amplitude of two S.H.M s. Case I: For phase difference = 0 If 1 2 = 0 then 1 = 2 In this case both S.H.M s have same initial phase angle From equation (viii), R= Formula: A1 A 2 2 [ ] For phase difference = If 1 2 = then, cos ( 1 2) = 1 From equation (viii), R= To find: 2 A1 A2 2 2A1A 2 = R = (A1+ A2) If A1 = A2 = A then, R = 2A Case II: Solution: Given: [1] 2 A1 A2 2 2A1A 2 = A1 A 2 2 R = (A1 A2) If A1 = A2 = A then, R = 0 Since particle has resultant amplitude zero, therefore it will be at rest. [ ] M = 6 1024 kg, R = 6400 km = 6.4 106 m, G = 6.67 10 11 N.m2/kg2 For geostationary satellite, period of revolution is one day. T = 1 day = (24 3600)s. Height (h) 4 2 3 T2 = (R + h) GM [1] Calculation: From formula, GMT 2 (R + h)3 = 4 2 1 R+h 6.67 10 11 6 1024 (24 3600) 2 3 = 4 (3.142) 2 [ ] 1 6.67 0.6 242 362 1025 10 11 104 3 = 4 (3.142) 2 1 = anti log log 6.67 log 0.6 2log 24 2log 36 log 4 2log 3.14 106 3 6 = anti log 0.8241 1.7782 2 1.3802 2 1.5563 0.6021 2 0.4972 10 1 3 1 = anti log 0.8241 1.7782 2.7604 3.1126 0.6021 0.9944 106 3 1 = antilog 4.8788 106 3 = antilog[1.6263] 106 R + h = 4.23 107 m = 42.3 106 m h = 42.3 106 6.4 106 h = 35.900 106 m = 35,900 km The height of geostationary satellite from the surface of the earth is 35,900 km. [ ] [1] 143 Target Publications Pvt. Ltd. H.S.C. Model Answer Paper OR Q.4. Expression for kinetic energy of a rotating body: i. Suppose a rigid body is rotating with constant angular velocity about an axis ZZ through a point O as shown in the figure. ii. Let the body consists of n particles of masses m1, m2, m3, ., mn situated at distances r1, r2, r3, , rn respectively from the axis of rotation. iii. Linear velocity of particles of masses m1, m2, mn are given by v1 = r1 , v2 = r2 , v3 = r3 ..., vn = rn , respectively. Z [1] m1 v1 m2 v r1 rn n mn r2O r3 v3 v2 m 3 Z iv. Kinetic energy of particle of mass m1, 1 1 2 = m1r12 2 (K.E)1 = m1 v1 2 2 Kinetic energy of particle of mass m2, 1 = m 2 r22 2 (K.E)2 = 1 m 2 v 2 2 2 2 v. Similarly kinetic energy of particle of masses m3, m4 mn are given by, 1 (K.E)3 = m3 r32 2, 2 1 (K.E)4 = m 4 r42 2, 2 . . (K.E)n = 1 2 m n rn2 2 vi. Total K.E of the rotating body is given by, K.E = (K.E)1 + (K.E)2 + (K.E)3 + + (K.E)n 1 1 1 1 = m1r12 2 + m 2 r22 2 + m3 r32 2 + + m n rn2 2 2 2 2 2 K.E = 1 2 2 2 2 m1r12 m 2 r2 m3 r3 ... m n rn 2 K.E = 1 n mi ri2 2 2 i 1 m r =I K.E = 1 2 I 2 [1] n i 1 144 2 i i [1] [1] Target Publications Pvt. Ltd. Solution: Given: To find: Physics 2A = 0.16 m A = 0.08 m, vmax = 0.12 m/s, x = 1.7 10 2m Period (T), magnitude of velocity (v) Formulae: i. vmax = A ii. v= Calculation: From formula (i), v 0.12 = 1.5 rad/s = max = A 0.08 2 2 3.14 T= = 4.1865 s. But = T 1.5 The period of body is 4.1865 s. From formula (ii), v = 1.5 = 1.5 A2 x 2 [1] [ ] (0.08) 2 (1.7 10 2 ) 2 [(8) 2 (1.7) 2 ] 10 4 [ ] 1 log(61.11)]} 10 2 2 1 = {antilog[0.1761 + 1.7861]} 10 2 2 = {antilog[1.0692]} 10 2 v = 11.73 10 2 m/s = 0.1173 m/s The magnitude of velocity is 0.1173 m/s. v = {antilog[log(1.5) + [1] SECTION II Q.5. Select and write the most appropriate answer from the given alternatives for each subquestion: i. (B) v air c = = 1.5 air med = v med v med c 1.5 vmed = ii. (D) [1] iii. (D) Specific resistance is the same for two wires as the material is the same. [1] iv. [1] (A) L Vs A Vs A = = s. Hence option (B) is wrong. V A R A V R (V / A) V A 1 option (A) is correct. L (Vs / A) A Vs s Options (C) and (D) are incorrect. [1] v. (B) [1] vi. (A) [1] vii. (D) [1] 145 Target Publications Pvt. Ltd. H.S.C. Model Answer Paper Q.6. Attempt any SIX: i. ii. Given: N = 100 turns per unit length, A = 2 10 4 m2, I = 6 A, = 30 , B = 0.3 T To find: Magnetic moment (M), torque ( ) Formulae: i. M = NIA ii. = MB sin Calculation: From formula (i), M = 100 6 2 10 4 = 0.12 Am2 Magnetic moment of solenoid d is 0.12 Am2. From formula (ii), = 0.12 0.3 sin 30 = 0.018 N.m Torque experienced by solenoid is 0.018 N m. Let R1 = 5 , R2 = 5 , R3 = 5 , R4 = 15 . Let X be resistance connected across R4. R 4X 15X Equivalent resistance R 4 R 4 X 15 X Balancing condition of network, R1 R 3 R 2 R 4 Photoelectric current X iv. a. b. 146 [ ] [ ] [ ] [ ] The minimum negative potential given to collector plate for which photoelectric current stops or becomes zero is called stopping potential or cut off potential. It is denoted by V0. The graph of photoelectric current vs collector plate potential: Y [ ] [ ] 5 5 5 15X 15 X 15X = 5 (15 + X) 3X = 15 + X 2X = 15 X = 7.5 The resistance to be connected across R4 is 7.5 iii. [1] [1] Intensity I1 < I2 < I3 V0 O Collector plate potential I3 I2 I1 X To avoid obscuration of details of micro-objects by diffraction effects, microscope of high magnifying power must have high resolving power. 2 sin , where sin is termed as numerical aperture. R.P. of microscope = Thus, R.P. sin [1] [ ] Target Publications Pvt. Ltd. c. d. e. v. Physics To increase , the diameter of objective would have to be increased. This would degrade image by decreasing resolving power. Oil has higher refractive index ( oil > air) hence to increase resolving power of microscopes of high magnifying power, the object is immersed in oil that is in contact with objective. Usually cedar oil having refractive index 1.5, close to that of the objective glass is used. [ ] [ ] [ ] I-V characteristic of a zener diode is as shown below: +I Vz V O +V [1] I Zener diode characteristics a. b. c. vi. vii. Zener diode is p n junction diode manufactured to operate in breakdown region. Its forward bias characteristic is same as that of ordinary junction diode. This means current does not flow until bias is less than barrier potential. Current increases rapidly beyond it with increase in forward voltage. In reverse bias, initially a small reverse saturated current flows and at particular value of reverse voltage, increases suddenly. This voltage is zener breakdown voltage (Vz) v = 8 106 m/s, mP = 1.67 10 27 kg, de Broglie wavelength ( P) h h Formula: P = p mP v Calculation: From formula, 6.63 10 34 P = 1.67 10 27 8 106 = 4.9626 10 14 m de Broglie wavelength of given proton is 4.9626 10 14 m. [ ] [ ] Given: To find: E = 250 sin t v E0 = 250 V, R = 1250 R.M.S. current (Irms), average power (Pav) E I E ii. Irms = 0 iii. Erms = 0 Formulae: i. I0 = 0 R 2 2 Calculation: From formula (i), 250 I0 = 1250 = 0.2 A From formula (ii), 0.2 Irms = 2 = 0.1414 A R.M.S. current through resistor is 0.1414 A [1] [1] Given: To find: iv. Pav = Irms Erms [1] [ ] 147 Target Publications Pvt. Ltd. H.S.C. Model Answer Paper From formula (iii), 250 Erms = = 176.78 V 2 From formula (iv), Pav = 0.1414 176.78 Pav 25 W Average power dissipated in one cycle is around 25 W. [ ] viii. No. Amplitude Modulation In AM, alternation in amplitude of the desired signal amounts to marked distortion In AM, use of an excessively large modulating signal may result in distortion because of over modulation. i. ii. iii. Frequency Modulation Noise can be easily minimised in FM system. The average power in modulated wave is greater than that contained in unmodulated wave. No restriction is placed on the modulation index. The instantaneous frequency deviation is proportional to the instantaneous magnitude of the signal. The average power in frequency modulated wave is the same as that contained in the unmodulated wave. (Any of the above two points) (1 2) [2] Q.7. Attempt any THREE i. A.C circuit with resistance: a. Suppose an alternating source of e.m.f is applied between the terminals of a resistor of resistance R as shown in figure below. The instantaneous value of e.m.f is given by, e = e0 sin t .(i) R b. c. d. e. 148 By Ohm s law, the instantaneous current flowing through the circuit is given by e I = R But, e = e0 sin t e sin t I= 0 .(ii) R Equation (ii) represents instantaneous current in the circuit. For maximum current through the circuit, sin t = 1. e .(iii) Imax = 0 = I0 R Equation (iii) represents peak value of current From equation (ii) and (iii), I = I0 sin t .(iv) Equation (iv) represents instantaneous current of a.c circuit with resistance only. From equation (iv) it is observed that instantaneous current varies sinusoidally with peak current. [1] [ ] [ ] [1] Target Publications Pvt. Ltd. Working of P-N junction diode as half-wave rectifier: a. A rectifier, which rectifies only one half cycle of each a.c input supply, is called a half wave rectifier. The circuit diagram is as shown, P1 S1 P + D N _ Id + RL S2 P2 d.c out put Vo = Id RL b. a.c input ii. Physics _ Half-wave rectifier P 1 P2 S1 S 2 D RL : : : : Primary coil of step down transformer Secondary coil of step down transformer P-N junction diode Load resistance [1] c. When a.c input is applied to a junction diode, it gets forward biased during one half cycle and reverse biased during the next opposite half cycle. d. The a.c supply is fed across the primary coil P1P2 of a step down transformer. The secondary coil S1S2 of the transformer is connected to the junction diode D and a load resistance RL. The output d.c. voltage is obtained across the load resistance RL. The output d.c. voltage is given by Vo = Id RL. e. Suppose that during the first half of the input, a.c voltage terminal S1 becomes positive w.r.t S2. Then, P region of diode D becomes positive w.r.t N region. This makes the junction diode forward biased, thus the conventional current flows in the direction of the arrow-heads through RL. f. During the negative half cycle, the terminal S2 is at positive potential w.r.t S1. Thus, P region of diode D is negative w.r.t N region. This makes the diode reverse biased. Thus diode does not allow current through it and no current will flow through RL. g. During the next half cycle, output is again obtained as the junction diode gets forward biased. Thus, a half wave rectifier gives pulsating unidirectional and intermittent d.c output voltage V across the load resistance RL. h. [1] Graph of a.c input and d.c output voltage with respect to time is as shown, +V a.c input voltage o +ve V +V d.c output +ve voltage o V + ve + ve ve ve +ve +ve time time [1] 149 Target Publications Pvt. Ltd. iii. iv. H.S.C. Model Answer Paper Given: S = 5 , G = 495 , For parallel combination Vg = VS Ig G = (I Ig)S Ig G = IS IgS Ig(G + S) = IS Ig S = I G S 5 5 = = 495 5 500 Ig 1 = 1% = I 100 The fraction of the total current passing through galvanometer is 1%. 2 4 2 2 4 [ ] [ ] [ ] [ ] [1] 2 A1 = 100 cm = 100 10 m , A2 = 400 cm = 400 10 m Q1 = Q2 , V1 = V2, d1 = 0.4 mm = 4 10 4 m To find: Distance between plates (d2) A Q Formulae: i. C = 0 ii. C= d V Calculation: From formula (i), A C1 = 0 1 .(1) d1 Given: C2 = 0 A 2 d2 .(2) Since, Q1 = Q2 , V1 = V2 From formula (ii), C1 = C2 From equation (1) and (2), 0 A 1 A = 0 2 d1 d2 d2 = [1] A2 d1 A1 400 10 4 4 10 4 100 10 4 = 16 10 4 m = 0.16 cm Distance between plates of the second capacitor is 0.16 cm. Q.8. Origin of spectral line: i. According to Bohr s third postulate, when an electron in a hydrogen atom jumps from higher energy level to the lower energy level, the difference of energies of the two energy levels is emitted as a radiation of particular wavelength called spectral line. ii. The wavelength of the spectral line depends upon the energy associated with the two energy levels, between which the transition of the electron takes place. iii. If the energy absorbed is equal to difference between the energies of the two levels then it jumps to a higher permitted orbit and revolves in it. In this case, electron is said to be in the excited state. iv. In the excited state, the electron is not stable and tries to attain stability by going back to the ground state by emitting the extra amount of energy it had gained in one or more jumps. v. The energy is emitted as electromagnetic waves and produces a spectral line of the corresponding frequency or wavelength. [ ] [ ] = 150 [1] [1] Target Publications Pvt. Ltd. Physics Bohr s formula for spectral lines in hydrogen spectrum: i. Let, En = Energy of electron in nth higher orbit Ep = Energy of electron in pth lower orbit ii. According to Bohr s third postulate, En Ep = h En Ep = h .(1) iv. But En = me 4 2 2 2 8 0 h n .(2) Ep = iii. me4 2 2 2 8 0 h p [ ] .(3) [ ] From equations (1), (2) and (3), me4 me4 2 2 2 2 2 2 8 h n 8 0 h p = 0 h me 4 1 1 = 2 3 2 2 8 0 h n p c me4 1 1 = 2 3 2 2 8 0 h p n where, c = speed of electromagnetic radiation 1 me 4 1 1 2 3 2 2 8 0 h c p n v. But, [ = c ] [1] me4 = R = Rydberg s constant 2 3 8 0 hc 1 1 1 .(4) =R 2 2 n p Equation (4) represents Bohr s formula for hydrogen spectrum. [1] Solution: 3 4 , w = , vw vg = 0.24 108 m/s 2 3 To find: Velocity of light (c) c Formula: = v Calculation: From formula, c c and w = g = vg vw Given: g = [ ] c c and vw = w g vg = vw vg = [ ] 1 1 w g 1 1 0.24 108 = c 4 / 3 3 / 2 c c =c w g [ ] [ ] 151 Target Publications Pvt. Ltd. H.S.C. Model Answer Paper 3 2 0.24 108 = c 4 3 9 8 =c 12 1 =c 12 c = 0.24 108 12 = 2.88 108 3 108 m/s Velocity of light in air is 3 108 m/s. [1] OR Q.8. Principle of transformer: It is based on the principle of mutual induction i.e. whenever the magnetic flux linked with a coil changes, an e.m.f is induced in the neighbouring coil. Construction: i. A transformer consists of two sets of coils P and S insulated from each other. The coil P is called the primary coil and coil S is called the secondary coil. ii. The two coils are wound separately on a laminated soft iron core. iii. The a.c input voltage is applied across the primary and the induced output a.c voltage is obtained across the secondary, which is used to drive current in the desired circuit. iv. The two coils are electrically insulated from each other but they are magnetically linked. v. To minimise eddy currents, the soft iron core is laminated. [1] Soft iron core Input a.c. voltage P S Load P S core Working: i. When an alternating voltage is applied to the primary coil the current through the coil goes on changing. Hence, the magnetic flux through the core also changes. ii. As this changing magnetic flux is linked with both the coils, an e.m.f is induced in each coil. iii. The amount of the magnetic flux linked with the coil depends upon the number of turns of the coil. Equation of transformation: i. Let, be the magnetic flux linked per turn with both the coils at certain instant t . ii. Let NP and NS be the number of turns of primary and secondary coil, NP = magnetic flux linked with the primary coil at certain instant t NS = magnetic flux linked with the secondary coil at certain instant t iii. Induced e.m.f produced in the primary and secondary coil is given by, d P d eP = = NP .(1) dt dt d d .(2) eS = S = NS dt dt 152 [1] [1] Target Publications Pvt. Ltd. iv. Physics Dividing equation (2) by (1), eS N = S .(3) eP NP Equation (3) represents equation of transformer. Solution: Given: [1] 1 = 4950 = 4.95 10 7m, e = 1.6 10 19 C, V01 = 0.6 V, h = 6.63 10 34 J.s, V02 = 1.1 V. To find: Work function (W0), wavelength of second source ( 2) hc Formulae: i. c = ii. h W0 = eV0 iii. W0 = eV0 Calculation: From formula (i), 3 108 = 6.06 1014 Hz 1 = 4.95 10 7 From formula (ii), W0 = 6.63 10 34 6.06 1014 (1.6 10 19 0.6) = 4.018 10 19 0.96 10 19 = 3.058 10 19 J 3.058 10 19 eV W0 = 1.6 10 19 W0 = 1.911 eV The work function of surface is 1.911 eV. From formula (iii), hc 2 = eV02 W0 = [1] [1] 6.63 10 34 3 108 (1.6 10 19 1.1) (1.6 10 19 1.911) 3 6.63 10 26 19.89 = 10 7 19 3.011 1.6 (1.1 1.911) 1.6 10 = 4.129 10 7 m = 4129 2 The Wavelength of second source is 4129 . = [1] 153

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