{"id":4425,"date":"2016-05-16T09:49:00","date_gmt":"2016-05-16T04:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-physics-alternating-current\/"},"modified":"2019-02-18T16:02:44","modified_gmt":"2019-02-18T10:32:44","slug":"ncert-solutions-class-12-physics-alternating-current","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-physics-alternating-current\/","title":{"rendered":"NCERT Solutions class 12 physics Alternating Current"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-physics-alternating-current\/#NCERT_Class_12_Physics_Chapter-wise_Solutions\" >NCERT Class 12 Physics Chapter-wise Solutions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-physics-alternating-current\/#NCERT_Solutions_for_Class_12_Chapter_7_Alternating_Current\" >NCERT Solutions for Class 12 Chapter 7 Alternating Current<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-physics-alternating-current\/#NCERT_Solutions_class_12_physics_Alternating_Current\" >NCERT Solutions class 12 physics Alternating Current\u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-physics-alternating-current\/#NCERT_Solutions_for_Class_12_Physics\" >NCERT Solutions for Class 12 Physics<\/a><\/li><\/ul><\/nav><\/div>\n<p><strong>NCERT Solutions class 12 physics Alternating Current Class 12 Physics<\/strong>\u00a0solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Physics chapter wise NCERT solution for Physics part 1 and Physics part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p style=\"text-align: center;\"><strong>Download\u00a0<a href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-12-physics\/1251\/ncert-solutions\/5\/\">NCERT Solutions for Physics\u00a0<\/a>as PDF.<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignright\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/Class%2012%20physics%20book%2012.jpg\" alt=\"NCERT Solutions class 12 physics Alternating Current\u00a0\" width=\"106\" height=\"130\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Class_12_Physics_Chapter-wise_Solutions\"><\/span><strong>NCERT Class 12 Physics Chapter-wise Solutions<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>1 \u2013 Electric Charges and Fields<\/li>\n<li>2 \u2013 Electrostatic Potential and Capacitance<\/li>\n<li>3 \u2013 Current Electricity<\/li>\n<li>4 \u2013 Moving Charges and Magnetism<\/li>\n<li>5 \u2013 Magnetism and Matter<\/li>\n<li>6 \u2013 Electromagnetic Induction<\/li>\n<li>7 \u2013 Alternating Current<\/li>\n<li>8 \u2013 Electromagnetic Waves<\/li>\n<li>9 \u2013 Ray Optics and Optical Instruments<\/li>\n<li>10 \u2013 Wave Optics<\/li>\n<li>11 \u2013 Dual Nature of Radiation and Matter<\/li>\n<li>12 \u2013 Atoms<\/li>\n<li>13 \u2013 Nuclei<\/li>\n<li>14 \u2013 Semiconductor Electronic: Material, Devices and Simple Circuits<\/li>\n<li>15 \u2013 Communication Systems<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_12_Chapter_7_Alternating_Current\"><\/span>NCERT Solutions for Class 12 Chapter 7 Alternating Current<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>7.1 Introduction<\/li>\n<li>7.2 AC Voltage Applied to a Resistor<\/li>\n<li>7.3 Representation of AC Current and Voltage by Rotating Vectors \u2014 Phasors<\/li>\n<li>7.4 AC Voltage Applied to an Inductor<\/li>\n<li>\u00a07.5 AC Voltage Applied to a Capacitor<\/li>\n<li>7.6 AC Voltage Applied to a Series LCR Circuit<\/li>\n<li>7.7 Power in AC Circuit: The Power Factor<\/li>\n<li>7.8 LC Oscillations<\/li>\n<li>7.9 Transformers<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_physics_Alternating_Current\"><\/span>NCERT Solutions class 12 physics Alternating Current<strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1:A 100 <img decoding=\"async\" style=\"height: 17px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image001.png\" \/>\u00a0resistor is connected to a 220 V, 50 Hz ac supply.<\/p>\n<p>(a) What is the rms value of current in the circuit?<\/p>\n<p>(b) What is the net power consumed over a full cycle?<\/p>\n<p>2:\u00a0(a) The peak voltage of an ac supply is 300 V. What is the rms voltage?<\/p>\n<p>(b) The rms value of current in an ac circuit is 10 A. What is the peak current?<\/p>\n<p>3: A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine the rms value of the current in the circuit.<\/p>\n<p>4: A 60 <img decoding=\"async\" style=\"height: 23px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image017.png\" \/>\u00a0capacitor is connected to a 110 V, 60 Hz ac supply. Determine the rms value of the current in the circuit.<\/p>\n<p>5:\u00a0 In Exercises 7.3 and 7.4, what is the net power absorbed by each circuit over a complete cycle. Explain your answer.<\/p>\n<p>6:\u00a0 Obtain the resonant frequency <img decoding=\"async\" style=\"height: 15px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image026.png\" \/>\u00a0of a series <em>LCR<\/em> circuit with <img decoding=\"async\" style=\"height: 23px; width: 154px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image027.png\" \/>\u00a0and <em>R<\/em> = 10<img decoding=\"async\" style=\"height: 17px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image001.png\" \/>\u00a0. What is the <em>Q<\/em>-value of this circuit?<\/p>\n<p>7:\u00a0A charged 30 <img decoding=\"async\" style=\"height: 23px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image017.png\" \/>capacitor is connected to a 27 mH inductor. What is the angular frequency of free oscillations of the circuit?<\/p>\n<p>8:\u00a0Suppose the initial charge on the capacitor in Exercise 7.7 is 6 mC. What is the total energy stored in the circuit initially? What is the total energy at later time?<\/p>\n<p>9:\u00a0A series <em>LCR<\/em> circuit with <em>R<\/em> = 20<img decoding=\"async\" style=\"height: 17px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image001.png\" \/>\u00a0, <em>L<\/em> = 1.5 H and <em>C<\/em> = 35 <img decoding=\"async\" style=\"height: 23px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image017.png\" \/>is connected to a variable-frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?<\/p>\n<p>10:\u00a0 A radio can tune over the frequency range of a portion of MW broadcast band: (800 kHz to 1200 kHz). If its <em>LC<\/em> circuit has an effective inductance of 200<img decoding=\"async\" style=\"height: 20px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image052.png\" \/>\u00a0, what must be the range of its variable capacitor?<\/p>\n[<em>Hint:<\/em> For tuning, the natural frequency i.e., the frequency of free oscillations of the <em>LC<\/em> circuit should be equal to the frequency of the radio wave.]\n<p>11:\u00a0 Figure 7.21 shows a series <em>LCR<\/em> circuit connected to a variable frequency 230 V source. <em>L<\/em> = 5.0 H, <em>C<\/em> = 80<img decoding=\"async\" style=\"height: 23px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image017.png\" \/>, <em>R<\/em> = 40 <img decoding=\"async\" style=\"height: 17px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image001.png\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" id=\"Picture 25\" class=\"alignnone\" style=\"height: 92px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image070.jpg\" alt=\"NCERT Solutions class 12 physics Alternating Current\" width=\"132\" height=\"92\" \/><\/p>\n<p>(a) Determine the source frequency which drives the circuit in resonance.<\/p>\n<p>(b) Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.<\/p>\n<p>(c) Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the <em>LC<\/em> combination is zero at the resonating frequency. 12:\u00a0An <em>LC<\/em> circuit contains a 20 mH inductor and a 50 <img decoding=\"async\" style=\"height: 23px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image017.png\" \/>\u00a0capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be <em>t<\/em> = 0.<\/p>\n<p>(a) What is the total energy stored initially? Is it conserved during <em>LC<\/em> oscillations?<\/p>\n<p>(b) What is the natural frequency of the circuit?<\/p>\n<p>(c) At what time is the energy stored<\/p>\n<p>(i) completely electrical (i.e., stored in the capacitor)? (ii) completely magnetic (i.e., stored in the inductor)?<\/p>\n<p>(d) At what times is the total energy shared equally between the inductor and the capacitor?<\/p>\n<p>(e) If a resistor is inserted in the circuit, how much energy is eventually dissipated as heat?<\/p>\n<p>13:\u00a0 A coil of inductance 0.50 H and resistance 100 <img decoding=\"async\" style=\"height: 17px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image001.png\" \/>\u00a0is connected to a 240 V, 50 Hz ac supply.<\/p>\n<p>(a) What is the maximum current in the coil?<\/p>\n<p>(b) What is the time lag between the voltage maximum and the current maximum?<\/p>\n<p>14:\u00a0Obtain the answers (a) to (b) in Exercise 7.13 if the circuit is connected to a high frequency supply (240 V, 10 kHz). Hence, explain the statement that at very high frequency, an inductor in a circuit nearly amounts to an open circuit. How does an inductor behave in a dc circuit after the steady state?<\/p>\n<p>15:\u00a0 A 100 <img decoding=\"async\" style=\"height: 23px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image017.png\" \/>\u00a0capacitor in series with a 40 <img decoding=\"async\" style=\"height: 17px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image001.png\" \/>resistance is connected to a 110 V, 60 Hz supply.<\/p>\n<p>(a) What is the maximum current in the circuit?<\/p>\n<p>(b) What is the time lag between the current maximum and the voltage maximum?<\/p>\n<p>16:\u00a0Obtain the answers to (a) and (b) in Exercise 7.15 if the circuit is connected to a 110 V, 12 kHz supply? Hence, explain the statement that a capacitor is a conductor at very high frequencies. Compare this behavior with that of a capacitor in a dc circuit after the steady state.<\/p>\n<p>17:\u00a0 Keeping the source frequency equal to the resonating frequency of the series <em>LCR<\/em> circuit, if the three elements, <em>L<\/em>, <em>C<\/em> and <em>R<\/em> are arranged in parallel, show that the total current in the parallel <em>LCR<\/em> circuit is minimum at this frequency. Obtain the current rms value in each branch of the circuit for the elements and source specified in Exercise 7.11 for this frequency.<\/p>\n<p>18: A circuit containing a 80 mH inductor and a 60 <img decoding=\"async\" style=\"height: 23px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image017.png\" \/>\u00a0capacitor in series is connected to a 230 V, 50 Hz supply. The resistance of the circuit is negligible.<\/p>\n<p>(a) Obtain the current amplitude and rms values.<\/p>\n<p>(b) Obtain the rms values of potential drops across each element.<\/p>\n<p>(c) average power transferred to the inductor?<\/p>\n<p>(d) What is the average power transferred to the capacitor?<\/p>\n<p>(e) What is the total average power absorbed by the circuit? [&#8216;Average&#8217; implies &#8216;averaged over one cycle&#8217;.]\n<p>19:\u00a0Suppose the circuit in Exercise 7.18 has a resistance of 15 <img decoding=\"async\" style=\"height: 17px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image001.png\" \/>\u00a0. Obtain the average power transferred to each element of the circuit, and the total power absorbed.<\/p>\n<p>20 : A series <em>LCR<\/em> circuit with <em>L<\/em> = 0.12 H, <em>C<\/em> = 480 nF, <em>R<\/em> = 23 <img decoding=\"async\" style=\"height: 17px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image001.png\" \/>is connected to a 230 V variable frequency supply.<\/p>\n<p>(a) What is the source frequency for which current amplitude is maximum. Obtain this maximum value.<\/p>\n<p>(b) What is the source frequency for which average power absorbed by the circuit is maximum. Obtain the value of this maximum power.<\/p>\n<p>(c) For which frequencies of the source is the power transferred to the circuit half the power at resonant frequency? What is the current amplitude at these frequencies?<\/p>\n<p>(d) What is the <em>Q<\/em>-factor of the given circuit?<\/p>\n<p>21:\u00a0 Obtain the resonant frequency and <em>Q<\/em>-factor of a series <em>LCR<\/em> circuit with <em>L<\/em> = 3.0 H, <em>C<\/em> = 27<img decoding=\"async\" style=\"height: 23px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image017.png\" \/>\u00a0, and <em>R<\/em> = 7.4 <img decoding=\"async\" style=\"height: 17px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image001.png\" \/>\u00a0. It is desired to improve the sharpness of the resonance of the circuit by reducing its &#8216;full width at half maximum&#8217; by a factor of 2. Suggest a suitable way.<\/p>\n<p>22:\u00a0 Answer the following questions:<\/p>\n<p>(a) In any ac circuit, is the applied instantaneous voltage equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit? Is the same true for rms voltage?<\/p>\n<p>(b) A capacitor is used in the primary circuit of an induction coil.<\/p>\n<p>(c) An applied voltage signal consists of a superposition of a dc voltage and an ac voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the dc signal will appear across <em>C<\/em> and the ac signal across <em>L<\/em>.<\/p>\n<p>(d) A choke coil in series with a lamp is connected to a dc line. The lamp is seen to shine brightly. Insertion of an iron core in the choke causes no change in the lamp&#8217;s brightness. Predict the corresponding observations if the connection is to an ac line.<\/p>\n<p>(e) Why is choke coil needed in the use of fluorescent tubes with ac mains? Why can we not use an ordinary resistor instead of the choke coil?<\/p>\n<p>24:\u00a0 At a hydroelectric power plant, the water pressure head is at a height of 300 m and the water flow available is<img decoding=\"async\" style=\"height: 23px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image240.png\" \/>\u00a0. If the turbine generator efficiency is <img decoding=\"async\" style=\"height: 23px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image241.png\" \/>estimate the electric power available from the plant (g=<img decoding=\"async\" style=\"height: 24px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image242.png\" \/>\u00a0.<\/p>\n<p>25:\u00a0 A small town with a demand of 800 kW of electric power at 220 V is situated 15 km away from an electric plant generating power at 440 V. The resistance of the two wire line carrying power is 0.5 <img decoding=\"async\" style=\"height: 17px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/physics\/ch07\/image001.png\" \/>\u00a0per km. The town gets power from the line through a 4000\u2013220 V step-down transformer at a sub-station in the town.<\/p>\n<p>(a) Estimate the line power loss in the form sof heat.<\/p>\n<p>(b) How much power must the plant supply, assuming there is negligible power loss due to leakage?<\/p>\n<p>(c) Characterise the step up transformer at the plant.<\/p>\n<p>26:\u00a0 Do the same exercise as above with the replacement of the earlier transformer by a 40,000-220 V step-down transformer (Neglect, as before, leakage losses though this may not be a good assumption any longer because of the very high voltage transmission involved). Hence, explain why high voltage transmission is preferred?<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_12_Physics\"><\/span><strong>NCERT Solutions for Class 12 Physics<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 12 Physics PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 physics includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Physics have total 20 chapters. 12 Physics NCERT Solutions in PDF for free Download on our website. Ncert physics class 12 solutions PDF and physics ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide<\/p>\n<p>To download\u00a0NCERT Solutions for class 12 Physics, Chemistry, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions class 12 physics Alternating Current Class 12 Physics\u00a0solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. 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