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            <h1>Class XII Physics</h1>
            <p>Generate Customized Sample Papers</p>
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                <h2 class="section-title">Physics Paper Generator</h2>
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                            <label for="chapter1">1. Electric Charge and Fields</label>
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                            <label for="chapter2">2. Electrostatic Potential and Capacitance</label>
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                            <label for="chapter4">4. Moving Charges and Magnetism</label>
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                            <label for="chapter7">7. Alternating Current</label>
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                            <label for="chapter8">8. Electromagnetic Wave</label>
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                            <label for="chapter11">11. Dual Nature of Radiation and Matter</label>
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                            <label for="chapter13">13. Nuclei</label>
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                            <label for="chapter14">14. Semiconductor Electronics, Materials, Devices and Simple Circuits</label>
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                            <label for="chapter15">15. Communication system</label>
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        let schoolName = '';
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        const questions = {
            physics: {
                "Chapter 1": {
                    mcq: [ 
                        { question: "A uniform electric field pointing in positive X-direction exists in a region. Let A be the origin, B be the point on the X-axis at x = +1 cm and C be the point on the Y-axis at y = +1 cm. Then the potential at points A, B and C satisfy:", options: ["V_A < V_B", "V_A > V_B", "V_A < V_C", "V_A > V_C"], answer: "V_A < V_B" },
                        { question: "A conducting wire connects two charged conducting spheres of radii r₁ and r₂ such that they attain equilibrium with respect to each other. The distance of separation between the two spheres is very large as compared to either of their radii. The ratio of the magnitudes of the electric fields at the surfaces of the spheres of radii r₁ and r₂ is:", options: ["r₁/r₂", "r₂/r₁", "r₂²/r₁²", "r₁²/r₂²"], answer: "r₂/r₁" },
                        { question: "The diffraction effect can be observed in:", options: ["sound waves only", "light waves only", "ultrasonic waves only", "sound waves as well as light waves"], answer: "sound waves as well as light waves" },
                        { question: "A capacitor consists of two parallel plates, with an area of cross-section of 0.001 m², separated by a distance of 0.0001 m. If the voltage across the plates varies at the rate of 10⁸ V/s, then the value of displacement current through the capacitor is:", options: ["8.85 × 10⁻³ A", "8.85 × 10⁻⁴ A", "7.85 × 10⁻³ A", "9.85 × 10⁻³ A"], answer: "8.85 × 10⁻³ A" },
                        { question: "In a series LCR circuit, the voltage across the resistance, capacitance and inductance is 10 V each. If the capacitance is short circuited the voltage across the inductance will be:", options: ["10 V", "10√2 V", "10/√2 V", "20 V"], answer: "10√2 V" }
                    ],
                    assertion: [ 
                        { statement1: "On increasing the current sensitivity of a galvanometer by increasing the number of turns may not necessarily increase its voltage sensitivity.", statement2: "The resistance of the coil of the galvanometer increases on increasing the number of turns.", options: ["Both Assertion and Reason are true and Reason is the correct explanation of Assertion", "Both Assertion and Reason are true but Reason is not the correct explanation of Assertion", "Assertion is true but Reason is false", "Both Assertion and Reason are false"], answer: "Both Assertion and Reason are true and Reason is the correct explanation of Assertion" },
                        { statement1: "In a hydrogen atom there is only one electron but its emission spectrum shows many lines.", statement2: "In a given sample of hydrogen there are many atoms each containing one electron; hence many electrons in different atoms may be in different orbits so many transitions from higher to lower orbits are possible.", options: ["Both Assertion and Reason are true and Reason is the correct explanation of Assertion", "Both Assertion and Reason are true but Reason is not the correct explanation of Assertion", "Assertion is true but Reason is false", "Both Assertion and Reason are false"], answer: "Both Assertion and Reason are true and Reason is the correct explanation of Assertion" }
                    ],
                    twoMark: [ 
                        "A platinum surface having work function 5.63 eV is illuminated by a monochromatic source of 1.6 × 10¹⁵ Hz. What will be the minimum wavelength associated with the ejected electron?",
                        "A beam of light consisting of two wavelengths, 4000 Å and 6000 Å, is used to obtain interference fringes in a Young's double-slit experiment. What is the least distance from the central maximum where the dark fringe is obtained?",
                        "State Gauss's theorem in electrostatics. Using this theorem, derive an expression for the electric field due to an infinitely long straight wire of linear charge density λ.",
                        "Define electric flux and write its SI unit. Use Gauss's law to obtain the expression for the electric field due to a uniformly charged infinite plane sheet of charge."
                    ],
                    threeMark: [ 
                        "Find the expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d when (I) a dielectric slab of thickness t and (II) a metallic slab of thickness t, where (t < d) are introduced one by one between the plates of the capacitor. In which case would the capacitance be more and why?",
                        "Draw a ray diagram for the formation of image by a Cassegrain telescope. Why these types of telescopes are preferred over refracting type telescopes? (Write 2 points)",
                        "Draw the energy band diagram for P-type semiconductor at (i) T=0K and (ii) room temperature."
                    ],
                    fiveMark: [ 
                        "Explain briefly, with the help of a labelled diagram, the basic principle of the working of an a.c. generator. In an a.c. generator, coil of N turns and area A is rotated at an angular velocity ω in a uniform magnetic field B. Derive an expression for the instantaneous value of the emf induced in coil. What is the source of energy generation in this device?",
                        "A giant refracting telescope at an observatory has an objective lens of focal length 15 m. If an eyepiece of focal length 1.0 cm is used, what is angular magnification of the telescope in normal adjustment? If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is 3.48 × 10⁶ m, and the radius of lunar orbit is 3.8 × 10⁸ m."
                    ],
                    caseStudy: [ 
                        { case: "Case Study Based Question: Motion of Charge in Magnetic Field\nAn electron with speed v₀ << c moves in a circle of radius r₀ in a uniform magnetic field. This electron is able to traverse a circular path as the magnetic force acting on the electron is perpendicular to both v₀ and B, as shown in the figure. This force continuously deflects the particle sideways without changing its speed and the particle will move along a circle perpendicular to the field. The time required for one revolution of the electron is T₀.", questions: ["If v = 2v₀, then the radius of the circular path now becomes", "If v = 2v₀, then the time required for one revolution of the electron (T₀) will change to", "A charged particle is projected in a magnetic field B = (2i + 4j) × 10² T. The acceleration of the particle is found to be a = (xi + 2j) m/s². Find the value of x.", "If the given electron has a velocity not perpendicular to B, then trajectory of the electron is"] },
                        { case: "Case Study Based Question: Photoelectric effect\nIt is the phenomenon of emission of electrons from a metallic surface when light of a suitable frequency is incident on it. The emitted electrons are called photoelectrons. Nearly all metals exhibit this effect with ultraviolet light but alkali metals like lithium, sodium, potassium, cesium etc. show this effect even with visible light. It is an instantaneous process i.e. photoelectrons are emitted as soon as the light is incident on the metal surface. The number of photoelectrons emitted per second is directly proportional to the intensity of the incident radiation. The maximum kinetic energy of the photoelectrons emitted from a given metal surface is independent of the intensity of the incident light and depends only on the frequency of the incident light. For a given metal surface there is a certain minimum value of the frequency of the incident light below which emission of photoelectrons does not occur.", questions: ["In a photoelectric experiment plate current is plotted against anode potential. Which statement is correct about the curves A, B and C?", "Photoelectrons are emitted when a zinc plate is", "The threshold frequency for photoelectric effect on sodium corresponds to a wavelength of 500 nm. Its work function is about", "The maximum kinetic energy of photoelectrons emitted from a surface when photons of energy 6 eV fall on it is 4 eV. The stopping potential is"] }
                    ]
                },
                "Chapter 2": {
                    mcq: [ 
                        { question: "A long straight wire of circular cross section of radius 'a' carries a steady current I. The current is uniformly distributed across its cross section. The ratio of magnitudes of the magnetic field at a point a/2 above the surface of wire to that of a point a/2 below its surface is:", options: ["4:1", "1:1", "4:3", "3:4"], answer: "1:1" },
                        { question: "The distance of closest approach of an alpha particle is d when it moves with a speed V towards a nucleus. Another alpha particle is projected with higher energy such that the new distance of the closest approach is d/2. What is the speed of projection of the alpha particle in this case?", options: ["V / 2", "√2 V", "2 V", "4 V"], answer: "2 V" },
                        { question: "A point object is placed at the centre of a glass sphere of radius 6 cm and refractive index 1.5. The distance of virtual image from the surface of the sphere is:", options: ["2 cm", "4 cm", "6 cm", "12 cm"], answer: "6 cm" },
                        { question: "Colours observed on a CD (Compact Disk) is due to:", options: ["Reflection", "Diffraction", "Dispersion", "Absorption"], answer: "Diffraction" },
                        { question: "The number of electrons made available for conduction by dopant atoms depends strongly upon:", options: ["doping level", "increase in ambient temperature", "energy gap", "options (A) and (B) both"], answer: "options (A) and (B) both" }
                    ],
                    assertion: [ 
                        { statement1: "Nuclei having mass number about 60 are least stable.", statement2: "When two or more light nuclei are combined into a heavier nucleus then the binding energy per nucleon will decrease.", options: ["Both Assertion and Reason are true and Reason is the correct explanation of Assertion", "Both Assertion and Reason are true but Reason is not the correct explanation of Assertion", "Assertion is true but Reason is false", "Both Assertion and Reason are false"], answer: "Both Assertion and Reason are false" },
                        { statement1: "de Broglie's wavelength of a freely falling body keeps decreasing with time.", statement2: "The momentum of the freely falling body increases with time.", options: ["Both Assertion and Reason are true and Reason is the correct explanation of Assertion", "Both Assertion and Reason are true but Reason is not the correct explanation of Assertion", "Assertion is true but Reason is false", "Both Assertion and Reason are false"], answer: "Both Assertion and Reason are true and Reason is the correct explanation of Assertion" }
                    ],
                    twoMark: [ 
                        "P and Q are two identical charged particles each of mass 4 × 10⁻²⁶ kg and charge 4.8 × 10⁻¹⁹ C, each moving with the same speed of 2.4 × 10⁵ m/s as shown in the figure. The two particles are equidistant (0.5 m) from the vertical Y-axis. At some instant, a magnetic field B is switched on so that the two particles undergo head-on collision. Find (I) the direction of the magnetic field and (II) the magnitude of the magnetic field applied in the region.",
                        "Binding energy per nucleon vs mass number curve for nuclei is shown in the figure. W, X, Y and Z are four nuclei indicated on the curve. Identify which of the following nuclei is most likely to undergo (i) Nuclear Fission (ii) Nuclear Fusion. Justify your answer.",
                        "A cylindrical conductor of length l and cross-section area A is connected to a DC source. Under the influence of electric field set up due to source, the free electrons begin to drift in the opposite direction of the electric field. (I) Draw the curve showing the dependency of drift velocity on relaxation time. (II) If the DC source is replaced by a source whose current changes its magnitude with time such that I = I₀ sin 2πνt, where ν is the frequency of variation of current, then determine the average drift velocity of the free electrons over one complete cycle."
                    ],
                    threeMark: [ 
                        "Identify the circuit elements X and Y as shown in the given block diagram and draw the output waveforms of X and Y. If the centre tapping is shifted towards Diode D₁ as shown in the diagram, draw the output waveform of the given circuit.",
                        "A boy is holding a smooth, hollow and non-conducting pipe vertically with charged spherical ball of mass 10 g carrying a charge of +10 mC inside it which is free to move along the axis of the pipe. The boy is moving the pipe from East to West direction in the presence of magnetic field of 2T. With what minimum velocity, should the boy move the pipe such that the ball does not move along the axis. Also determine the direction of the magnetic field.",
                        "A light ray entering a right-angled prism undergoes refraction at the face AC as shown in Fig. 1. (I) What is the refractive index of the material of the prism in Fig. 1? (II) (a) If the side AC of the above prism is now surrounded by a liquid of refractive index 2/√3, as shown in Fig. 2, determine if the light ray continues to graze along the interface AC or undergoes total internal reflection or undergoes refraction into the liquid. (b) Draw the ray diagram to represent the path followed by the incident ray with the corresponding angle values."
                    ],
                    fiveMark: [ 
                        "With the help of a diagram, explain the principle of a device which changes a low ac voltage into a high voltage. Deduce the expression for the ratio of secondary voltage to the primary voltage in terms of the ratio of the number of turns of primary and secondary winding. For an ideal transformer, obtain the ratio of primary and secondary currents in terms of the ratio of the voltages in the secondary and primary coils. Write any two sources of the energy losses which occur in actual transformers.",
                        "A compound microscope consists of an objective lens of focal length 2.0 cm and an eyepiece of focal length 6.25 cm separated by a distance of 15 cm. How far from the objective should an object be placed in order to obtain the final image at (a) the least distance of distinct vision (25 cm) and (b) infinity? What is the magnifying power of the microscope in each case?"
                    ],
                    caseStudy: [ 
                        { case: "Case Study Based Question: Motion of Charge in Magnetic Field\nAn electron with speed v₀ << c moves in a circle of radius r₀ in a uniform magnetic field. This electron is able to traverse a circular path as the magnetic force acting on the electron is perpendicular to both v₀ and B, as shown in the figure. This force continuously deflects the particle sideways without changing its speed and the particle will move along a circle perpendicular to the field. The time required for one revolution of the electron is T₀.", questions: ["If v = 2v₀, then the radius of the circular path now becomes", "If v = 2v₀, then the time required for one revolution of the electron (T₀) will change to", "A charged particle is projected in a magnetic field B = (2i + 4j) × 10² T. The acceleration of the particle is found to be a = (xi + 2j) m/s². Find the value of x.", "If the given electron has a velocity not perpendicular to B, then trajectory of the electron is"] },
                        { case: "Case Study Based Question: Photoelectric effect\nIt is the phenomenon of emission of electrons from a metallic surface when light of a suitable frequency is incident on it. The emitted electrons are called photoelectrons. Nearly all metals exhibit this effect with ultraviolet light but alkali metals like lithium, sodium, potassium, cesium etc. show this effect even with visible light. It is an instantaneous process i.e. photoelectrons are emitted as soon as the light is incident on the metal surface. The number of photoelectrons emitted per second is directly proportional to the intensity of the incident radiation. The maximum kinetic energy of the photoelectrons emitted from a given metal surface is independent of the intensity of the incident light and depends only on the frequency of the incident light. For a given metal surface there is a certain minimum value of the frequency of the incident light below which emission of photoelectrons does not occur.", questions: ["In a photoelectric experiment plate current is plotted against anode potential. Which statement is correct about the curves A, B and C?", "Photoelectrons are emitted when a zinc plate is", "The threshold frequency for photoelectric effect on sodium corresponds to a wavelength of 500 nm. Its work function is about", "The maximum kinetic energy of photoelectrons emitted from a surface when photons of energy 6 eV fall on it is 4 eV. The stopping potential is"] }
                    ]
                }
            }
        };

        function getRandomQuestions(selectedChapters, type, count) {
            let allQuestions = [];

            if (selectedChapters.includes("Full Paper")) {
                for (let chapter in questions.physics) {
                    if (questions.physics[chapter][type]) {
                        allQuestions = allQuestions.concat(questions.physics[chapter][type]);
                    }
                }
            } else {
                selectedChapters.forEach(chapter => {
                    if (questions.physics[chapter] && questions.physics[chapter][type]) {
                        allQuestions = allQuestions.concat(questions.physics[chapter][type]);
                    }
                });
            }

            allQuestions = allQuestions.sort(() => Math.random() - 0.5);
            return allQuestions.slice(0, count);
        }

        function showChapterSelection() {
            document.getElementById('startScreen').classList.add('hidden');
            document.getElementById('chapterSelection').classList.remove('hidden');
        }

        function toggleChapters() {
            const fullPaperCheckbox = document.getElementById('fullPaper');
            const checkboxes = document.querySelectorAll('input[name="chapter"]:not(#fullPaper)');
            checkboxes.forEach(cb => cb.disabled = fullPaperCheckbox.checked);
        }

        function backToStart() {
            document.getElementById('generatedPaperContainer').classList.add('hidden');
            document.getElementById('startContainer').classList.remove('hidden');
            document.getElementById('chapterSelection').classList.add('hidden');
            document.getElementById('startScreen').classList.remove('hidden');
            questionCounter = 1;
        }

        function promptSchoolName() {
            schoolName = prompt("Write your school/institute name").toUpperCase();
            if (!schoolName) {
                alert("School/Institute name is required!");
            } else {
                promptSession();
            }
        }

        function promptSession() {
            sessionYear = prompt("Enter the academic session (e.g., 2024-25)").toUpperCase();
            if (!sessionYear) {
                alert("Academic session is required!");
            } else {
                generatePaper();
            }
        }

        function generatePaper() {
            document.getElementById('startContainer').classList.add('hidden');
            const generatedPaperContainer = document.getElementById('generatedPaperContainer');
            generatedPaperContainer.classList.remove('hidden');
            generatedPaperContainer.innerHTML = '';
            
            let paperContent = `
                <div class="header">
                    <h2>${schoolName}</h2>
                </div>
                <div class="content-area">
                    <div class="paper-header">
                        <h3>SAMPLE QUESTION PAPER PHYSICS-042</h3>
                        <h3>CLASS - XII</h3>
                        <h3>Academic Session ${sessionYear}</h3>
                    </div>
                    <div class="paper-meta">
                        <div>Maximum Marks: 70</div>
                        <div>Time Allowed: 3 hours</div>
                    </div>
                    <div class="instructions">
                        <p><strong>General Instructions:</strong></p>
                        <ol>
                            <li>There are 33 questions in all. All questions are compulsory.</li>
                            <li>This question paper has five sections: Section A, Section B, Section C, Section D and Section E.</li>
                            <li>All the sections are compulsory.</li>
                            <li><strong>Section A</strong> contains <strong>sixteen questions</strong>, <strong>twelve MCQ and four Assertion Reasoning based of 1 mark each</strong>, <strong>Section B</strong> contains <strong>five questions of two marks each</strong>, <strong>Section C</strong> contains seven questions of three marks each, <strong>Section D</strong> contains <strong>two case study-based questions of four marks each</strong> and <strong>Section E</strong> contains <strong>three long answer questions of five marks each</strong>.</li>
                            <li>There is no overall choice. However, an internal choice has been provided in one question in Section B, one question in Section C, one question in each CBQ in Section D and all three questions in Section E. You have to attempt only one of the choices in such questions.</li>
                            <li>Use of calculators is not allowed.</li>
                            <li>You may use the following values of physical constants where ever necessary:
                                <ul style="margin-top: 10px; list-style-type: none; padding-left: 0;">
                                    <li>i. c = 3 × 10⁸ m/s</li>
                                    <li>ii. mₑ = 9.1 × 10⁻³¹ kg</li>
                                    <li>iii. mₚ = 1.7 × 10⁻²⁷ kg</li>
                                    <li>iv. e = 1.6 × 10⁻¹⁹ C</li>
                                    <li>v. μ₀ = 4π × 10⁻⁷ T m A⁻¹</li>
                                    <li>vi. h = 6.63 × 10⁻³⁴ J s</li>
                                    <li>vii. ε₀ = 8.854 × 10⁻¹² C² N⁻¹ m⁻²</li>
                                    <li>viii. Avogadro's number = 6.023 × 10²³ per gram mole</li>
                                </ul>
                            </li>
                        </ol>
                    </div>
            `;

            const selectedChapters = document.getElementById('fullPaper').checked 
                ? ["Full Paper"] 
                : Array.from(document.querySelectorAll('input[name="chapter"]:checked')).map(cb => cb.value);

            // Section A - MCQs
            const mcqs = getRandomQuestions(selectedChapters, 'mcq', 12);
            paperContent += `
                <div class="question-section">
                    <h4 class="section-heading">SECTION A (16x1=16 marks)</h4>
                    <p>Question 1 to 12 are multiple choice questions. Only one of the choices is correct. Select and write the correct choice as well as the answer to these questions.</p>
            `;
            mcqs.forEach((q, i) => {
                paperContent += `
                    <div class="question">
                        <p class="question-text">Q${questionCounter++}. ${q.question}</p>
                        ${q.options.map((opt, j) => 
                            `<p class="option">${String.fromCharCode(65 + j)}. ${opt}</p>`
                        ).join('')}
                    </div>
                `;
            });

            // Section A - Assertion Reasoning
            const assertions = getRandomQuestions(selectedChapters, 'assertion', 4);
            paperContent += `
                    <h4 class="section-heading" style="margin-top: 30px;">For Questions 13 to 16, two statements are given – one labelled Assertion (A) and other labelled Reason (R). Select the correct answer to these questions from the options as given below:</h4>
                    <p style="margin-bottom: 15px;">
                        A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.<br>
                        B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.<br>
                        C. If Assertion is true but Reason is false.<br>
                        D. If both Assertion and Reason are false.
                    </p>
            `;
            assertions.forEach((q, i) => {
                paperContent += `
                    <div class="question">
                        <p class="question-text">Q${questionCounter++}. Assertion (A): ${q.statement1}</p>
                        <p class="option">Reason (R): ${q.statement2}</p>
                        ${q.options.map((opt, j) => 
                            `<p class="option">${String.fromCharCode(65 + j)}. ${opt}</p>`
                        ).join('')}
                    </div>
                `;
            });

            // Section B - 2 marks
            const twoMarks = getRandomQuestions(selectedChapters, 'twoMark', 5);
            paperContent += `
                </div>
                <div class="question-section">
                    <h4 class="section-heading">SECTION B (05x2=10 marks)</h4>
                    <p>Question No. 17 to 21 are short answer questions carrying 2 marks each.</p>
            `;
            twoMarks.forEach(q => {
                paperContent += `
                    <div class="question">
                        <p class="question-text">Q${questionCounter++}. ${q}</p>
                    </div>
                `;
            });

            // Section C - 3 marks
            const threeMarks = getRandomQuestions(selectedChapters, 'threeMark', 7);
            paperContent += `
                </div>
                <div class="question-section">
                    <h4 class="section-heading">SECTION C (07x3=21 marks)</h4>
                    <p>Question No. 22 to 28 are short answer questions carrying 3 marks each.</p>
            `;
            threeMarks.forEach(q => {
                paperContent += `
                    <div class="question">
                        <p class="question-text">Q${questionCounter++}. ${q}</p>
                    </div>
                `;
            });

            // Section D - Case Studies
            const caseStudies = getRandomQuestions(selectedChapters, 'caseStudy', 2);
            paperContent += `
                </div>
                <div class="question-section">
                    <h4 class="section-heading">SECTION D (02x4=08 marks)</h4>
                    <p>Question No. 29 to 30 are case-based/data-based questions carrying 4 marks each.</p>
            `;
            caseStudies.forEach(cs => {
                paperContent += `
                    <div class="question">
                        <p class="question-text">Q${questionCounter++}. ${cs.case}</p>
                        ${cs.questions.map((subQ, j) => 
                            `<p class="option">${j + 1}. ${subQ}</p>`
                        ).join('')}
                    </div>
                `;
            });

            // Section E - 5 marks
            const fiveMarks = getRandomQuestions(selectedChapters, 'fiveMark', 3);
            paperContent += `
                </div>
                <div class="question-section">
                    <h4 class="section-heading">SECTION E (03x5=15 marks)</h4>
                    <p>Question No. 31 to 33 are long answer questions carrying 5 marks each.</p>
            `;
            fiveMarks.forEach(q => {
                paperContent += `
                    <div class="question">
                        <p class="question-text">Q${questionCounter++}. ${q}</p>
                    </div>
                `;
            });

            // Add buttons below the generated paper
            paperContent += `
                    </div>
                    <div class="action-buttons">
                        <button class="btn btn-primary" onclick="downloadPDF()">Download as PDF</button>
                        <button class="btn btn-success" onclick="window.print()">Print</button>
                        <button class="btn btn-danger" onclick="backToStart()">Back to Start</button>
                    </div>
                </div>
            `;

            generatedPaperContainer.innerHTML = paperContent;
        }

        async function downloadPDF() {
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            // Create a temporary div with optimized settings
            const tempDiv = document.createElement('div');
            tempDiv.style.position = 'absolute';
            tempDiv.style.left = '-9999px';
            tempDiv.style.width = '794px'; // A4 width in pixels (210mm)
            tempDiv.style.backgroundColor = 'white';
            tempDiv.style.padding = '20px';
            tempDiv.innerHTML = element.innerHTML;
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            try {
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                let remainingHeight = tempDiv.scrollHeight;
                let pageNum = 1;
                
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                    const canvas = await html2canvas(tempDiv, {
                        scale: 2,
                        windowHeight: pageHeight * 3.78, // mm to px
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                        useCORS: true,
                        backgroundColor: '#ffffff',
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                    const imgData = canvas.toDataURL('image/jpeg', 0.92);
                    
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                        pdf.addPage('a4', 'portrait');
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                    pdf.addImage(imgData, 'JPEG', 12.7, 12.7, pageWidth, canvas.height * pageWidth / canvas.width);
                    
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                document.body.removeChild(tempDiv);
                pdf.save(`${schoolName}_Physics_Paper.pdf`);
                
            } catch (error) {
                console.error('PDF generation error:', error);
                alert('Error generating PDF. Please try again.');
                document.body.removeChild(tempDiv);
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