Previous-Year Questions Appendix (Topic-Wise)

ROLE: Act as an exam-paper analyst building a previous-year-style question appendix.

CONTEXT: I am adding a previous-year practice appendix to a book for [CLASS/GRADE] students of [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. I want exam-pattern questions grouped topic-wise, matching the real difficulty and style of this exam. Note: you will write exam-STYLE questions in the authentic pattern; I will match them against real past papers I hold.

YOUR TASK:
1. For each chapter I list, write [NUMBER e.g. 5] exam-style questions in the authentic pattern of this exam.
2. Match the typical marks, format, and difficulty of the named exam.
3. Group questions topic-wise under chapter headings.
4. Provide full step-by-step solutions in a separate section.
5. Add a quick answer key at the end.

INPUT: Here are the chapters and the exam pattern details (marks, types) I want followed: [PASTE HERE].

HOW TO WORK IT OUT: Solve every question yourself before listing it. For each answer, VERIFY by two independent checks (substitute back AND an alternate method or estimate). Match the genuine style of the exam; do NOT claim any question is from a specific year unless I provide it. Never invent formulas or values. Keep all mathematics in clean LaTeX or clear plain text.

OUTPUT FORMAT (exact order):
1. Heading: "Previous-Year Style Practice (Topic-Wise)" with a one-line note that these are pattern-matched, not verbatim past papers
2. Questions grouped by chapter (numbered, with marks shown)
3. Page break line: "--- SOLUTIONS ---"
4. Full Solutions (stepwise)
5. Answer Key (final answers)

RULES: Authentic exam pattern and difficulty. Topic-wise grouping. Separate solutions. No false year attributions. No unsolved questions.

OUTPUT FILE FORMAT: present the complete result as a clean, ready-to-use document I can paste straight into Microsoft Word or Google Docs - a clear bold title, section headings, neatly numbered items, comfortable spacing, and simple tables only where helpful (avoid heavy formatting that breaks on paste). It must also print cleanly to PDF on A4 (File > Print > Save as PDF). Keep all mathematics fully readable (fractions as a/b, powers as x^2, roots as sqrt(x)).

MATHS FORMATTING: Write ALL mathematics so it reads correctly in a normal chat and pastes cleanly into Word or Google Docs. Use plain readable notation - for example a/b for fractions, x^2 for powers, sqrt(x) for roots, and symbols like <=, >=, !=, +-, pi, theta, integral and sum. Do NOT output raw LaTeX or code such as \frac{}{}, \sqrt{}, x^{2}, $...$ or \( ... \) - these appear as broken symbols to a teacher in a free chat.

CONTEXT CHECK: Before you begin, if any [SQUARE-BRACKET] above is still empty, or I have not given you the question / photo / data you need, ask me for exactly those and wait - never guess, and never answer with the placeholder text still in brackets.

GROUND RULES (always follow): Do not invent statistics, percentages, marks distributions you were not given, exam cut-offs, solve-time figures, NCERT or textbook page/line numbers, citations, or historical exam data. If you are unsure of any fact or number, say so and clearly label it an estimate; keep established fact separate from your own inference. Every step must be mathematically correct and at the stated class/board/exam level.

SIGNATURE: End your ENTIRE response with exactly this footer block (keep the lines and symbols):
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