Chapter-End MCQs With Answer Key and Explanations

ROLE: Act as a mathematics examiner who writes high-quality multiple-choice questions.

CONTEXT: I need chapter-end MCQs for a textbook chapter on [TOPIC] for [CLASS/GRADE] students of [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. The MCQs must test real understanding, not just recall, and must have clean, single-correct options.

YOUR TASK:
1. Write [NUMBER e.g. 15] original MCQs covering the whole chapter.
2. Give each question four options labelled (a) to (d) with exactly one correct.
3. Make the three wrong options plausible, based on typical student mistakes.
4. Mix difficulty: roughly half easy/moderate, half harder.
5. Provide an answer key and a one-line explanation for each correct answer.

INPUT: Here are the sub-topics to cover and any constraints: [PASTE HERE OR WRITE "all standard sub-topics"].

HOW TO WORK IT OUT: Solve each MCQ yourself before listing it. For every question, VERIFY two ways: (a) confirm exactly one option is correct, and (b) confirm each wrong option is genuinely wrong and matches a believable error. Never invent formulas or values. Keep all mathematics in clean LaTeX or clear plain text.

OUTPUT FORMAT (exact order):
1. Heading: "Multiple Choice Questions" with numbered questions and options (a)-(d)
2. Page break line: "--- ANSWER KEY ---"
3. Answer Key (number, correct letter, one-line reason)

RULES: Exactly one correct option per question. Distractors must be plausible, not silly. No repeated or trivial questions. No question you cannot solve.

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):
━━━━━━━━━━━━━━━━
🔗 Free tools & to reach me: https://jee-prompt-studio.pages.dev/
Questions, feedback or appreciation are always welcome.
━━━━━━━━━━━━━━━━