MCQ Bank with Smart Distractors and Answer Key

ROLE: Act as an expert mathematics question-paper setter who writes multiple-choice questions with high-quality distractors.

CONTEXT: I teach [CLASS/GRADE] mathematics for [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. The chapter is [CHAPTER NAME] and the sub-topic is [SUB-TOPIC]. My students are at [easy / medium / hard] level. I want [NUMBER, e.g. 10] single-correct MCQs.

YOUR TASK:
1. Create [NUMBER] MCQs of mixed difficulty (about 40 percent easy, 40 percent medium, 20 percent hard) strictly inside the named chapter and sub-topic.
2. Each question must have exactly four options A, B, C, D with ONE correct answer.
3. For every question, design the three wrong options as SMART DISTRACTORS - each must match a specific, common student mistake (for example sign error, wrong formula, forgetting a unit, off-by-one, mixing up two rules). Never use random or silly options.
4. Keep the difficulty appropriate for the class and exam named above.

INPUT: Here is a sample question that shows the exact level and style I want: [PASTE ONE SAMPLE QUESTION HERE]. If I leave this blank, use standard textbook level for the class and chapter above.

HOW TO WORK IT OUT: Solve every question fully on your own first. Then VERIFY each correct answer by two independent methods (for example solve it a second way, or substitute the answer back). Confirm that exactly one option is correct and the other three are genuinely wrong. Do not invent formulas or values. Keep all mathematics fully legible using clean, simple notation (write fractions, powers and roots clearly).

OUTPUT FORMAT:
SECTION 1 - QUESTIONS: List Q1 to Q[NUMBER]. Under each question show options A, B, C, D on separate lines. Do not reveal answers here.
SECTION 2 - ANSWER KEY AND DISTRACTOR LOGIC: A table with columns: Q No | Correct Option | Why it is correct (one line) | What mistake each wrong option represents.
SECTION 3 - DIFFICULTY TAG: List each Q No with Easy, Medium or Hard.

RULES: Stay strictly inside the chapter. No duplicate questions. No trick wording that confuses good students. Every distractor must be defensible as a real error. If you are unsure an answer is correct, redo it before printing.

FORMAT THE OUTPUT — PRIMARY DELIVERABLE:
Return the complete material as a clean, print-ready A4 handout that can be pasted into Word or Google Docs and saved as PDF. Use a clear title, logical sections, readable mathematics and page-break markers where needed. Keep student material separate from the answer key or teacher notes.


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.
At the very end add a footer line: 'Prepared by [YOUR NAME]', and put 'Compiled by [YOUR NAME]' in the title block at the top.

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.
━━━━━━━━━━━━━━━━