DPP with Rising Marks (1 to 5 Marks)

ROLE: Act as a mathematics exam-setter who designs questions weighted by marks like a real exam.

CONTEXT: I want a DPP where questions carry increasing marks, for [CLASS/GRADE] students preparing for [BOARD or EXAM e.g. CBSE / ICSE / State Board]. Topic = [TOPIC]. Total marks = [TOTAL e.g. 20].

YOUR TASK:
1. Create a sheet whose questions rise in marks: start with 1-mark questions, move through 2 and 3 marks, and end with 4 or 5-mark long questions.
2. Higher-mark questions must genuinely require more steps and reasoning, matching how the chosen board awards marks.
3. Make the marks add up exactly to the total.
4. Provide a step-wise MARKING SCHEME showing where each mark is earned, plus hints and full solutions.

INPUT: Topic = [TOPIC]. Class = [CLASS/GRADE]. Board/Exam = [BOARD or EXAM]. Total marks = [TOTAL]. If unclear, assume and state it.

HOW TO WORK IT OUT: Solve each question yourself first and confirm the workload matches its marks. Verify each final answer by two independent checks. Make the marks total exactly. Never invent formulas or values. Keep all maths legible in clean LaTeX or clear plain text.

OUTPUT FORMAT, in this exact order:
1. TITLE BLOCK: 'Marks-Weighted DPP - [TOPIC] - Total [TOTAL] marks' with class, board/exam, and 'Compiled by [YOUR NAME]'.
2. SECTION A - QUESTIONS: numbered questions, each showing its marks in brackets, ordered low to high marks, printable.
3. SECTION B - HINTS: one one-line hint per question.
4. SECTION C - MARKING SCHEME: for each question, how each mark is awarded step by step.
5. SECTION D - ANSWER KEY AND FULL SOLUTIONS: final answers with clean working.

RULES: Marks must rise across the sheet and sum exactly to the total. Long questions must deserve their marks. Marking scheme must match the official board style.

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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