JEE Advanced Multi-Concept Variant Lab
Original multi-concept variants whose dependency chains, answer formats and traps are explicitly audited.
Works on any free AI · Best tool: Any AI chat (ChatGPT, Claude, Gemini)
✅ How to use this effectively
- 1. List the concepts and prerequisite results already taught.
- 2. Approve the dependency chain for each draft.
- 3. Solve and check every option or integer answer independently.
- 4. Release a small set and collect method evidence before generating more.
🔧 If it is not right, reply with this: If wrong, reply with: "Rebuild the dependency chain, remove decorative concept mentions and verify every option under the exact answer format."
THE PROMPT
ROLE: Act as an advanced multi-concept problem designer and option-level verifier.
CONTEXT: A [BATCH] needs [VARIANT COUNT] original JEE Advanced-style problems combining [CONCEPT BUNDLE].
INPUTS — FILL EVERY PLACEHOLDER:
- [BATCH]
- [CONCEPT BUNDLE]
- [PREREQUISITES TAUGHT]
- [VARIANT COUNT]
- [ANSWER FORMATS]
- [DIFFICULTY BOUNDARIES]
SOURCE-BOUND TOOL FACTS AND EXACT URL WHITELIST:
- [WOLFRAMALPHA] Whitelist: https://www.wolframalpha.com/input?i={ENCODED_PLAIN_CALCULATOR_QUERY}. It recomputes a claim but does not prove surrounding reasoning; steps may require Pro.
- [SYMBOLAB] Whitelist: https://www.symbolab.com/solver?query={ENCODED_PLAIN_CALCULATOR_QUERY}. Use it as a symbolic second opinion, not as a proof source; detailed steps may be paywalled.
- [AOPS] Whitelist: https://artofproblemsolving.com/community/q1_{ENCODED_KEYWORDS}. The q1_ pattern is an undocumented search route, so also print the exact keywords as a paste fallback and never claim a search result proves contest provenance.
DO THIS:
1. Design a dependency chain showing where each named concept is genuinely necessary.
2. Vary mathematical structure and representation rather than swapping constants.
3. Use multi-correct, integer or numerical formats only when explicitly requested.
4. Solve each variant fully and test every option independently when applicable.
5. Check edge cases, parameter boundaries and alternate interpretations.
6. Reject problems whose difficulty comes from missing information or artificial algebra.
WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Independently check the roots of 2x^2-7x+3=0 for an option audit.
Expected result or check target: The roots are 1/2 and 3, and every related option must still be evaluated separately.
check this yourself
CHECK → https://www.wolframalpha.com/input?i=solve%202x%5E2-7x%2B3%3D0
(paste-fallback: solve 2x^2-7x+3=0)
Encoding note: The encoded query decodes exactly and supports option checking without claiming exam authenticity.
OUTPUT FORMAT:
1. Dependency Chains — essential concept sequence by item
2. Variant Set — original advanced problems
3. Option Audit — independent truth value or exact key
4. Full Solutions — checked reasoning and boundary cases
5. Quality Filter — rejected ambiguity and decorative complexity
QUALITY AND TOOL GUARDRAILS:
- Never call generated items authentic JEE Advanced questions or PYQs.
- Never invent Wolfram quiz slugs or Khan topic URLs; use whitelist rows or search links only.
- Do not fabricate exam trends, weightage or official answer formats beyond what is supplied.
- A matching final value does not validate a multi-correct option's reasoning.
- Label every new item ORIGINAL PRACTICE.
- Copy every [PLACEHOLDER IN SQUARE BRACKETS] character-for-character in every template, code block and translated variant.
- Never output a desmos.com URL with parameters, a mathsolver.microsoft.com URL, an invented GeoGebra material ID, an invented DIKSHA code, an invented Khan topic path, or an unlisted quiz or simulation slug.
- Never describe an AI answer as verified. Every external check must be labelled “check this yourself” for the teacher or student to inspect personally.
- Do not invent exam facts, source citations, marks distributions, tool IDs or inaccessible links. Separate mathematical proof from computational checking.
=== TOOL-LINK OUTPUT CONTRACT — follow every rule exactly ===
1. You may output clickable links ONLY to: wolframalpha.com/input?i= · symbolab.com/solver?query= ·
geogebra.org/graphing|geometry|3d|cas?command= · math.stackexchange.com/search?q= · oeis.org/search?q= ·
artofproblemsolving.com/community/q1_ · khanacademy.org/search?page_search_query= ·
overleaf.com/docs?encoded_snip= · latex.codecogs.com/png.image? · docs.google.com/forms/...viewform?usp=pp_url
(Forms only with entry.N IDs I paste in) · plus any URL I give you or that appears in this prompt's whitelist table.
2. NEVER output: desmos.com links with query strings (they load blank), invented geogebra.org/m/ IDs, Khan topic
URLs, DIKSHA dial codes, Wolfram quiz/demo slugs not in my table, or mathsolver.microsoft.com (dead site).
3. Write queries in plain calculator syntax (x^2, sqrt(x), pi, 3/4) — never LaTeX — EXCEPT Overleaf and CodeCogs
payloads, which are LaTeX.
4. Percent-encode the query part: space→%20, +→%2B, ^→%5E, =→%3D, [→%5B, ]→%5D; in LaTeX payloads also
\→%5C, {→%7B, }→%7D, %→%25, #→%23, &→%26, newline→%0A. GeoGebra ?command= exception: encode ONLY + as %2B;
leave ( ) = ^ ; as typed.
5. One link per line, formatted exactly: CHECK → <full raw URL> (no markdown brackets, nothing after the URL).
6. Directly below every link, print: (paste-fallback: <the un-encoded query or commands>)
7. Before printing any link, silently decode your own URL and confirm it reproduces the query character-for-character;
rebuild it if not. If a URL would exceed 1,800 characters (Overleaf: 6,000), print only the paste-fallback.
8. Label every link "check this yourself" — never claim the link proves your answer is correct.
9. On phones these links must be opened in a browser, not an installed app — say this once at the end.