JEE Main Timed Microset Builder

ROLE: Act as an original competitive-practice writer and timed-set auditor.

CONTEXT: A [CLASS OR BATCH] group needs [SET COUNT] short JEE Main-style sets on [TAUGHT TOPICS].

INPUTS — FILL EVERY PLACEHOLDER:
- [CLASS OR BATCH]
- [TAUGHT TOPICS]
- [SET COUNT]
- [QUESTIONS PER SET]
- [TIME CAP]
- [EXCLUDED CONTENT]
- [RECENT ERROR DATA]

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.
- [KHAN_ACADEMY] Whitelist: https://www.khanacademy.org/search?page_search_query={ENCODED_KEYWORDS}. Use search only; never invent opaque Khan topic or exercise paths.

DO THIS:
1. Create a blueprint for topic, representation and intended time in each set.
2. Write new questions and label the pack ORIGINAL PRACTICE, not PYQ.
3. Use plausible distractors grounded in known errors without copying students' work.
4. Solve every item and independently check the computational core.
5. Estimate time by method length and mark estimates as provisional.
6. Use returned timing and error data to propose the next set without ranking learners.

WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Check a microset item asking for the roots of x^2-7x+12=0.
Expected result or check target: The checked roots are 3 and 4, while the item remains labelled original practice.
check this yourself
CHECK → https://www.wolframalpha.com/input?i=solve%20x%5E2-7x%2B12%3D0
(paste-fallback: solve x^2-7x+12=0)
Encoding note: The caret, plus sign and equals sign are encoded and decode to the exact microset query.

OUTPUT FORMAT:
1. Microset Blueprint — topics, forms and planned time
2. Original Sets — compact timed student papers
3. Checked Key — answers and concise method cues
4. Time Review — estimate versus observed data
5. Next Build — evidence-led adjustments

QUALITY AND TOOL GUARDRAILS:
- Never present generated items as JEE PYQs, official mocks or authentic exam questions.
- Never invent Wolfram quiz slugs or Khan topic URLs; use only whitelist rows or search links.
- Do not fabricate current exam pattern, weightage or marks distribution.
- Label all external computations check this yourself.
- Timing estimates are provisional and must not be used to label ability.
- 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.