JEE Negative-Marking Form and Score Sheet

ROLE: Act as a JEE mock-paper setter, option-level verifier and Google Apps Script assessment developer.

CONTEXT: A teacher needs a timed [JEE LEVEL] phone mock on [SYLLABUS] with real negative-marking totals rather than only Google Forms’ positive quiz score.

INPUTS — FILL EVERY PLACEHOLDER:
- [JEE LEVEL]
- [SYLLABUS]
- [QUESTION COUNT]
- [TIME LIMIT]
- [DIFFICULTY MIX]
- [POSITIVE MARKS, DEFAULT 4]
- [NEGATIVE MARKS, DEFAULT 1]

DO THIS:
1. Draft single-correct JEE-style MCQs without calling them authentic PYQs unless the teacher supplies a source.
2. Check each option independently and give a concise solution plus a check-this-yourself link for each computational answer.
3. Generate one complete executable FormApp script that creates a non-required-choice mock so blanks remain possible, a linked score sheet and an installable submission trigger.
4. Have the trigger award the stated positive score for correct, subtract the stated penalty for wrong and award zero for blank, then append the official total to the score sheet.
5. State clearly that native Google Forms quiz points cannot display negative scores and that the linked-sheet total is the official mock score.
6. Log the edit URL, respondent URL and score-sheet URL and include a three-case test protocol.

WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Create a six-question JEE Main negative-marking mock on quadratic equations.
Expected result or check target: The verified roots of 2x^2-7x+3=0 are 1/2 and 3, and the grader awards +4 only for the matching option.
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 space is %20, ^ is %5E, + is %2B and = is %3D.

OUTPUT FORMAT:
1. MOCK BLUEPRINT
2. OPTION-BY-OPTION VERIFIED KEY
3. COMPLETE FORMAPP SCRIPT WITH GRADING TRIGGER
4. RUN IT — script.google.com → New project → paste → Run → View → Logs
5. NEGATIVE-MARKING TEST CASES
6. STUDENT SHARING NOTE

QUALITY AND TOOL GUARDRAILS:
- Output one COMPLETE executable Google Apps Script code block using FormApp and an installed submission trigger; no TODOs or pseudocode.
- After the code, print exactly: script.google.com → New project → paste → Run → View → Logs.
- Never claim native Forms quiz scoring supports negative points; calculate the official +4/-1/0 score in the linked sheet.
- Never present invented questions as real PYQs and never claim a URL creates the form.
- 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.