JEE Advanced Physics Solver

A verified-against-internet solver tuned for JEE Advanced's higher rigor and stricter marking. Advanced punishes sloppiness more than Main — one wrong selection in a multi-correct MCQ can zero the whole question — so the verification loop is not optional, it's the whole value of the skill.

JEE Advanced context (for tuning answers)

• Paper format: two 3-hour papers. Each has ~18 physics questions. Mixed question types:
• Single-correct MCQ (4 options, one right): +3 / −1.
• Multi-correct MCQ (4 options, one or more right): +4 for fully correct, partial credit (+1 per correct if no wrong), −2 for any wrong.
• Integer/numerical answer (two decimal or integer): +3/+4, 0.
• Matrix match / paragraph / comprehension: shorter clusters with shared stems.
• Time pressure: slower than Main — 5–8 min per hard problem is reasonable.
• Syllabus: NCERT-based but with deeper treatment. Expect:
• Multi-concept problems (mechanics + thermodynamics; optics + interference; EM + modern).
• Calculus at JEE-level rigor (but not beyond — no contour integrals).
• Limiting cases, dimensional analysis as a check, and sometimes "select all that apply" where you must prove each.
• Exact symbolic answers are common (e.g., "express in terms of m, g, L" rather than "give a number").
• Default constants: g = 10 unless specified, π = 3.14, c = 3×10⁸ m/s, ε₀ = 8.85×10⁻¹², h = 6.63×10⁻³⁴ J·s.

The workflow

All seven steps, in order. For multi-correct questions, steps 4–5 must evaluate every option independently.

0. Make sure WebSearch is loaded

Before step 1, check whether the WebSearch tool is available. If it isn't in your current tool list, load it via ToolSearch with {"query": "select:WebSearch,WebFetch", "max_results": 2}. The internet cross-check in step 3 is especially important for JEE Advanced because of the official-key weighting and multi-correct traps — if WebSearch genuinely cannot be loaded, continue without it but flag explicitly in the draft that the internet cross-verification was unavailable.

1. Extract the problem cleanly

• Transcribe the full problem including diagrams described in words. Advanced problems often have subtle setups (wedge on a wedge, two pulleys with different masses) — draw the figure out in words in your reasoning.
• Echo the restatement and name the question type explicitly (single-correct / multi-correct / integer / matrix).
• For multi-correct: list all four options verbatim — you'll evaluate each.

2. Classify and identify coupling

Name the topic(s). Advanced commonly couples two areas in one question — identify them both. Examples:

• "Block on rotating turntable with friction" → rotation + friction + circular motion.
• "Gas in a cylinder undergoing two processes" → thermodynamics + kinematics (if piston moves).
• "Charged particle in a magnetic field with gravity" → EM + projectile.

Flag all conservation laws available (energy, momentum, angular momentum, charge) — they are Advanced's favorite shortcuts.

3. Internet search for existing solutions

Search patterns that work well for Advanced problems:

• "[first 15 distinctive words]" JEE Advanced solution
• JEE Advanced [year] Paper [1/2] Q[number] solution
• [topic] [key numbers or setup] JEE Advanced answer key
• IIT JEE Advanced [year] physics [topic] solution

For problems that have appeared in past papers, the official answer key (NTA / JEE Advanced official site) is the highest-trust source — weigh it above coaching sites. For multi-correct, coaching sites sometimes disagree on which options are correct; the official key settles it.

Capture:

• All four option labels (for multi-correct, note which are marked correct in the key).
• The method — Advanced solutions often reveal a clever approach you'd miss.
• Sources that agree vs. disagree; count by sites, not links.

If the search returns nothing relevant after 2 queries, note it and move to step 4. Advanced problems in the last year or two sometimes have thin coverage online.

4. Build your own solution independently

Before looking at the internet's method, derive cold:

a. State the concept(s) — if multi-concept, list each. b. Write governing equations symbolically — Advanced usually wants you to see the full structure before plugging numbers. c. Choose the cleverest path — look for conservation laws, symmetry, energy arguments, or non-obvious frames. A force-balance solution where an energy argument would work is a warning sign. d. Solve symbolically, keeping exact forms (√2, π, etc.) until the last step. e. SymPy verification: use scripts/verify.py as a starting point but expect to write bespoke code for Advanced problems. Keep Rational throughout; call N(expr, 6) only at the end. f. For multi-correct: evaluate each of the four options as a separate claim. Mark each as True or False with a one-line reason. Don't stop at the first correct option.

5. Cross-verify and iterate

Lay your answer beside the internet's:

• Single-correct: same option letter = done. Different = investigate.
• Multi-correct: same set of correct options. A difference of even one option means disagreement — investigate.
• Integer / numerical: same value (allowing for rounding tolerance the question specifies).

When disagreeing:

• Check for the Advanced-specific traps (see below).
• Re-derive under the assumption each version is right — which assumption makes your version match? Which makes the internet's? That usually reveals the missing case.
• Iteration cap: 3. If still disagreeing after 3 attempts, flag it explicitly: "⚠️ My SymPy-verified answer is {X}. Most online sources say {Y}. Disagreement remains after 3 iterations. My best guess at the cause: {reason}. Please adjudicate before sending."
• Never silently override a SymPy-verified answer to match a popular coaching answer — Advanced keys have been wrong in the past, and a teacher flagging the mismatch to students can be more valuable than a "correct" answer delivered with false confidence.

6. Compose the WhatsApp-ready reply

Advanced problems often need more detail than Main. Use this format, but feel free to extend the Steps section:

*[Topic] — JEE Advanced*

*Concept:* [principle; if multi-concept, list both]

*Key formula:* [governing equation(s)]

*Given:* [quantities, units, sign conventions]

*Derivation:*
1. [symbolic setup]
2. [key manipulation — conservation, substitution]
3. [simplify to closed form]
4. [substitute numbers]

*Answer:* [value with units, option letter(s) if MCQ]

For multi-correct questions, list each option's verdict:

*Options:*
(A) ✓ — [one-line reason]
(B) ✗ — [one-line reason]
(C) ✓ — [one-line reason]
(D) ✗ — [one-line reason]
*Correct: A and C*

For integer-type, give the exact integer and note the range if the question specifies tolerance.

Formatting:

• WhatsApp *bold* for headings.
• No LaTeX. Unicode for Greek, operators, and superscripts where readable.
• Under ~500 words for the full derivation reply.

7. Stage for teacher approval

Default: stage, don't auto-send.

1. Show the draft clearly marked, with the disagreement flag at top if iteration didn't converge.
2. Target batch: "JEE Advanced" or "IIT batch" — resolve via .auto-memory/project_whatsapp_mapping.md.
3. Say: "Draft ready for [batch]. Say 'send it', 'edit: ...', or 'just for me'."
4. Call WhatsApp list_chats + send_message only on explicit confirm.

JEE Advanced–specific watchouts

These trip students and LLMs alike — always check:

• Multi-correct "partial match": evaluating only the first correct option costs marks. Work through all four, always.
• Limiting cases: Advanced often asks "in the limit t → ∞" or "as M → ∞". Substitute first, then simplify. Taking the limit after too many substitutions can drop terms incorrectly.
• Symbolic vs numeric answer: if the problem gives symbols (m, g, L) with no numeric values, the answer is symbolic. Don't invent numbers.
• Moment of inertia — axis through which point: Advanced loves shifted-axis problems. Always check if the axis is through CM or at an offset.
• Non-inertial frames: if the problem's frame is accelerating, add pseudo-forces. Advanced will sometimes give you two frames and ask for comparisons.
• Thermodynamic processes: "slowly" = quasi-static. "Adiabatic" = no heat. "Free expansion" = irreversible, isothermal ideal gas. Each has different work/heat behavior.
• Interference and diffraction intensities: I ∝ cos²(Δφ/2) for two-source. Don't confuse with I ∝ (sinα/α)² for diffraction.
• Circuit steady state vs transient: in steady state, inductors = short, capacitors = open. Many Advanced problems switch from transient to steady in the same question.
• Relativistic electrons: almost always non-relativistic in JEE, but check if kinetic energies exceed ~10 keV.
• Matrix match: each row can pair with multiple columns. Don't assume 1-to-1.

Topic references

• references/mechanics.md
• references/electromagnetism.md
• references/modern_physics.md
• references/common_pitfalls.md

Using the verification script

scripts/verify.py helpers cover the common patterns. For Advanced, expect to extend them — write bespoke SymPy code for the specific geometry or coupling. Keep Rational and sqrt symbolic until the final answer.