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PV = nRT fails at high pressure and low temperature. Learn why, how the compressibility factor Z measures it, and how van der Waals' a and b fix it.

Understand torque as the turning effect of force, angular momentum as rotational momentum, and why conserving L makes a skater speed up, with a fully worked example.

Identical or distinct objects, labelled or unlabelled boxes? Learn the stars and bars method and the grouping formulas for JEE, with worked examples.

Why does water boil at 373 K when heavier H₂S boils near 213 K? Learn hydrogen bonding, why ice floats and how ortho and para isomers differ.

A practical guide to making short notes, formula sheets and reaction maps that actually improve recall for NEET and JEE, including what to leave out.

Why the same rod is easy to spin about its middle and hard about its end, and how the parallel-axis theorem I = I₍cm₎ + Md² lets you shift axes without integrating.

Learn to count arrangements when people must sit together or apart, using gluing, subtraction and the gap method, with fully worked JEE examples.

Why is O₂ attracted to a magnet? Learn how molecular orbitals form, how to calculate bond order, and how to predict magnetic behaviour step by step.

Learn how to find the hybridisation of any atom in seconds using the steric number, and how s-character controls bond length and acidity.

A practical five-step triage method to clear pending NEET and JEE chapters: audit, rank by marks per hour, split your week, and learn question-first.

Why does a bursting shell's centre of mass keep its parabola? Learn the weighted-average idea, F_ext = M a_cm, and the boat trick for NEET and JEE.

A simple swap test that tells you whether a counting problem needs nPr or nCr, with worked JEE-style examples and the common traps.