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The calculations JEE sets most: degree of dissociation from vapour density, simultaneous equilibria, pH of mixtures and very dilute solutions, polyprotic acids, and precipitation with Ksp, with a full timed paper.

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1. Degree of dissociation and simultaneous equilibria: For A to 2B, Kp = 4α²P/(1 - α²); for AB to A + B, Kp = α²P/(1 - α²). Higher pressure lowers α. The vapour density gives α from how far the density falls. When two equilibria share a gas, write both constants with the same partial pressure and solve them together.
2. pH of mixtures and polyprotic acids: A very dilute strong acid needs water's own ions: solve x² − cx − Kw = 0. A strong acid swamps a weak one. Two weak acids give [H+] = √(K₁c₁ + K₂c₂). In a titration, pH = pKa half-way and the end point is basic. A polyprotic acid gets its pH from the first step.
3. Precipitation and selective solubility: A solid forms when the ionic product passes Ksp. Of two ions, the one needing less of the reagent comes out first, and Ksp tells how much is left when the second starts. Controlling [H+] or [OH-] picks which sulfides and hydroxides form. A buffer or a complex can dissolve far more than pure water.