Chemistry of Non-metallic Elements and their Compounds

Chemistry of Non-metallic Elements and their Compounds
Carbon – occurrence, isotopes, allotropes (graphite, diamond, fullerene); CO and CO₂ production, properties and uses.
Nitrogen and Phosphorus – occurrence, isotopes, allotopes, isolation from natural sources and purification, reactivity of the free elements. Preparation, properties, reactions of NH₃, PH₃ , NO, NO₂ , HNO₂, HNO₃, P₄O₁₀, H₃PO₃ and H₃PO₄.
Oxygen and Sulfur – Occurrence, isotopes, allotropic forms, isolation from natural sources and purification, properties and reactions of the free elements. Water, unusual properties of water, heavy water (production and uses). Hydrogen peroxide and ozone (production, purification, properties and uses).

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Integral calculus

Integral calculus : Integration as a reverse process of differentiation, indefinite integral of standard functions.
Integration by parts. Integration by substitution and partial fraction.

Differential calculus

Differential calculus : Functions, composition of two functions and inverse of a function, limit, continuity, derivative, chain rule, derivatives of implicit functions and of functions defined parametrically. Rolle’s Theorem and Lagrange’s Mean Value theorem (statement only).

Co-ordinate Geometry: Circle

Circle : Equation of a circle with a given center and radius. Condition that a general equation of second degree in x, y may represent a circle. Equation of a circle in terms of endpoints of a diameter . Parametric equation of a circle. Intersection of a line with a circle.

Co-ordinate Geometry: Conics

Conics : Definition, Directrix, Focus and Eccentricity, classification based on eccentricity.

Co-ordinate Geometry: Parabola

Parabola :Standard equation. Reduction of the form x = ay²+by+c or y = ax²+bx+c to the standard form y² = 4ax or x² = 4ay respectively. Elementary properties and parametric equation of a parabola.