Nutrition and Digestive System

Nutrition and Digestive System : Basic constituents of food and their nutritional significance. Vitamins – dietary sources, functions and deficiency symptoms of water and fat soluble vitamins. Structure and functions of the alimentary canal and the digestive glands. Functions of the digestive juices (saliva, gastric juice, pancreatic juice, intestinal juice), Biles.

Digestion and absorption of carbohydrates, lipids and proteins. Diseases – Peptic and Gastric ulcers, Gastritis; fasting and obesity.

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Principle of Mathematical Induction

Principle of Mathematical Induction : Statement of the principle. Proof by induction for the sum of squares, sum of cubes of first n natural numbers, divisibility properties like 2²ⁿ–1 is divisible by 3 (n≥1), 7 divides 3²ⁿ⁺¹+2ⁿ⁺²(n≥1).

Permutation and combination

Permutation and combination : Permutation of n different things taken r at a time (r≤n). Permutation of n things not all different. Permutation with repetitions (circular permutation excluded).

Quadratic Equations

Quadratic Equations : Quadratic equations with real coefficients; Relations between roots and coefficients; Nature of roots; Formation of a quadratic equation, sign and magnitude of the quadratic expression ax²+bx+c (a,b,c are rational numbers and a≠0).

Complex Numbers

Complex Numbers: Definition and properties of complex numbers; Complex conjugate; Triangle inequality; Square root of complex numbers; Cube roots of unity; D’Moivre’s theorem (statement only) and its elementary applications.

Logarithms

Logarithms :Definition; General properties; Change of base.