Nervous and Muscular system

Nervous and Muscular system : Brief outline of human brain structure.

Cranial Nerves : Distribution and Function.Spinal cord – Structure and major functions, Reflex arc (types) and reflex action : Conditional and unconditional reflexes.

Autonomic : sympathetic and parasympathetic (definition only) nervous system.

Synapse : Structure and mechanism of synaptic transmission.

Different types of muscles and their structure, properties of muscles
(i) Excitability (ii) Contractility (iii) All or none law (iv) Refractory period (v) Summation of stimuli (vi) Tetanus (vii) Rigor mortis; Machanism of muscle contraction.

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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.