Growth, Reproduction, and Ageing

Growth, Reproduction, and Ageing :
A. In Plants :
Different parts of a typical flower (China rose). Types of flower : regular and irregular, actinomorphic, zygomorphic.Aestivation in Musaceae & Malvaceae.Floral formula : Definition, symbols used in floral formulae in Musaceae (e.g. Banana) and Malvaceae (eg. China rose) ; Pollination – Definition, self and cross pollination; Merits and demerits of self and cross pollination. Fertilization – Process of double fertilization. Dispersal of fruits and seeds – Types with examples. Phases and factors of Growth, Differences between growth and development, Abscission senescence, ageing and growth of seeding and the role of gibberellic acid.

B. In Animals :
Primary and secondary sex organs and secondary sex characters – Testis – Histology, Functions of Testosterone.
Spermatogenesis (outline). Ovary – Histology : Functions of estrogen and progesterone; Oogenesis (outline);
structure of mature Graafian follicle.
Menstrual cycle (brief idea). Fertilization and Implantation.

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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.