- Arithmetic, geometric and harmonic progressions: Arithmetic, geometric and harmonic means and relation among them, sum to first n terms of arithmetic, geometric and arithmetic-geometric series, simple applications.
- Theory of quadratic equations: Its rational, irrational and complex roots, relation between roots and coefficients of a quadratic equation, nature of roots, formation of quadratic equation, symmetric functions of the roots, quadratic expression, its maximum and minimum values, simple applications.
- Complex numbers: Its real and imaginary parts, polar form and conjugate of a complex number, Argand diagram, cube roots of unity, triangle inequality, simple problems.
- Permutation and combination: Fundamental theorem of counting, permutation as arrangement and combination as selection. Permutation and combination of like and unlike things. Circular permutation is to be excluded. Simple applications.
- Binomial Theorem: Binomial theorem for a positive integral index, general term, middle term (terms), equidistant terms, simple applications.
- Infinite series: Infinite geometric series, Binomial theorem for fractional and negative index, exponential series, logarithmic series, simple applications.
- Matrices and determinants: Matrices upto third order, addition, subtraction, scalar multiplication and multiplication of matrices. Determinants upto third order, Properties of determinants, Minors and confactors, application of determinants for evaluation of area of a triangle and solution of a system of linear equations by using Cramer’s rule. Inverse of a 2 X 2 matrix, simple applications.
- Probability Theory: Random experiment and their outcomes, events, sample space, equally likely, mutually exclusive and exhaustive cases, classical definition of probability, addition and multiplication theorems, simple applications.
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