Mathematics

This chapter covers the basics of sets, different types of relations, and various kinds of functions, including their properties and graphical representations.

Study of complex numbers, representation in argand plane, algebra of complex numbers, and solving quadratic equations with real and complex coefficients.

Operations on matrices, adjoint and inverse, properties of determinants, and solving systems of linear equations using matrices.

Fundamental principle of counting, permutations, combinations, and their applications.

Principle of mathematical induction and its applications in proving formulas and inequalities.

Binomial theorem, expansion, general term, and applications.

Arithmetic, geometric, and harmonic progressions, means, and sum of special series.

Limits of functions, continuity, differentiability, and their relationship.

Indefinite integrals, definite integrals, properties of definite integrals, and area under curves.

Order and degree, formation of differential equations, and methods of solving differential equations.

Cartesian coordinates, distance formula, section formula, area of triangle, and introduction to straight lines.

Different forms of straight lines, slope, angle between lines, distance from a point, and concurrency of lines.

Circle: standard form, general form, tangents. Parabola, ellipse, hyperbola: standard equations and properties.

Direction cosines, direction ratios, equations of lines and planes, angle between lines and planes, shortest distance.

Vectors and scalars, addition, dot product, cross product, and scalar triple product.

Statistics: mean, median, mode, variance, standard deviation. Probability: events, addition and multiplication theorems, Baye's theorem, probability distributions.

Trigonometric functions, identities, equations, inverse functions, and properties of triangles.

Statements, logical connectives, truth tables, tautology, contradiction, and logical equivalence.