Notes

Sequence and Series * A collection of numbers arranged in a defined order according to some definite rule is called a sequence. * The members or numbers that are listed in a sequence are called its terms. * If the number of terms in a sequence is finite or countable, then it is called a ... Read more

Binomial Theorem for Positive Integral Indices * The number of terms in an expansion is one more than the power of the binomial. * The coefficients of the first and the last terms of an expansion are both 1. (x + y)n=nC0xn+ nc1xn – 1y + nC2xn – 2y2+…. + nCn – 1xyn – 1 ... Read more

Fundamental Principle of Counting * If an event can occur in m different ways, following which another event can occur in n different ways, then the total number of the occurrence of the events in the given order is m × n. Introduction to Permutation * A permutation is an arrangement in a definite order ... Read more

Introduction to Linear Inequalities * Inequalities: Two real numbers or two algebraic expressions related by the symbols, ‘<’, ‘>’, ‘≤’ or ‘≥’, from an inequality. * The values of x for which the statements holds true are called the solutions of the inequality. * Equal numbers may be added to (or subtracted from) both the ... Read more

Introduction to Complex Numbers * A number whose square is negative is called an imaginary number. * A number of the form a + ib, where a and b are real numbers, is called a complex number and is represented by Z. In the complex number z = a + ib, * a: Real part ... Read more

Mathematical Induction * A statement that has a definite truth value, that is, true or false, is called a mathematical statement. * Deductive reasoning involves logical steps to arrive upon a particular case from a general case. * An Inductive reasoning is the counter part of deductive reasoning. * The principle used to prove mathematical ... Read more

Trigonometric Functions * Quadrilateral Angles: Angles that are integral multiples of \frac{π}{2} are called quadrilateral angles.  Some identities: * Cos2θ  + sin2 θ= 1 * Sec2 θ = 1 + tan²θ * Cosec2θ = 1 + cot2θ Sin (2nπ + θ) = sin θ, where n is any integer. Cos (2nπ + θ) = cos θ, where ... Read more

Cartesian Product of Sets * Ordered pair: A pair entries grouped in a particular order, which are separated by a comma and enclosed within brackets. * If two ordered pairs are equal then their corresponding first elements and second elements are equal. * The Cartesian product of two non-empty finite sets P and Q is ... Read more