Text Book of Algebra for IIT-JEE

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The book is written in such a simple and easy to understand language that even an average student will not only understand it fully but willalso enjoy its reading. The book contains exhaustive theory, carefully selected illustrative examples & different levels of graded exercises to ensure that student really understands the concepts and their applications. Many problems have been solved in more than one way so that the students can have simplistic view of complex problems and at the same time uplift the problem solving ability of the student. The book has been completely reoriented as per the new pattern of IIT JEE. Contains complete Theory, Multiple Choice Questions, Multiple matching Questions, Assertion & Reasoning and Comprehension Based Questions after every chapter. Table Of Contents 1. Equations & inequations Introduction Section I : Quadratic Equations and Expressions Section II : Logarithm Section III : General Equations Inequations Miscellaneous solved examples Exercise I, Exercise II, Exercise III 2. Inequalities Introduction Basic Results Section- I : A real perfect square is non negative Section - II : Inequalities based on AM ³ GM ³ HM Section -III : Some Classical Inequalities Section -IV : Inequalities by monotonocity Section -V : Miscellaneous Inequalities Exercise I, Exercise II, Exercise III 3. Polynomials Introduction Basic Properties Section -I : Problems based on factor and remainder theorem Section - II : advanced problems in polynomials Exercise I, Exercise II, Exercise III 4. Sequence and series Introduction Section I : Sequence Section II : Arithmetic Progression The sum of n terms of an A.P. Properties op an A.P. Arithmetic Means Section III : Geometric Progression The sum of n terms of G. P. Sum of an infinite G. P. Geometric Means Section IV : Special Sequences Harmonic progression Arithmetic-geometric series (AGP) summation of series Other cases of summation Exercise I, Exercise II, Exercise III 5. Complex numbers Introduction Definitions and Terms Geometric interpretation Section I : General Problems on Complex Numbers and De Moivre’s Theorem De Moivre Theorem Solved Examples Section II : Application of Complex Numbers in Geometry Exercise I, Exercise II, Exercise III 6. Determinants Introduction Section I : Properties of Determinant Solved Examples Section II : Theory of Linear Equations Exercise I, Exercise II, Exercise III 7. Matrices Introduction Definition Algebra of Matrices Proof of some Theoretical Results Section I : General problems on Matrices Exercise I, Exercise II, Exercise III 8 . Permutations Combinations Introduction Section I : Problems based on fundamental principle of counting Section II : Factorial and nPr Section III : circular permutations and permutation of objects not all of which are distinct Circular permutations Section IV : Combinations Properties of nCr : Exercise I, Exercise II, Exercise III 9. Combinatorics Introduction Typical Situations Section I : Problems based on Typical Situations in Combinatorics Section II : Problems based on Typical Distributions Section III : Problems based on multinomial expansions Section IV : problems based on principle of exclusion & inclusion Section V : Combinatorial Number Theory Miscellaneous Solved Examples Exercise I, Exercise II, Exercise III 10. Binomial theorem Introduction Section I : Problems based on Binomial Expansion Section II : Greatest term and greatest coefficient Section III : integer and fractional part problems Section iv : Problems on Binomial coefficients (non series) Section V : Problems on binomial series involving binomial coefficients linearly Section VI : Problems on Binomial Series involving binomial coefficients non linearly Miscellaneous solved examples Exercise I, Exercise II, Exercise III 11. Probability Introduction Definitions and Terms Theorems and Results Independence of Three Events Fundamental Probability Inequality Binomial Probability Formula Baye’s Theorem Section I : Simple Probability Problems Problems on Cards Section II : Set theoretic Probability theory Section III : Bayes Theorem based problems Section IV : Advanced problems on Probability Exercise I, Exercise II, Exercise III