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Algebra (Weightage 32%)  

Topics from Algebra

  • Complex numbers as ordered pairs of reals (3 concepts)
  • Representation of complex numbers in the form of a+ib and their represenation in a plane (1 concepts)
  • Argand diagram (8 concepts)
  • Algebra of complex numbers (4 concepts)
  • Modulus and argument(or amplitude) of a complex number (25 concepts)
  • Square root of a complex number (1 concepts)
  • Triangle inequality (2 concepts)
  • Quadratic equations in real and complex number system and their solutions (5 concepts)
  • Matrices, algebra of matrices, types of matrices (54 concepts)
  • Determinants and matrices of order two and three (2 concepts)
  • Test of consistency and solution of simultaneous linear equation in two or three variables using determinants and matrices (14 concepts)
  • Fundamental principle of counting (3 concepts)
  • Permutation as an arrangement and combination as selection (17 concepts)
  • Meaning of P(n,r) and C( n,r), Simple applications (38 concepts)
  • Bionomial theorem for a positive integral index, general term and middle term (21 concepts)
  • Properties of bionomial coefficients and simple applications (21 concepts)
  • Geometric means between two given numbers (2 concepts)
  • Relation between A.M. and G.M. (3 concepts)
  • Sum upto n terms of special series: Sn, Sn2, Sn3 (7 concepts)
  • Arithmetic, Geometric & Harmonic Progressions (7 concepts)
  • Principle Of Mathematical Induction And Its Simple Applications (10 concepts)
  • Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots (38 concepts)
  • Properties of determinants, evaluation of determinants (14 concepts)
  • Adjoint and evaluation of inverse of a square matrix using deteminants and elementary transformations (14 concepts)
  • Arithmetic and geometric progressions,insertion of arithmetic (32 concepts)
  • Principle of Mathematical Induction (2 concepts)
  • Complex Number (4 concepts)
  • Geometrical Representation and Different Forms of Complex Number (6 concepts)
  • De-Moivre's Theorem (1 concepts)
  • Cube Root and nth Root of Unity (2 concepts)
  • Geometry with Complex Number (3 concepts)
  • Quadratic Equations and Roots (3 concepts)
  • Transformation of Quadratic Equations and Common Roots (2 concepts)
  • Graphs of Quadratic Equations (4 concepts)
  • Quadratic Expression in two Variables (1 concepts)
  • Location of Roots (3 concepts)
  • Polynomial Equation and Remainder Theorem (1 concepts)
  • Other Types of Equations and their Inequalities (4 concepts)
  • Introduction (1 concepts)
  • Fundamental principle of counting (1 concepts)
  • Permutation (10 concepts)
  • Combination (17 concepts)
  • Binomial Expansion and their Properties (3 concepts)
  • Analysis of Coefficients of Binomial Expansion (4 concepts)
  • Application of Binomial Expansion (8 concepts)
  • Multinomial Theorem (1 concepts)
  • Series Involving Binomial Coefficients (5 concepts)
  • Binomial Theorem For Any Index (2 concepts)
  • Sequences, Series And Progression (1 concepts)
  • Arithmetic Progression (6 concepts)
  • Geometric Progression (9 concepts)
  • Harmonic Progression (3 concepts)
  • Arithmetico-Geometric Progression (2 concepts)
  • Application Of A.M.-G.M. (3 concepts)
  • Summation By Sigma(?) Operator (3 concepts)
  • Method Of Differences (3 concepts)
  • Sum of Some Special Series (Vn Method) (2 concepts)
  • Matrices and Types of Matrices (4 concepts)
  • Mathematical Operation on Matrices (5 concepts)
  • Special Matrices and their Properties (11 concepts)
  • Elementary Row Operations and Inverse of a Matrix by Elementary Row Operations (3 concepts)
  • Determinant (2 concepts)
  • Adjoint of Matrix (4 concepts)
  • Inverse of a Matrix (Using Adjoint) (4 concepts)
  • Multiplication of Determinant (1 concepts)
  • Properties of Determinants (3 concepts)
  • System of Simultaneous Linear equations (4 concepts)
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