Indian Institutes of Technology
Joint Entrance Examination, IIT-JEE - 2012
Algebra: Algebra of complex numbers,
addition, multiplication, conjugation, polar representation, properties of
modulus and principal argument, triangle inequality, cube roots of unity,
Quadratic equations with real coefficients, relations between
roots and coefficients, formation of quadratic equations with given roots,
symmetric functions of roots.
Arithmetic, geometric and harmonic progressions, arithmetic,
geometric and harmonic means, sums of finite arithmetic and geometric
progressions, infinite geometric series, sums of squares and cubes of the first
n natural numbers.
Logarithms and their properties.
Permutations and combinations, Binomial theorem for a
positive integral index, properties of binomial coefficients.
Matrices as a rectangular array of real numbers, equality of
matrices, addition, multiplication by a scalar and product of matrices,
transpose of a matrix, determinant of a square matrix of order up to three,
inverse of a square matrix of order up to three, properties of these matrix
operations, diagonal, symmetric and skew-symmetric matrices and their
properties, solutions of simultaneous linear equations in two or three