Syllabus for JEE-2010 Mathematics
Algebra: Algebra of complex numbers, addition, multiplication,
conjugation, polar representation, properties of modulus and principal argument,
triangle inequality,cube roots of unity, geometric interpretations.
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 variables.
Addition and multiplication rules of probability, conditional probability, Bayes
Theorem, independence of events, computation of probability of events using
permutations and combinations.
Trigonometry: Trigonometric functions, their periodicity and graphs,
addition and subtraction formulae, formulae involving multiple and sub-multiple
angles, general solution of trigonometric equations.
Relations between sides and angles of a triangle, sine rule, cosine rule,
half-angle formula and the area of a triangle, inverse trigonometric functions
(principal value only).
Analytical geometry: Two dimensions: Cartesian coordinates, distance
between two points, section formulae, shift of origin.