As you want to get the details of syllabus of Education Common Entrance Test of Mathematics so here it is for you:

Sets – relations – binary operations – semi groups – groups – subgroups -normal subgroups- homomorphism-Functions permutations permutation groups – cyclic groups – quotient group – automorphism.

Rings – Integral domains – fields – characteristic – homomorphism – Ideals – Prime Ideals – maximal ideals – Rings of permutations – polynomials – polynomial rings.

Vector spaces – linearly independent vectors – Basis – dimension – linear transformation — Null space — Range — Rank of a linear transformation.

Elementary matrix operations – Elementary matrices – Determinants – properties – rank of matrix – inverse of a matrix –
Eigen vectors – Eigen values – systems of linear equations.

Three dimensional geometry — Coordinates — distance formula – direction cosines – plane – angle between two planes – perpendicular distance from a point – Equation of a line – skew lines – shortest distance – The sphere – tangent plane power of a point – polar plane and pole – radical plane – coaxial system of spheres – The circle – radius – centre.

Real numbers – properties – functions – range – sequences – series – limits – continuity – differentiability – differentiation – mean value theorems — L’Hospital rules — Integration definite integrals – Reimann integral.

Differential equations – first order and first degree – different forms – Exact differential equations – change of variables – equation of first order but not of first degree – higher order linear differential equations – system of linear differential equations.

Elements of Number theory – Divisibility – primes – congruences – solutions of congruences – congruences of degree 1 The Euler function O.

Quadratic equations – quadratic expressions – change of sign – roots – maximum – minimum values

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