### NERIST NEE III 2015 Mathematics Syllabus:

**Algebra:** Arithmetic, Geometric and Harmonic Progressions; Permutation and Combination; Binomial expansion for positive index; middle term; greatest term; binomial expansion for general index. Determination up to third order, their properties and application to solve linear algebraic equations (Cramer’s rule); concept of a matrix; types of matrices; equality of matrices; operations of additions; scalar multiplication and multiplication of matrices; determinant of a square matrix; transpose; adjoint and inverse of a matrix; consistency and inconsistency of a system of linear equations; solving a system of linear equations in two or three variables using inverse of a matrix.

**Trigonometry:** Inverse trigonometric functions; solution of inverse trigonometric equations.

**Coordinate Geometry (2D):** Points and their coordinates in a plane; distance formula; area of a triangle; condition for the collinearity of three points and section formula; various forms of equations of a line; intersection of lines; angles between two lines; condition of concurrency of three lines distance of a point from a line; pair of lines; tangents and normal to a circle; simple problems on parabola ellipse and hyperbola.

**Differential Calculus:** Integration of rational and irrational functions; integration of transcendental functions; definite integration; area bounded by curves; length of arc and volume of surface revolution.

**Differential Equation:** Linear differential equations of first and second order & their applications.

**Vector Calculus:** Gradient; divergence & curl; line integral; surface integral & volume integral

**Coordinate Geometry (3D):** Points and coordinates on 3 dimensional space; Distance between points; direction cosines; direction ratios; projections; equations to a plane; angle between planes; distance of a point from a plane; angle between lines & planes; condition of co planarity of two lines; shortest distance between two lines; condition for the intersection of two lines.

**Probability:** Problems on probabilities; conditional probability; Bye’s theorem; Binomial & Poisson distributions.