Unit 1: Permutation and Combination (10 Hours)

• Basic Principle of counting
• Permutation of (a) set of objects all different
• (b) Set of objects not all different
• (c) circular arrangement
• (d) repeated use of the same object
• Combination of things all different
• Properties of combination.

Unit 2: Binomial Theorem (10 Hours)

• Binomial theorem for a positive integral index
• General term
• Binomial coefficients
• Binomial theorem for any index (Without proof)
• Application to approximation
• Euler's number
• Expansion of ex, ax and log(1+x) (without proof)

Unit 3: Elementary Group Theory (8 Hours)

• Binary operation
• Binary operation on sets of integers and their properties
• Definition of a Group
• Groups whose element are not numbers
• Finite and infinite groups
• Uniquences of identity
• Uniquences of inverse
• Cancellation law
• Abelian Group

Unit 4: Conic Sections (12 Hours)

• Standard equation of parabola, Ellipse and Hyperbola
• Equations of tangent and normal to a parabola at a given point

Unit 5: Co - Ordinates in Space (12 Hours)

• Co - ordinate axes
• Co - ordinate planes
• The octants
• Distance between two points
• External and internal point of division
• Direction cosines and ratios
• fundamental relation between direction cosines
• Projections
• Angle between two lines
• General equation of a plane
• Equation of a plane in intercept and normal form
• Plane through three given points
• Plane through the intersection of two given planes
• Parallel and perpendicular planes
• Angle between two planes
• Distance of a point from a plane.

Unit 6: Vectors and Its Applications (14 Hours)

• Cartesian representation of vectors
• Collinear and non - collinear vectors
• Coplanar and non-Coplanar vectors
• Linear combination of vectors
• Scalar product of two vectors
• Angle between two vectors
• Geometric interpretation of scalar product
• Properties of Scalar Product
• Condition of perpendicularity
• Vector product of two vectors
• Geometric interpretation of vector product
• Properties of vector product
• Application of product of vectors in plane trigonometry.

Unit 7: Derivative and Its Application (14 Hours)

• Derivative of inverse trigonometric, exponential and logarithmic functions by definition
• Relationship between continuity and differentiability
• Rules for differentiating hyperbolic function and inverse hyperbolic function
• Composite function and function of the type f(x)^g(x)
• L'Hospital's rule (for 0/0, ¥/¥)
• Differentials
• Tangent and Normal
• Geometric interpretation and application of Rolle's theorem and Mean value theorem.

Unit 8: Antiderivatives (7 Hours)

Unit 9: Differential Equations and their Applications (7 Hours)

Unit 10: Dispersion, Correlation and Regression (12 Hours)

Unit 11: Probability (8 Hours)

Unit 12: Statics (9 Hours)

Unit 13: Statics (Continued) (9 Hours)

Unit 14: Dynamics (9 Hours)

Unit 15: Dynamics (Continued) (9 hours)

Unit 16: Linear Programming (11 Hours)

Unit 17: Computational Method (9 Hours)

Unit 18: Computational Method (Continued) (8 Hours)

Unit 19: Numerical Integration (8 Hours)