NATIONAL SCHOOL OF SCIENCES

Department of Mathematics

Syllabus for First Terminal Examination – 2074

Grade-XII

Permutation and Combination:

- Basic Principle of counting, Permutation of a set of objects all different, Permutation of a set of objects not all different, Circular Permutation, Combination, All related theorems.

Binomial Theorem:

- Binomial Theorem, General term, Middle term(s), Binomial coefficients, Application of binomial theorem, Exponential and Logarithmic series.

Group Theory:

- Binary operation and properties, Cayley's Table, Congruent Modulo, Definition of group, Order and types of group, All related theorems, Properties of group.

Conic Section:

- Parabola, equation of tangent and normal to the parabola. ( Except Ellipse and Hyperbola)

Derivatives:

- Continuity and differentiation, Derivative of inverse circular function, exponential function, logarithmic function and trigonometric function from the first principle, Derivative of hyperbolic functions, Application of derivative, Tangents and normal, L'Hospital's rule, Rolle's Theorem and Mean Value theorem.

Linear Programming:

- Solution set of inequalities, Mathematical formulation of the problem, Mathematical model of LPP, solution of LPP by Graphical and Simplex method.

System of Linear Equations:

- Gauss elimination method, Gauss Jordan Inverse method.

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