#### Unit 1: Algebra (44)

- Permutation and combination
- 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 objects
- Combination of things all different, Properties of combination

- Binomial Theorem
- Binomial theorem for a positive integer, general term, Binomial coefficient
- Binomial theorem for any index (without proof), application to approximation
- Euler's number, Expansion of \( e^x,a^x \log(1+x)\) (without proof)

- Complex numbers
- Polar form of complex numbers
- De Moivre's theorem and its application in finding the roots of a complex number
- Properties of cube roots of unity
- Euler's formula

- Sequence and series
- Sum of finite natural numbers, sum of squares of first n-natural numbers, Sum of cubes of first n-natural numbers
- principle of mathematical induction and use it to find sum.

- Matrix based system of linear equation
- Solution of a system of linear equations by Cramer's rule up to three variables
- Solution of a system of linear equations by matrix method (row-equivalent and inverse) up to three variables

#### Unit 2: Trigonometry (12)

- Properties of a triangle (Sine law, Cosine law, tangent law, Projection laws, Half angle laws)

Click Here - Solution of triangle (simple cases)

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#### Unit 3: Analytic Geometry (20)

#### Unit 4: Vectors (12)

- Product of Vectors: Scalar product of two vectors, angle between two vectors, geometric interpretation of
scalar product, properties of scalar product, application of scalar product in geometry and trigonometry,
vector product of two vectors, geometrical interpretation of vector product, properties of vector
product, application of vector product in geometry and trigonometry.

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#### Unit 5:Statistics and Probability (12)

- Correlation and Regression: Correlation, nature of correlation, correlation coefficient by Karl Pearson's method, interpretation of correlation coefficient, properties of correlation coefficient (without proof), rank correlation (only elementary concept), regression equation, regression line of y on x and x on y

Click Here - Probability: Dependent cases, conditional probability (without proof).

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#### Unit 6:Computational Methods (12) or Mechanics

- Numerical computation: Roots of algebraic and transcendental equation (bisection and Newton-Raphson method)

Click Here - Numerical integration:Trapezoidal rule and Simpson's rule

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#### Unit 7:Mechanics(12) or Computational Methods

- Statics: Forces and resultant forces, parallelogram law of forces, composition and resolution of
forces, Resultant of coplanar forces acting on a point.

Click Here - Dynamics: Motion of particle in a straight line, Motion with uniform acceleration, motion under the
gravity, motion down a smooth inclined
plane.

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