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#### UNIT:1(Algebra) Complex Numbers

• Algebra of complex numbers, addition, multiplication, conjugation.
• Polar representation, properties of modulus and principal argument.
• Triangle inequality, cube roots of unity.
• Geometric interpretations.

• Quadratic equations with real coefficients.
• Relations between roots and coefficients.
• Formation of quadratic equations with given roots.
• Symmetric functions of roots.

#### UNIT:1 Sequence & Series

• Arithmetic, geometric & harmonic progressions.
• Arithmetic, geometric & harmonic means.
• Sums of finite arithmetic and geometric progressions, infinite geometric series.
• Sums of squares and cubes of the first n natural numbers.

#### UNIT:1 Logarithms and their properties.

• Logarithms and their properties.

#### UNIT:1 Permutation & Combination

• Problems on permutations & combinations.

#### UNIT:1 Binomial Theorem

• Binomial theorem for a positive integral index.
• Properties of binomial coefficients.

#### UNIT:1 Matrices & Determinants

• Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix.
• Determinant of a square matrix of order up to three, the inverse of a square matrix of order up to three.
• Properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties
• Solutions of simultaneous linear equations in two or three variables.

#### UNIT:1 Probability

• Addition and multiplication rules of probability, conditional probability.
• Bayes Theorem, independence of events.
• Computation of probability of events using permutations & combinations.

#### UNIT:2(Trigonometry) Trigonometric Functions

• Trigonometric functions, their periodicity and graphs, addition and subtraction formulae.
• Formulae involving multiple and sub-multiple angles.
• The general solution of trigonometric equations.

#### UNIT:2(Trigonometry) Inverse Trigonometric Functions

• Real valued functions of a real variable, into, onto and one-to-one functions.
• Sum, difference, product, and quotient of two functions
• Composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.
• Even and odd functions, the inverse of a function, continuity of composite functions, intermediate value property of continuous functions.

#### (Unit-3 : Vectors) Properties of Vectors

• The addition of vectors, scalar multiplication.
• Dot and cross products
• Scalar triple products & their geometrical interpretations.

#### Unit-4 : Differential Calculus -Functions

• Vectors and scalars, the addition of vectors.
• Components of a vector in two dimensions and three-dimensional space.
• Scalar and vector products, scalar and vector triple product.

#### Unit-4 : Differential Calculus-Limits & Continuity

• Limit and continuity of a function
• Limit and continuity of the sum, difference, product and quotient of two functions.
• L'Hospital rule of evaluation of limits of functions.

#### Unit-4 : Differential Calculus: Derivatives

• The derivative of a function, the derivative of the sum, difference, product and quotient of two functions.
• Chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.
• Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative.
• Tangents and normals, increasing and decreasing functions, maximum and minimum values of a function.
• Rolle's Theorem and Lagrange's Mean Value Theorem..

#### Unit-5 : Integral calculus: Integration

• Integration as the inverse process of differentiation.
• Indefinite integrals of standard functions, definite integrals, and their properties..
• Fundamental Theorem of Integral Calculus.
• Integration by parts, integration by the methods of substitution and partial fractions.

#### Unit-5 :Integral calculus:Application of Integration

• Application of definite integrals to the determination of Areas involving simple curves.

#### Unit-5 :Integral calculus:Differential Equations

• Formation of ordinary differential equations.
• The solution of homogeneous differential equations, separation of variables method.
• Linear first order differential equations.