// May 7th, 2011 // No Comments » // Bits Pilani
1. Algebra
1. Complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, roots of complex numbers, geometric interpretations.
2. Theory of Quadratic equations, quadratic equations in real and complex number system and their solutions, relation between roots and coefficients, nature of roots, equations reducible to quadratic equations.
3. Logarithms and their properties.
4. Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, arithmetico-geometric series, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.
5. Exponential series.
6. Permutations and combinations, Permutations as an arrangement and combination as selection, simple applications.
7. Binomial theorem for a positive integral index, properties of binomial coefficients.
8.Matrices and determinants of order two or three, properties and evaluation of determinants, addition and multiplication of matrices, adjoint and inverse of matrices, Solutions of simultaneous linear equations in two or three variables.
9. Sets, Relations and Functions, algebra of sets applications, equivalence relations, mappings, one-one, into and onto mappings, composition of mappings.
10. Mathematical Induction
11. Linear Inequalities, solution of linear inequalities in one and two variables.
2. Trigonometry
1. Trigonometric ratios, functions and identities.
2. Solution of trigonometric equations.
3. Properties of triangles and solutions of triangles
4. Inverse trigonometric functions
5. Heights and distances
3. Two-dimensional Coordinate Geometry
1. Cartesian coordinates, distance between two points, section formulae, shift of origin.
2. Straight lines and pair of straight lines: Equation of straight lines in various forms, angle between two lines, distance of a point from a line, lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrent lines.
3. Circles and family of circles : Equation of circle in various form, equation of tangent, normal & chords, parametric equations of a circle , intersection of a circle with a straight line or a circle, equation of circle through point of intersection of two circles, conditions for two intersecting circles to be orthogonal.
4. Conic sections: parabola, ellipse and hyperbola their eccentricity, directrices & foci, parametric forms, equations of tangent & normal, conditions for y=mx+c to be a tangent and point of tangency.
4. Three dimensional Coordinate Geometry
1. Direction cosines and direction ratios, equation of a straight line in space and skew lines.
2. Angle between two lines whose direction ratios are given
3. Equation of a plane, distance of a point from a plane, condition for coplanarity of three lines.
5. Differential calculus
1. Domain and range of a real valued function, Limits and Continuity of the sum, difference, product and quotient of two functions, Differentiability.
2. Derivative of different types of functions (polynomial, rational, trigonometric, inverse trigonometric, exponential, logarithmic, implicit functions), derivative of the sum, difference, product and quotient of two functions, chain rule.
3. Geometric interpretation of derivative, Tangents and Normals.
4. Increasing and decreasing functions, Maxima and minima of a function.
5. Rolle’s Theorem, Mean Value Theorem and Intermediate Value Theorem.
6. Integral calculus
1. Integration as the inverse process of differentiation, indefinite integrals of standard functions.
2. Methods of integration: Integration by substitution, Integration by parts, integration by partial fractions, and integration by trigonometric identities.
3. Definite integrals and their properties, Fundamental Theorem of Integral Calculus and its applications.
4. Application of definite integrals to the determination of areas of regions bounded by simple curves.
7. Ordinary Differential Equations
1. Variables separable method.
2. Solution of homogeneous differential equations.
3. Linear first order differential equations
8. Probability
1. Addition and multiplication rules of probability.
2. Conditional probability
3. Independent events
4. Discrete random variables and distributions
9. Vectors
1. Addition of vectors, scalar multiplication.
2. Dot and cross products of two vectors.
3. Scalar triple products and their geometrical interpretations.
10. Statistics
1. Measures of dispersion
2. Measures of skewness and Central Tendency
11. Linear Programming
1. Formulation of linear Programming
2. Solution of linear Programming, using graphical method.
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