MATHEMATICS - II(A)
UNIT I: COMPLEX NUMBERS
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Geometrical and Polar representation of complex number in Argand plane-Argand diagram
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Geometrical and Polar representation of complex number in Argand plane-Argand diagram
UNIT II: DE MOIVRE’S THEOREM
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De Moivre’s Theorem - Integral and Rational Indices, nth roots of unity
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Geographical Interpretations- Illustrations
UNIT III: QUADRATIC EXPRESSIONS
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Equations in one Variable
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Sign of quadratic expressions - Change in signs and Maximum and Minimum
UNIT IV: THEORY OF EQUATIONS
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Relation between the roots and the coefficients in an Equation
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Solving an equation when two or more of its roots are connected by certain relations
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Equations with real coefficients - occurrence of complex roots in conjugate pairs and its consequences
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Transformation of equations - Reciprocal equations
UNIT V: PERMUTATIONS AND COMBINATIONS
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Permutations of n dissimilar things taken r at a time
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Permutations when repetitions are allowed
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Permutations with Constant repetitions
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Combinations- Definitions and Certain Theorems
UNIT VI: BINOMIAL THEOREM
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Binomial Theorem for Rational Index
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Approximations using Binomial Theorem
UNIT VII: PARTIAL FRACTIONS
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Partial Fractions of f(x)/g(x)
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When g(x) contains non-repeated linear factors
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Partial Fractions of f(x)/g(x)
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When g(x) contains repeated and I or non-repeated linear factors
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Partial Fractions of f(x)/g(x)
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When g(x) contains irreducible factors
UNIT VIII: MEASURE OF DISPERSION
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Variance and Standard Deviation of ungrouped /grouped data
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Coefficient of Variation and analysis of frequency distributions with equal means but different variances
UNIT X: RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
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Theoretical discrete distributions Binomial and Poisson distributions
MATHEMATICS - II(B)
UNIT I: CIRCLE
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Position of a point in the plane of a circle
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Position of a straight line in the plane of a circle condition for a line to be tangent
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Chord of contact and polar
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Relative Positions of two circles
UNIT II: SYSTEM OF CIRCLES
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Angle between two intersecting circles
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Radical axis of two circles
UNIT VII: DEFINITE INTEGRALS
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Define Integral as the limit of sum
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Interpretation of definite integral as an area
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The Fundamental Theorem of Integral Calculus
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Applications of definite integral to areas
UNIT VIII: DIFFERENTIAL EQUATION
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Formation of differential equations - Degree and order of an ordinary differential Equation
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Solving Differential Equations
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Variables separable method
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Homogenous Differential Equation
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Non-Homogeneous Different Equations
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Linear Differential Equations
BETA
