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Unit
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Topics
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Unit-I: Sets and Functions
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1. Sets: Definitions, representations, empty sets, finite and infinite sets, equal sets, subsets, universal set, Venn diagrams, operations on sets.
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2. Relations & Functions: Ordered pairs, Cartesian products, relations, functions, domain, co-domain, range, various types of functions (constant, polynomial, etc.), operations on functions.
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3. Trigonometric Functions: Definitions, identities, angles in radians and degrees, domain, range, graphs, and applications of trigonometric functions.
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Unit-II: Algebra
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1. Complex Numbers and Quadratic Equations: Introduction to complex numbers, algebraic properties, Argand plane.
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2. Linear Inequalities: Solutions, graphical representation of linear inequalities in one variable.
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3. Permutations and Combinations: Counting principles, permutations, combinations, and related formulas.
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4. Binomial Theorem: Statement, proof, and applications of the binomial theorem, Pascal’s triangle.
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5. Sequence and Series: Arithmetic Mean (A.M.), Geometric Progression (G.P.), general term, sum of G.P., and relation between A.M. and G.M.
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Unit-III: Coordinate Geometry
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1. Straight Lines: Slope, angle between lines, forms of line equations (parallel, point-slope, slope-intercept, two-point, intercept), distance from a point.
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2. Conic Sections: Circles, ellipses, parabolas, hyperbolas, standard equations, and properties.
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3. Introduction to Three-Dimensional Geometry: Coordinate axes, planes, point coordinates, distance between points in 3D.
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Unit-IV: Calculus
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1. Limits and Derivatives: Introduction to derivatives, limits of various functions, derivative rules (sum, difference, product, quotient), and polynomial/trigonometric derivatives.
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Unit-V: Statistics and Probability
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1. Statistics: Measures of Dispersion (range, mean deviation, variance, standard deviation) for ungrouped and grouped data.
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2. Probability: Events, mutually exclusive events, exhaustive events, axiomatic probability, and calculations for different event types ('not', 'and', 'or').
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