Mathematics
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Set Theory and its Applications
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Union, Intersection, Difference, Complement, Power Set, Number of elements in Union and
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Intersection of finite sets
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Relations and Functions
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Reflexive, Symmetric, transitive and equivalence relations
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Injective, Subjective, objective functions
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Inverse of a function
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Number System
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Natural Numbers, Integers,
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Rational and irrational numbers,
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Real numbers
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Absolute values of numbers
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Triangle inequality
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Quadratic and linear equations
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Fundamental theorem of algebra, Roots, Discriminates, Nature of roots, relation between roots and coefficients
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Calculus of one variable
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Limit, Continuity, derivative, Tangent, Normal, increasing and decreasing functions
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Integrals
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Methods of Integration, Integrals of some particular functions, Integration by partial fractions, Integration by parts, Definite integrals
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Sequence and series
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AP and GP, Monotonic sequence, Exponential series, Logarithmic series, Taylor's series,
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Maclaurin's series
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Coordinate geometry
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Distance formula, section formula, Area of a triangle, Locus and its equation, Locus and its equation, Straight line, circle, conic section
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Analytical solid geometry
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Plane, straight line, sphere,
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Probability
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Trial, Sample point, sample space, Event, Addition theorem, Binomial distribution
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Trigonometry
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Angle associated with 90, 180, 270, 360 compounded angle formula, Submultiple angle formula, Trigonometry equations, Inverse trigonometric functions, Height and Distance
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Mensuration
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Circumference of a circle, Length of the arc of a circle, Area of a circle, Sector and segment, Area of a circle annulus, Area of a sectional region, Area of segment, Surface area and volume of a prism, Right circular cylinder, Cone and sphere
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