| MATHEMATICS
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| UNIT 1: |
SETS, RELATIONS AND FUNCTIONS: |
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Sets and their representation; Union, intersection and
complement of sets and their algebraic properties; Power set;
Relation, Types of relations, equivalence relations,
functions;. one-one, into and onto functions, composition of
functions. |
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| UNIT 2: |
COMPLEX NUMBERS AND QUADRATIC
EQUATIONS: |
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Complex numbers as ordered pairs of reals,
Representation of complex numbers in the form a+ib and their
representation in a plane, Argand diagram, algebra of complex
numbers, modulus and argument (or amplitude) of a complex
number, square root of a complex number, triangle inequality,
Quadratic equations in real and complex number system and their
solutions. Relation between roots and co-efficients, nature of
roots, formation of quadratic equations with given roots. |
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| UNIT 3: |
MATRICES AND DETERMINANTS: |
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Matrices, algebra of matrices, types of matrices,
determinants and matrices of order two and three. Properties of
determinants, evaluation of determinants, area of triangles
using determinants. Adjoint and evaluation of inverse of a
square matrix using determinants and elementary
transformations, Test of consistency and solution of
simultaneous linear equations in two or three variables using
determinants and matrices. |
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| UNIT 4: |
PERMUTATIONS AND COMBINATIONS: |
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Fundamental principle of counting, permutation as an
arrangement and combination as selection, Meaning of P (n,r)
and C (n,r), simple applications. |
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| UNIT 5: |
MATHEMATICAL INDUCTION: |
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Principle of Mathematical Induction and its simple
applications. |
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| UNIT 6: |
BINOMIAL THEOREM AND ITS SIMPLE
APPLICATIONS: |
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Binomial theorem for a positive integral index,
general term and middle term, properties of Binomial
coefficients and simple applications. |
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| UNIT 7: |
SEQUENCES AND SERIES: |
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Arithmetic and Geometric progressions, insertion of
arithmetic, geometric means between two given numbers. Relation
between A.M. and G.M. Sum upto n terms of special series: Sn,
Sn2, Sn3. Arithmetico - Geometric
progression. |
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| UNIT 8: |
LIMIT, CONTINUITY AND
DIFFERENTIABILITY: |
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Real - valued functions, algebra of functions,
polynomials, rational, trigonometric, logarithmic and
exponential functions, inverse functions. Graphs of simple
functions. Limits, continuity and differentiability.
Differentiation of the sum, difference, product and quotient of
two functions. Differentiation of trigonometric, inverse
trigonometric, logarithmic, exponential, composite and implicit
functions; derivatives of order upto two. Rolle's and
Lagrange's Mean Value Theorems. Applications of derivatives:
Rate of change of quantities, monotonic - increasing and
decreasing functions, Maxima and minima of functions of one
variable, tangents and normals. |
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| UNIT 9: |
INTEGRAL CALCULUS: |
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Integral as an anti - derivative. Fundamental
integrals involving algebraic, trigonometric, exponential and
logarithmic functions. Integration by substitution, by parts
and by partial fractions. Integration using trigonometric
identities.
Evaluation of simple integrals of the type Integral as limit of
a sum. Fundamental Theorem of Calculus. Properties of definite
integrals. Evaluation of definite integrals, determining areas
of the regions bounded by simple curves in standard form.
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| UNIT 10: |
Differential Equations: |
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Ordinary differential equations, their order and
degree. Formation of differential equations. Solution of
differential equations by the method of separation of
variables, solution of homogeneous and linear differential
equations of the type:
dy
-- + p (x) y = q (x)
dx |
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| UNIT 11: |
CO-ORDINATE GEOMETRY: |
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Cartesian system of rectangular co-ordinates in a
plane, distance formula, section formula, locus and its
equation, translation of axes, slope of a line, parallel and
perpendicular lines, intercepts of a line on the coordinate
axes.
Straight lines
Various forms of equations of a line, intersection of lines,
angles between two lines, conditions for concurrence of three
lines, distance of a point from a line, equations of internal
and external bisectors of angles between two lines, coordinates
of centroid, orthocentre and circumcentre of a triangle,
equation of family of lines passing through the point of
intersection of two lines.
Circles, conic sections
Standard form of equation of a circle, general form of the
equation of a circle, its radius and centre, equation of a
circle when the end points of a diameter are given, points of
intersection of a line and a circle with the centre at the
origin and condition for a line to be tangent to a circle,
equation of the tangent. Sections of cones, equations of conic
sections (parabola, ellipse and hyperbola) in standard forms,
condition for y = mx + c to be a tangent and point (s) of
tangency. |
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| UNIT 12: |
Three Dimensional Geometry: |
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Coordinates of a point in space, distance between two
points, section formula, direction ratios and direction
cosines, angle between two intersecting lines. Skew lines, the
shortest distance between them and its equation. Equations of a
line and a plane in different forms, intersection of a line and
a plane, coplanar lines. |
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| UNIT 13: |
Vector Algebra: |
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Vectors and scalars, addition of vectors, components
of a vector in two dimensions and three dimensional space,
scalar and vector products, scalar and vector triple product. |
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| UNIT 14: |
STATISTICS AND PROBABILITY: |
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Measures of Dispersion: Calculation of mean, median,
mode of grouped and ungrouped data. Calculation of standard
deviation, variance and mean deviation for grouped and
ungrouped data.
Probability: Probability of an event, addition and
multiplication theorems of probability, Baye's theorem,
probability distribution of a random variate, Bernoulli trials
and Binomial distribution. |
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| UNIT 15: |
Trigonometry: |
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Trigonometrical identities and equations.
Trigonometrical functions. Inverse trigonometrical functions
and their properties. Heights and Distances. |
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| UNIT 16: |
MATHEMATICAL REASONING: |
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Statements, logical operations and, or, implies,
implied by, if and only if. Understanding of tautology,
contradiction, converse and contrapositive. |
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