MP PET 2013 Mathematics Syllabus

MP PET 2013 Mathematics Syllabus is Made Available for the Students who are preparing for MP PET 2013 Entrance Test. Students who are aspiring to appear for MP PET 2013 Entrance Test can check MP PET 2013 Syllabus. Students who aspires for Admission through MPPET 2013 Can check the MP PET 2013 Syllabus Details for Maths, Physics, Chemistry and Other Programs.

ALGEBRA:
Algebra of Complex numbers, Graphical representation of complex numbers modules, and argument of complex numbers, conjugated of a complex number, triangle inequality, cube roots of unity, arithmetic, geometric and harmonic progression. Arithmetic, geometric and harmonic means between two numbers.Sum of squares and cubes of first natural numbers.Theory, geometric equation, relations between roots and coefficients. Quadratic expressions, quadratic equations in one variable, permutations and combinations. Bionomial (any index) theorem exponential and logarithmic series, determinants up to third order and their order and their elementary properties matrices types of matrices, adjoint and inverse of matrix, elementary, applications is solving simultaneous equation upto three variables.

TRIGONOMETRY:
Trigonometry functions and their graphs, addition and subtraction formulae; formulae involving multiple and submultiple angles, general solutions of trigonometrical equations, relation between sides and angles of a traingle. Solution of traingles, inverse: trignometrical functions, height and distance(simple problems).

CO-ORDINATE GEOMETRY OF TWO DIMENSIONS:
Rectangular cartesian coordinates, straight line, pair to straight lines, distance of a point from a line, angle between two lines.
Circle, tangents and normals, system of circles. Conic section, parabola, ellipse and hyperbola in standard forms with elementary
properties, tangents and normals.

CO-ORDINATE GEOMETRY OF THREE DIMENSIONS:

Rectangular co ordinate system, direction cosines and direction ratios, equation of place in standard forms.Perpendicular distance from a point, equation of a line angles between two lines.

VECTOR ALGEBRA:
Definition of vector, addition of vector, components in three dimensional space, scalar and vector products. triple products, simple applications in geometry and mechanics.

DIFFERENTIAL CALCULUS:
Function, polynomial, rational trignometric, logarithmic and exponential, inverse functions. Limit continuity and differentiability of functions, differentiation of rational, trigonometric and exponential functions. Application of derivative in elementary problem in mecharics, increasing and decreasing functions. Maxima and Minima of function of one variable, Roll’s theorem and mean value theorem.

INTEGTRAL CALCULUS:
Integration as the inverse process of differentation, integration by parts. By substitution and by partial fraction definite integral. Areas under simple curves.

DIFFERENTIAL EQUATIONS:
Formulation of differential equation, ordered degree solution of differential equations by separation of variable method. Homogeneous form linear differential equation of first order.

STATISTICS:
Probability addition and multiplication laws, conditional probability, Binomial distribution, simple problems in correlation and regression.

NUMERICAL METHODS:
Solution of euation by the methods of bisection, false position and Newton Raphson. Numerical integration by trapezoided and Simpson’s rule.

LINEAR PROGRAMMING:
Definition and formation of linear programming problems, solution by graphical method.

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KLUEEE 2013 Syllabus for MathematicsWBJEE 2013 Mathematics SyllabusOJEE 2013 Mathematics SyllabusMewar University MUEEE 2013 Mathematics SyllabusBITSAT 2013 Mathematics SyllabusVSAT 2013 Mathematics SyllabusSRMEEE 2013 Mathematics SyllabusJEE Advanced 2013 Mathematics SyllabusJEE (Main) 2013 Syllabus for Mathematics ExamGOA CET 2013 Mathematics Syllabus

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Mewar University MUEEE 2013 Mathematics Syllabus

Mewar University Entrance Exam MUEE 2013 Maths Syllabus has been Published.  All Students who aspires for Admission in Mewar University are  hereby informed to check the Mewar University Entrance Test 2013 Mathematics Syllabus.  Students who are preparing to Crack Mewar University MUEE 2013 Entrance Test can checkMewar University MUEE 2013 Syllabus for Mathematics. 

Click here for : Mewar University MUEEE 2013 Syllabus   

UNIT – 1 : SETS, RELATIONS AND FUNCTIONS 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.

UNIT – 2: COMPLEX NUMBERS AND QUADRATIC EQUATIONS 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.

UNIT – 3 : MATRICES AND DETERMINANTS 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.

UNIT – 4 ERMUTATIONS AND COMBINATIONS Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications.

UNIT – 5 :MATHEMATICAL INDUCTION Principle of Mathematical Induction and its simple applications.

UNIT-6: BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS Binomial theorem for a positive integral index, general term and middleterm, properties of Binomial coefficients and simple applications.

UNIT – 7 : SEQUENCES AND SERIES 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. Arithmetics - Geometric progression.

UNIT – 8 : LIMIT, CONTINUITY AND DIFFERENTIABILITY 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.

UNIT – 9 : INTEGRAL CALCULUS 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.

UNIT – 10 : DIFFERENTIAL EQUATIONS :  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:

UNIT – 11 : CO-ORDINATE GEOMETRY Cartesian system of rectangular co-ordinates in a plane, distance formula,section formula, locus and its equation, translation of axis, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axis. Straight lines Various forms of equations of a line, inter-section 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 inter-section 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.

UNIT – 12 : THREE DIMENSIONAL GEOMETRY : Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two inter-secting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, inter-section of a line and a plane, coplanar lines.

UNIT – 13 : VECTOR ALGEBRA 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.

UNIT – 14: STATISTICS AND PROBABILITY 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.

UNIT – 15 : TRIGONOMETRY Trigonometrical identities and equations. Trigonometrical functions. Inverse trigonometrical functions and their properties. Heights and Distances.

UNIT – 16 : MATHEMATICAL REASONING Statements, logical operations and, or, implies, implied by, if and only if. Understanding of tautology, contradiction, converse and contrapositive.

For More Information on : Mewar University MUEE 2013 Mathematics Syllabus  

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Mewar University MUEEE 2013 SyllabusBITSAT 2013 Mathematics SyllabusGITAM GAT 2013 Mathematics SyllabusVSAT 2013 Mathematics SyllabusVITEEE 2013 Mathematics SyllabusSRMEEE 2013 Mathematics SyllabusJEE Advanced 2013 Mathematics SyllabusJEE (Main) 2013 Syllabus for Mathematics ExamKEAM 2013 Entrance Test Mathematics SyllabusGOA CET 2013 Mathematics Syllabus

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GOA CET 2013 Mathematics Syllabus

GOA Common Entrance Test GOA CET 2013 Mathematics Syllabus is made available for the Students. All the Students who aspires to apply for GOA CET 2013 Entrance Test for Admission to VariousUndergraduate Engineering Programs in Engineering Colleges are hereby informed that the Directorate of Technical Education Goa State has Uploaded the GOA CET 2013 Syllabus. Students can check the GOA CET 2013 Physics, Chemistry and Mathematics Syllabus so that they can Prepare well and Crack the GCET 2013 Entrance Test. Students can get the Syllabus details by clicking on the Links given below.

UNIT –I : RELATIONS AND FUNCTIONS
1. Relations and Functions :
Types of relations : reflexive, symmetric, transitive and equivalence relations.  One to one and onto functions, composite functions, inverse of a function. Binary operations.
2. Inverse Trigonometric Functions.
Definition range, domain, principal value branches, Graphs of Triangle & inverse trigonometric functions. Elementary properties of inverse trigonometric functions. Periodicity of function and fundamental period.
UNIT – II : ALGEBRA
1. Matrices :
Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix. Symmetric and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication Non-commutatively of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to
square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).
2. Determinants :
Determinant of a square matrix (up to 3 x 3 matrices) properties of determinations, minors, of actors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables ( having unique solution ) using inverse of a matrix.

UNIT – III CALCULUS
1. Limits , Continuity and Differentiability :
Revision of algebraic limits, exponential limits, logarithmic limits, limits of  trigonometric and inverse trigonometric functions. Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concept of
exponential and logarithmic functions and their derivative. Logarithmic differentiation. Derivatives of ax, ex, log x , apx+q, eax+b, log ( ax + b ) using first principle. Derivative of functions expressed in parametric forms. Second order derivatives Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretations.
2. Applications of Derivatives :
Applications of derivatives rate of change, increasing/decreasing functions, tangents & normals, approximation, maxima and minima (First derivative test motivated geometrically and Second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).

3. Integrals :
Integration as inverse process of differentiation. Integration of a variety of functions by substitution by partial fractions and by parts, only simple integrals of the type to be evaluated. Definite integrals as a limit of a sum. Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

4. Applications of the Integrals :
Applications in finding the area under simple curves, especially lines, area of circles/parabolas/ellipses (in standard form only), are between the two above said curves (the region should be clearly identifiable).

5. Differential Equations :
Definition, order and degree, general and particular solutions of a differential equation.
Formation of differential equation whose general solution is given. Solution of
differential equations by methods of separation of variables, homogeneous differential
equations of first order and first degree. Solutions of linear differential equation of the
type.
UNIT – IV : VECTORS AND THREE–DIMENSIONAL

GEOMETRY
1. Vectors :
Vectors and scalars, magnitude and direction of a vector. Direction cosines /rations of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position
vector of a point dividing a line segment in a given ration. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors, scalar triple product , volume of a parallelepiped, vector triple product and its properties.
2. Three – dimensional Geometry :
Direction cosines/ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes, (iii) a line and a plane, Distance of a point from a plane.

UNITS – V : PROBABILTY
1. Probability :
Multiplication theorem on probability. Conditional probability, independent events, total probability, Baye’s theorem Random variable and its probability distribution, mean and variance of haphazard variable. Repeated independent (Bernoulli) trial and Binominal distribution

Recommended Books for GOA CET 2013 Mathematics Preparation :

Prescribed textbooks (Published by Goa Board of Secondary and Higher Secondary
Education, Porvorim)
1. Mathematics Part-I Textbook for Class XIIth
2. Mathematics Part-II Textbook for Class XIIth

For More Updates on : Goa Common Entrance Test GCET 2013 Admission

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GOA CET 2013 SyllabusSRMEEE 2013 Mathematics SyllabusSRMEEE 2013 SyllabusJEE Advanced 2013 Mathematics SyllabusJEE Advanced 2013 SyllabusJEE Main 2013 SyllabusJEE (Main) 2013 Syllabus for Mathematics ExamKEAM 2013 Entrance Test Mathematics SyllabusEAMCET Mathematics SyllabusSyllabus for IIT JEE- MATHEMATICS

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