## MP PAT 2018 Syllabus – Mathematics

MATHEMATICS (M)

**ALGEBRA:**Algebra of complex mumbers. Graphical representation of complex numbers modulus, 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. uadratic expressions, quadratic equations in one variable, Permutations and combinations. Bionomial Theorem (any index) exponential and logarithmic series. determinants upto third order and their order and their elementary properties matrices types of matrices, adjoint and inverse of matrix, elementary. Application in 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 trignometrical equations. Relations between sides and angles of a triangle. Solutions of triangles, inverse; trigonometrical functions, height and distance (Simple Problems).**CO-ORDINATE GEOMETRY OF TWO DIMENSIONS:**Rectangular cartesain 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 angle between two lines.**VECTOR ALGEBRA:**Definition of vector, addition of vector, components in three dimensional space. Scalar and vector products. Triple products, simple application 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 problems in mecharics, increasing and decreasing frunctions. Maxima and Minima of function of one variable. Roll’s theorem and mean value theorem.**INTEGRAL 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 seperation 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 equation 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.