#1
29th July 2014, 12:53 PM
 
 
TNPSC Mathematics Syllabus & Question Paper
Will you please provide the Mathematics Syllabus and question paper of TNPSC ?

#2
30th July 2014, 09:02 AM
 
 
Re: TNPSC Mathematics Syllabus & Question Paper
Detailed information regarding Mathematics Syllabus of TNPSC is given below which you are looking for . Mathematics UNIT I Basic Mathematics: Binomial, Exponential, Logrithmic series, summation of infinite series and approximation promblems. L Hospitals' rule, point wise convergence of sequence of functions, uniform convergence of sequences of funcitons, Consequences of Uniform convergence, Taylor's series. Theory of numbers : Prime and Composite numbers  Decomposition of composite number, Divisor of N, Euler function (N), Highest power of prime p contained in N. Divisibility of the product of r consecutive integers by r! Format's & Wilson's Theorems. Vector Spaces & Inner product spaces : Definitions and euqation of Vector space, subspace, liner Independence  bases  Dimension, Dual spaces, Inner products Spaces Orthogonality  Orthogonal complement. UNIT II ANALYTICAL GEOMETRY: Pairs of Straight lines  Angle between them  related problems  conditions for second degree equation to represent pair of straight line or Circle  System of Circles  Orthogonal and Coaxial system  Radical axis and radical centre  Limiting point  conics  parabola, ellipse and hyperbola  polar equations to straight line, circle and conic. Dimensions : Equation of a sphere with given centre and radius  General form of the euqation of a sphere  Diameter from  Circular section, tangent plane to a sphere  Radical plane  Coaxial system of spheres  Orthogonality  Equation of a Cone with its Vertex at the origin  Equation of a quadratic cone with given vertix and given guiding curve  necessary and sufficient condition for a general second degree equation to represent a cone, right circular cone  euqation of enveloping cone  general equation of a cylider  right circular cylinder. UNIT III CALCULUS: Differential: Higher order derivatives Leibnitz's theorem  simple problems using the above theorem. Maxima and Minima  conditions for external value  Standard function only  curvature  radius of curvature (Cartesian Coordinates only) Partial Differentiation: Total differentiation Coefficieng, Valvue of dy/dx and d2y/dx2 in case of implicit functions in x and y in terms of partial derivatives, Total differential, Jacobians. Integral: Methods of integration, Integration of rational and irrational algebraic functions, Bernaulli's formula for Integration by parts, reduction formulae  properties of difinite Integrals. Evaluation of double and triple integrals, change of order of integration, Double Integrals in polar Coordinates, application of double & triple Integrals to area, volume. Evaluation of Define integrals using Beta and gamma functions. UNIT IV STATICS: Gradient, Divergence, Curl, solenoidal & irrotational vectors, Directional derivative, Unit vector normal to a surface, tangent and normal planes to a surface 2, expansion formulea, Ordinary integrals of Vectors, line integrals, surface intergrals and volume Integrals. Gass stock, Green's theorems. Parallelogram and Triangle laws of force, Lamis theorem, parallel forces, moments, couples, three forces acting on a rigid body, conditons for equiliburium of Coplanar forces. Forces in 3 dimensions, Invariance of F2, Friction, Centre of Gravity, method of symmetry for uniformbodies like thin rod, thin parallelogram, Circular ring & lamina triangular lamina, trapezium lamina. UNIT V REAL ANALYSIS: Set and functions, sequences of real numbers  Definition, Limit, Convergent and divergent sequences, bounded sequences, monotonice sequence, series of real numbers, limit superior, Limit inferior, Cauchy, Sequence, convergent & divergent sequence, series with nonnegative terms, alternating series. Series of real numbers: rearrangement of series, Tests of absolute Covergence. Limits & matric spaces: Limit of a function on the real line, matric spaces, limits in matric spaces. Continuous functions on matric spaces, functions continuous at a point on the real line, reformulation, function continious on a matric space, open sets, closed sets, Discontinuous functions on 'R' Connectedness, Complexness and Compactness. UNIT VI OPERATIONS RESEARCH AND LINER PROGRAMMING: Origin and development of O.R.  Nature and characteristics of O.R. Models in O.R. General solutions, methods for O.R. models  uses and limitations of O.R. Linear Programming: Formulation of problems, Graphical solution  standard form. Definition of basic solution. degenerate Simplex method, Definition of artifical variable. Tranportation problem: Definition solutions to transport problem  intial feasible solution  optimality test  Degenerary  Travelling sales man problem Sequencing: Processing n jobs through m machines. UNIT VII ALGEBRA: Set theory  Relations  types of relations  Venn diagram  Groups  Sub group  order of an element  cyclic groups  normal groupsquotient groups  order of a Group Lagrange's theorem  homomorphism, automorphims, Cayley's theorm of permutation groups. Rings: Definition, examples  special classes of rings  Homomorphism, ideals and quotient rings  field of quotients of an integral domain  Euclidean rings. Matrices: Types of matrices  operation on matrices, singular and non singular matrices  Rank of a matrix and consistence of equation, eigen values & eigen vectors. Cayley  Hamilton theorem. Similar matrices, Diagonalisation of a matrix. UNIT VIII DIFFERENTIAL GEOMETRY: Curvature, Radius and centre of curvature in Cartesian Coordinates, Evalute  curvature in Polar Coordinates, pr equations, Angle between radius vector and tangent, Angle of intersection of two curves. Pedal equation of a curve, Envelopes, Asymptotes. Polar Coordinates : Equations of straight line, Circle in polars  equations of tangent, normal & polar Equations of Conics in polars  equations of tangent, normal, polar & asymptotes. UNIT IX DIRRERENTIAL EQUATIONS: Ordinary differential equations  first order but not of first degree. Total differntial equation Pdx + Qdy + Rdz = 0, second order differential equations with constant Coefficients. P.I. for the polynomials and eaxv, where V is Xn, Cos mx, Sin mx, n and m are constants. Differential equations of second order with variable Coefficients. Partial differential equations  formation of partial differential equations by elimination  Laplace transforms  Inverse laplace transform. UNIT X Dynamics: Virtual displacement, Principle of Virtual work. Kinematic: Velocity, Acceleration, components of velocity and acceleration work power, energy, Ractilinear motion  motion with constant acceleration  motion under gravity  motion along an inclined plane, motion under gravity in a resisting medium. Implusive forces and Impact: Implusive forces and Impact, Principles of Conservation of linear momentum, Collison of two smooth spheres  Direct impact of sphere on a fixed plane. Projectiles: Two dimensions motion of a particle  projectile, range on a horizontal plane  range on an inclined plane. Circular motion of a particle: Motion of a particle constrained to move along a smooth verticle circle under gravity  circular pendulum  simpel pendulum. Moments of Inertia: Momentsof Inertia of simple bodies of paralle and perpendicular axed theorem. Motion of a rigid body about a fixed axis. UNIT XI STATISTICS: Frequency distributions  Graphs of frequency distribution, measures of central tendency, measures of dispresion, normal probability curve, skewness, kur tosis, Probability  Addition and multiplicaiton theorem. Baye's theorem. Probability Distributions : Binomial, Poisson, Normal Bivariate data, Curve fitting  Method of least squares. Correlation and regression Coefficient  Regression lines  rank Correlation. Test of hypothesis  uses of X2  F tests  Tests involving means  Variances and proportions test of fit, test of independence in contingency table. 