META TAGS:-MPPSC GENERAL STUDIES SYLLABUS I MPPSC MAINS GENERAL STUDIES SYLLABUS I MPPSC NEW EXAM SYLLABUS I MPPSC GEOLOGY SYLLABUS I MPPSC MAINS AGRICULTURE SYLLABUS I MPPSC MAINS MILITARY SCIENCE SYLLABUS I MPPSC MAINS COMPLETE SYLLABUS I MPPSC MAINS PHILOSOPHY SYLLABUS I MPPSC MAINS HIND LITERATURE SYLLABUS I MPPSC MAINS ANTHROPOLOGY SYLLABUS I MPPSC MAINS LAW SYLLABUS I MPPSC MAINS ECONOMICS SYLLABUS I MPPSC MAINS POLITICAL SCIENCE SYLLABUS I MPPSC MAINS URDU LITERATURE SYLLABUS I MPPSC MAINS HISTORY SYLLABUS I MPPSC MAINS COMMERCE SYLLABUS I MPPSC MAINS CIVIL ENGINEERING SYLLABUS I MPPSC MAINS ELECTRICAL ENGINEERING SYLLABUS I MPPSC MECHANICAL ENGINEERING SYLLABUS I MPPSC MAINS PHYSICS SYLLABUS I MPPSC MAINS CHEMISTRY SYLLABUS I MPPSC SANSKRIT LITERATURE SYLLABUS I MPPSC MAINS ZOOLOGY SYLLABUS I MPPSC MAINS BOTANY SYLLABUS I MPPSC MAINS ALL SYLLABUS I
Group, Subgroup, cyclic group and their properties. Order of Elements of group Coset decomposition, Lagrange’s theorem. Normal subgroup, Quotient Group, Homomorphism, Isomorphism, Automorphism of Groups. Permutation, Permutation Groups, Cayley’s Theorem. Cauchy's Theorem and Sylow's Theorem for finite abelian and non abelian groups.
Ring Theory - Rings, Subrings, Ideals and quotient rings, Homomorphism & Isomorphism of rings, Integral domain, characterstic of an element. Polynomial rings, Field Polynomials over the rational fields. Unique factorization theorem.
2. Linear Algebra
Definition and examples of vector spaces, subspace, sum and direct sum of subspaces - Linear dependence and independence and their bases properties. Bases, Existence theorem for bases. Finite dimensional vector space. Dimension of a vector space. Dimension of sum of spaces. Quotient space and its dimension. Linear transformations and their representation as a matrix. The Algebra of Transformation. Rank Nullity Theorem. Eigen values and Eigen vectors of a linear transformation : Diagonalization of a matrix. Inner product space, Orthogonal vectors, orthogonal compliments. Orthonormal sets and bases. Bessel Inequality for finite dimensional space. Gram Schmidt’s orthogonalization process.
3. Differential Calculus
Convergence of sequence and series, limit & continuity of function. Differentiability. Successive differentiation, Leibnitze’s theorem. Applications of derivative, Tangent and normal, Asymptotes, Singular points, curve tracing. Mean value Theorem. Taylor's Theorem. Expansion in Taylor's and Maclaurin series. Maxima & minima of function of one variable.
4. Integral Calculus
Integration of rational, irrational and transcendental functions. Reduction formula. Definite integrals. Rectification quadrature, volume and surface of solid of revolution. Double & triple Integrals. Beta & Gamma functions, Change of order of Integration of double integral. Improper integrals and their convergence.
5. Differential Equation
Ordinary differential Equation of first order and higher degree. Homogeneous equation of first degree. Integrating factor. Linear Differential Equation with constant coefficients , Complementary functions and particular integrals. Linear Differential Equation with variable coefficients. Singular solutions linear Differential Equation and Equation reducible to linear form. Exact differential equation.method of variations of parameter. Simultaneous linear differential equations.
6. Vector Calculus
Differentiation of vector function ,Gradient, divergence & curl in Cartesian, cylindrical & spherical coordinate , Higher order derivatives. Vector integration, Gauss’s, Green’s & stoke’s Theorem, and their applications.
7. Analytical Geometry
Cartesian and polar coordinates in two and three dimensions. Second degree equations in two and three dimensions, Reduction to canonical forms. Straight lines, Shortest distance between two skew lines, plane, Sphere, Cone, Cylinder, Paraboloid, Ellipsoid, Hyperboloids of one and two sheets and their properties.
8. Statistics
Measures of central tendency:- mean, mode, median, measures of dispersion, range, inter quartile range, mean deviation, standard deviation skewness and kurtosis. Probability - Events, sample space, probability of an event, addition and multiplication Theorem, Baye's Theorem. Theoritical Distributions - Binomial, Poisson, Normal distributions and their properties & use. Method of least square, curve fitting, correlation & regression. Partial & multiple correlation (up to three variables)
Mathematics ( Code No. 07 ) Paper - II
1. Real Analysis & Metric Space
Riemann Integral, Integrability of continuous and monotonic functions. The fundamental theorem on Integral calculus. Mean value theorem of Integral calculus. Partial derivatives and differentiability of real valued functions of two variables. Schewarz & Young's theorem, Implicit function theorem. Definition and example of metric spaces. Neighbourhood , Limit points, interior points, open and closed sets. Closure and interior , Boundary points. Subspace of a metric space. Cauchy's sequence, completeness. Cantor intersection Theorem. Contraction principle. Real number as a complete ordered field, Dense subsets Baire category Theorem, Seperable, first countable and second countable space.
2. Complex Analysis
Continuity and differentiability of complex function. Analytic function, Cauchy - Riemann Equations, Cauchy's Theorem, Cauchy's Integral formula, Power series, Taylor's series, Laurent's series. Singularities, Cauchy's Residue Theorem, Cotour Integration, Conformal mapping, Bilinear transformations.
3. Advance Calculus
Functions of several variables, Limit, continuity and differentiability of function of two variables. Partial derivative, Change of variables, Euler's Theorem on homogenous functions. Taylor's Theorem for function of two variables. Maxima & minima and saddle point of function of two variable, Lagrange's method of multipliers. Indeterminate form.
4. Partial Differential Equations
Curve and surfaces in three dimensions, formulation of partial differential equations. solutions of equation of the type dx/P = dy/Q = dz / R . orthogonal trajectories. Paraffian Differential equation, partial differential equation of first order, solution by Cauchy's method. Charpit method of solution. Linear partial differential equation of second order with constant coefficient.
5. Linear Programming
Linear programming problem, basic solution, basic feasible solution & optional solutions, graphical method & simplex method of solution. Duality, Transportation and assignment problems. Travelling sales man problems.
6. Numerical Analysis
Numerical methods, solution of algebraic and transcendental equation of one variable by bisection, Regula-Falsi and Newton Raphson method. Solution of linear Equations by Gausian Elimination and Gauss Jordan (direct) method. Gauss seidel ( Iterative). Method, Newtons (forward & backward) & Lagrange method of interpolation. Numerical Integration : Simpson's one third rule. Gausion qudrature formula. Numerical solution of ordinary differential equations. Euler & Runge. Kutta Methods.
7. Boolean Algebra
Lattices and Algebraic structure. Duality Distributive and complementary lattice. Boolean lattices and Boolean algebras. Boolean functions & expressions. Propositional calculus. Design and implementation of Digital networks, switching circuits. graph, Paths & circuits, shortest paths - Eulerian paths & circuits. Application of graph for bridge problem, utility problem.
8. Mechanics
Statics - Analytical conditions of Equilibrium of coplanar forces. virtual works, catenary. Forces in three dimensions Poinsots Central axis. Stable & unstable equilibrium. Dynamics - Velocities & acceleration along radial & transverse directions and along tangential and normal direction. Simple .Harmonic motions - Elastic strings. Motion on smooth & rough plane curves. Motion in a resisting medium. Motion of a particle of varying mass.
The History of Modern India will cover history of the Country from about the middle of nineteenth century and would also include questions on important personalities who shaped the freedom movement and social reforms. The part relating to Indian culture will cover all aspects of Indian culture from the ancient to modern times.
2. Geography of India:
In this part, questions will be on the physical, economic and social geography of India.
3. Indian Polity:
This part will include questions on the Constitution of India, Political system, Indian Administrative system and related matters.
4. Current National issues:
This part is intended to test the Candidate's awareness of current national issues.
5. International Affairs & Institutions:
This part will include questions on important events in world affairs and on international institutions.
6. Indian Economy:
In this part, questions will be on the planning and economic development in India, economic & trade issues, Foreign Trade, the role and functions of I.M.F., World bank, ADB, W.T.O. etc..
7. Developments in the field of Science & Technology, Communication & Space:
In this part, questions will test the candidate's awareness of the developments in the field of Science & Technology, Communication and space and also basic ideas of computers.
8. India and the World:
This part is intended to test candidate's awareness of India's relationship with the world in various spheres, such as the following :
Role of India in the context of world.
Foreign Affairs, External security and related matters, Nuclear Policy.
9. Games & Sports:
Questions will assess the awareness of candidates in respect of games and sports at international and national level. It will also have questions pertaining to different awards and personalities in the context of India.
10. Indian Agriculture:
Attempt will be made to assess the general awareness of candidates in respect of crops, white revolution, green revolution, agriculture production and their impact on development of rural economy
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