Rajasthan Public Service Commission
RAS Pre-Syllabus: Mathematics (Code No. 20)
Sets, relations, equivalence relations, Natural numbers, Integers, Rational
numbers, Real and Complex numbers, division algorithm, greatest common division
polynomials, division algorithm, derivations, Integral, rational real and
complex roots of a polynomial, Relation between roots and Coefficients, repeated
roots, elementary symmetric functions, Groups, rings, fields and their
Addition and multiplication, elementary row and column operation, rank
determinants, inverse, solutions of systems of linear equations.
Real numbers, order completeness property, standard functions, limits,
continuity, properties of continuous functions in closed intervals,
differentiability, Mean value Theorem, Taylors Theorem, Maxima and Minima,
Application to curves tangent normal properties, Curvatute, asymptotes, double
points, points of inflection and tracing. Definition of a definite integral of
continuous function as the limit of a sum, fundamental theorem of integral
Calculus, methods of integration, rectification quadrature, volume and surfaces
of solids of revolution. Partial differentiation and its application. Simple
test of convergence of series of positive terms, alternating series and absolute
Differential Equations :
First order differential equations, Singular solutions, geometrical
interpretations, linear differential equations with constant coefficients.
Analytic Geometry of straight lines and conics referred to Cartesian and
polar Coordinates; three dimensional geometry for planes, straight lines,
sphere, Cone and Cylinder.
Concept of particle, lamina, rigid body, displacement, force, mass, weight,
concept of scalar and vector quantities, Vector Algebra, Combination and
equilibrium of coplanar forces, Newton's Laws of motion, motion of a particle in
a straight line; Simple Harmonic motion, projectile, circular motion, motion
under central forces (inverse square law), escape velocity.
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