B.Sc in Mathematics question paper

Hi I want the question paper of B.Sc in Mathematics of Jai Narain Vyas University?

[Kiran Chandar]

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Jai Narain Vyas University B.Sc in Mathematics question paper

Paper I
Algebra and Co-ordinate Geometry of Two Dimensions

Note : The paper is divided into five units. Two questions will be set from each unit. The candidates are required to attempt one question from each unit.

Unit1: The characteristic equation of a matrix. Eigen values and Eigen vectors. Cayley-Hamilton theorem and its use in finding the inverse of a matrix. Inequalities, continued fractions.

Unit 2: Relations between the roots and coefficients of general polynomial equations in one
variable. Symmetric functions of roots Transformation of equations. Descarte’s rule of
signs. Solution of cubic equations (Cardon method). Biquadratic equations.

Unit 3: Infinite series. Convergent series, tests for convergence of a series, comparison test, D’Alembert’s Ratio test, Cauchy’s root test, Raabe’s test, De Morgen and Bertrand’s test,
Cauchy’s condensation test, Gauss’s test. Alternating series, Leibnit’z test (Derivation ofabove tests not required).

Unit 4 : Polar equation of a conic, polar equations of tangent, normal, asymptotes, chord of contact, auxiliary circle, director circle of a conic and related problems.

Unit 5 : General equation of second degree. Tracing of conics.


Paper – II
Calculus

Unit 1: Polar Co-ordinates. Angle between radius rector and the tangent. Angle between curves in polar form. Length of polar substangent and polar subnormal, Pedal equation of a curve, Derivatives of an arc, curvature, various formulae, Centre of curvature and chord of curvature and related problems.

Unit2: Partial differentiation, Euler’s theorem on homogeneous functions, chain rule of partial differentiation, Maxima and Minima of functions of two independent variables and of three variables connected by a relation Lagrange’s Method of undetermined multipliers.

Unit 3: Asymptotes, double points, curve tracing, Envelopes and evolutes.

Unit 4: Rectification. Volume and Surfaces of solids of revolution. Theory of Beta and Gamma functions, Differentiation and integration under the sign of integration.

Unit 5: Evaluation of double and triple integrals and their applications in finding areas and volumes. Dirichlet’s integral. Change of order of integration and changing into polar coordinates.








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Jai Narain Vyas University - New Campus
Jodhpur, Rajasthan ‎

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