### Banasthali Vidyapith MCA Entrance Exam Syllabus

• Mathematics : Arithmetic, Geometric and Harmonic Progressions. Permutation and combination, application of binomial theorem, exponential and logarithmic series. Matrix algebra and determinants. Trigonometrically problems on height and distance. Complex numbers and their properties.
• Statistics : Measures of central tendency, frequency distribution and probability concepts.
• Coordinate Geometry : Straight line, circle, ellipse, parabola and hyperbola.
• Algebra – Groups : Definition and simple properties of groups and subgroups, permutation groups, cyclic groups, cosets, Lagrange’s theorem on the order of subgroups and of a finite groups, morphisms of groups, Caley’s theorem, normal subgroups and quotient groups, fundamental theorem of homomorphism of groups.
• Rings : Definition and examples of rings (integral domain, division rings, fields), simple properties of rings, sub rings and sub fields, ring homomorphism and ring isomorphism.
• Vector Spaces : Definition and simple properties, subspaces, linear depend- ence and linear independence of vector spaces, dimension of a finitely generated vector space, basic of vector space, dimension of a subspace.
• Calculus and Differential Equations : Successive differentiation, Leibnitz theorem, polar tangent, normal sub tangent and subnormal, derivative of an arc (Cartesian and polar), expansion of functions by Maclaurin’s and Tayolr’s series, indeterminate forms, integration of irrational algebraic and trigonometrical functions, definite integrals, differential equation of first order and any degree, linear differential equations with constant coefficients, linear homogeneous differential equation of any order, maxima and minima of one variables, partial derivatives including Euler’s theorem and it’s application.
• Real Analysis : Description of the real number system as a complete order field, bounded and unbounded sets of real numbers, supremum and infimum of a bounded set, neighbourhood of a point, real sequences and their convergence, Cauchy sequence, Cauchy’s general principal of convergence, convergence of series, comparison test, ratio test, root test, alternating series, Leibnitz test, continuous functions and their properties.

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