LNMU B.Sc. part-1 mathematics (sub./gen.) Syllabus

Lalit narayan mithila university, Darbhanga B.Sc. part-1mathematics (sub./gen.) Syllabus

Time- 3 hours
Full marks- 100

Sixteen questions to be set and Eight to be answered selecting at least one from each group. Group-A
set theory, Modern Algebra and Linear Algebra (7 questions) Set Theory:- De Morgan's laws, Cartesian product of sets. Equivalence relation, Partition of a set Fundamental theorem on equavalence relation. Countability of rational, real and algebraic number. (2 questions)
Abstract Algebra :- Nations of group, abelian group with simple examples, Uniqueness of identity and inverse, Cancellation laws in a group. Reversal rule. Definitions and examples of subgroup and cyclic group (1 question)
Definitions, simple examples and simple properties of Ring, integral doman and field (1 question)
Matrices, Transpose, Orthogonal, adjoint and in of the matrix Rank of Matrix (2 questions) Definition, examples and properties of vector space, vector subspace. (1 question)
Group-B 
Real Analysis (Four questions) :
Sequence and their convergence, Cauchy's general principle of covergence Bounded sequence, Monotonic sequences. (1 question) Convergent and divergent Series. Convergence of the positive term series. comparision test. Cauchy's root test. D' Alembert's ratio test. Raabe's test and Liebnitz's test questions) Continuity and differentiability of real function of single real variable with examples (1 question)
Group-C 
Analytic Geometry of Two and Three Dimensions (Five questions)
Analytic Geometry of Two dimensions :- System of circles. Coaxial circles. radical axis, General equation of second degree and its reduction to standard forms of parabola. Ellipse and Hyperbola. Equation of tangents and normal for general equation. (3 questions)
Analytic Geometry of three dimensions :- Rectangular Cartesian co-ordinates. Direction cosines. Angle between two straight lines. Equations of plane and straight line. condition for coplanarity of straight lines. Equation of shortest distance. (2 questions)

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