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Basic Mathematics

This is the collection of Sikkim Manipal University (SMU) question and answers for Basic Mathematics. It will help to prepare your examination. All question paper are classified as per semester, subject code and question type of Part A, Part B and Part C with multiple choice options as same as actual examination. SMU question papers includes year 2024, 2023, 2022 Sem I, II, III, IV, V, VI examinations of all subjects.

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Course Name        BCA (Bachelor of Computer Application)

Subject Code       BC0033 (Basic Mathematics)

Get Questions        PART - A    PART - B    PART - C

Basic Mathematics Syllabus.

Unit 1 Set Theory
Sets, types of sets, operation on sets, Venn diagrams, Cartesians product of two sets, Distributive laws

Unit 2 Mathematical logic
Proposition or statements, converse, inverse and contrapositive of an implication

Unit 3 Modern algebra
Binary operation, semi groups, monoid, group

Unit 4 Subgroups and other groups
Subgroups, cosets, cyclic groups, group of permutations

Unit 5 Basic graph theory
Definition of graphs, multigraphs, complete graphs, null graphs, bi-graphs, degrees, degree sequences

Unit 6 Data analysis
Data and statistical data, Frequency distribution, graphical representation, measures of central tendency, measures of dispersion

Unit 7 Permutation and combination
Fundamental principles, Permutation and Combination, Permutation of n different things taken r at a time, Permutation of things of which some are alike, circular permutation,
combinations, complementary combinations

Unit 8 Probability
Random experiment, sample space, event, probability additional theorem, classical approach, conditional probability, independent events, multiplication theorem, empirical

Unit 9 Elements of trigonometry
Radian and circular measure, trigonometric functions, identities, trigonometrical ratios of certain standard angles, allied angles, compound angles, multiple and sub multiple angles

Unit 10 Limits
Definition of limits, continuity, evaluation of limits, some of the standard limits with their derivations, exponential limit

Unit11 Continuity and differential calculus
Differentiation, equations of tangent and normal, pedal equations, polar coordinates, angle between radius vector and tangent, successive differentiation, indeterminate forms, partial

Unit 12 Integral Calculus
Integration by parts, integral as the limit of a sum, reduction formulae, integration of algebraic rational functions, integration of irrational functions, definite integrals and

Unit 13 Complex Trigonometry
Complex number definition, De Moivre’s theorem, Roots of a complex number, Exponential function of a complex variable, hyperbolic functions, logarithmic function of a
complex variable.

Unit 14 Matrices and determinants
Matrices, related matrices, matrix method of solution of simultaneous equations, elementary transformation of a matrix.

Unit 15 Infinite series
Convergence and divergence, series of positive terms, Binomial series, exponential series, logarithmic series.

Unit 16 Differential equations
First order differential equations, Practical approach to differential equations, first order and first degree differential equations, homogeneous equations, linear equations, Bernoulli’s
equations, exact differential equations.

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