Test No. & Name

105 - Computer Science & Statistics

Course Name

M.Sc. Computer Science & Statistics

Eligibility

B.Sc / B.A with any two of the following subjects: Mathematics, Statistics & Computers; B.C.A students with mathematics in Intermediate course.

Test A

Statistics: Measures of central tendency: Mean, Median and Mode. Measures of Dispersion: Range, Quartile Deviation, Mean Deviation, Standard Deviation and Coefficient of Variation. Random Experiment, Random Event, Elementary Events, Exhaustive Events, Mutually Exclusive Events, Independent Events. Classical definition of Probability-Relative Frequency approach to Probability-Sample Space, Sample Events. Addition and Multiplication Theorems. Random variable; Distribution functions, Probability density functions, Mean and Variance of Random Variables. Theoretical discrete distributions like Binomial, Poisson distribution-Mean and Variance of above distributions(without derivations). Reasoning and Mental Ability: According to GMAT syllabus.

Test B

Calculus : Differentiation: Definition, Differentiation of a function at a point and on an interval. Derivative of a function. Differentiation of Sum, Difference, Product and Quotient of function, Derivatives of Composite, Implicit, Parametric, Inverse circular, Hyperbolic and Inverse Hyperbolic functions, Logarithmic differentiation, Derivative of a function with respect to another function. Successive differentiation: Leibnitz theorem; Applications of Leibnitz theorem; Applications of Differentiation: Errors and approximations, geometrical interpretations of derivative, equations of tangent and normal at a point on the curve ; Lengths of tangent, normal, subtangent, subnormal at a point; derivative as a rate measure; increasing and decreasing functions; criteria for maxima and minima of functions in single variable- Partial differentiation of the first and second orders only. Integral Calculus : Integration as the inverse process of differentiation-Indefinite and definite integral - standard integral covering algebric, trigonometric, exponential and hyperbolic functions - methods of integration, substitution methods - integration by parts - evaluation of definite integral, properties of definite integral. Reduction Formulae. Definition of ordinary differential equations - degree and order of an ordinary differential equations - formation of differential equation - general and particular solution and premitive - solution of first order differential equations.

Test C

Matrix Theory : Types of matrices, addition and multiplication of matrices, inverse of a matrix, determinant of a matrix, determinant of second and third order - singular and non-singular matrices. Solution of simultaneous linear equations in two and three variables by Cramer''s rule - matrix inversion method and Gauss Jordan method. Trigonometry : Trigonometric ratios in compound angles, trigonometric ratios of multiple - sub multiple angles. Inverse circular functions, hyperbolic functions. Properties of triangles. Complex numbers and De Moivre''s Theorem.

Test D

SYLLABI FOR ENTRANCE TESTS IN SCIENCES, ENGINEERING, ARTS & COMMERCE

The syllabus prescribed hereunder for the tests is generally the same as the one followed for the B.Sc./ B.Com. / B.A. Degree under the Common Core Sheme 1995-98, unless otherwise specified.

Note

B.Sc. Applied Science candidates are also eligible to seek admission into all the courses* for which the B.Sc. Graduates of the following combinations of optional subjects are eligible to appear for AUCET-2006 tests: 1. Mathematics - Physics - Chemistry; 2. Mathematics - Physics - Statistics; 3. Mathematics - Physics - Electronics; **4. Mathematics - Physics - Computer Science.

* except the following chemistry courses, viz., Analytical, Bio-inorganic, Environmental, Inorganic, Foods, Drugs & Water Analysis, Organic, Physical, Nuclear, Marine Chemistry and Bio-Chemistry.

** If the specialization in B.Sc. Applied Science course is Computer Science.

Note

Note: The University has the right to offer or not to offer any of the courses notified.