(II) SYLLABI AND MODEL QUESTIONS FOR : M.Tech. in Industrial Mathematics and Computer Application of Kuvempu University / M.Tech. ( Computer Science and Technology / Computer Cognition Technology) of Mysore University.

 

Mathematics and computer science

 

Mathematics :

Analytical Geometry of 2-d Lines, Curves, Analytical Geometry of 3-d Lines, Planes and Conics, Differential Calculus Derivatives of any order, Derivatives of functions, curves, Polar coordinates, Partial differentiation, Integral Calculus Integrals of standard functions, Reduction formulae, Applications, Differential equations Up to second order homogeneous equations, Solutions using Laplace transforms

Probability Events, Sample space, Basic Theorems, conditional probability, Independence, Statistics Frequency tables, Histograms, Measures of averages and dispersion, Combinatorial analysis Permutations & Combinations, Linear and Non-Linear equations Solution, Application, Set theory Basic concepts, Operations on sets, Venn diagrams, De Morgans law, Power sets ,Relations Composite, Equivalence, Recurrence, Number system Binary, Ternary and others, Logic Operators, Truth tables, Tautologies, Algebraic structures- Groups, Rings, Sequences and Series- Convergence

Computer Science:

Fundamentals of Computers, Office Automation, Basics of Internet

C Computer Language :

Basic Data types, Fundamentals of C programming, Control structures, Bit wise operators, Storage classes, Functions, Arrays, Pointers.

MODEL QUESTIONS

 

Components:-

 

1) Mathematics:- 25 1 Marks Questions

15 2 Marks Questions

 

2) Fundamentals of Computers: 10 1 Marks Questions

5 2 Marks Questions

 

3) C Programming: - 15 1 Marks Questions

5 2 Marks Questions

 

 

Total: 50 1marks questions, 25 2 marks questions.

 

PART- I

Each question caries One mark

 

1.      The value of p is

a) 3 b) 3.142 c) 22/7 d) Irrational

 

2.      Which of the following is false?

a) Every field is an integral domain

b) Every finite integral domain is a field

c) An integral domain has zero divisors

d) Every integral domain is a ring

 

3.      If a finite set has five elements, then the number of subsets are:

a) 10 b) 32 c) 51 d) 25

 

4.      If 1, w, w2 are the cube roots of unity then w + w2

a) 1 b) 0 c) -1 d) 2

 

5.      The eccentricity of an ellipse with the major and minor axis in the ratio 5:3 is

a) 5/4 b) 5/3 c) 3/5 d) 4/5

 

PART II

Each question caries Two marks

 

1.      The value of c in Rolles theorem for the function f (x) = 1 x2 in [-1, 1] is

a) 0 b) 2 c) 4 d) 1

 

2.      The series: 1 + - 1/8 .

a) Divergent

b) Conditionally convergent

c) Absolutely convergent

d) None of these

 

3.      The equation of the circle passing through the points: (5, 3), (1, 5), (3, -1) is

a) x² + y² + 4x +4y +2 = 0 b) x² +y² 4x +4y +2 = 0

c) x² + y² + 4x 4y + 4 = 0 d) x² + y² 4x 4y 2 = 0

 

4.      Which declaration is correct if function f need to be defined?

a) extern int f( ); b) int f( ) c) (a) and (b) d) None

 

5.      The allowable operations on pointers are:

a) Increment b) Decrement c) Adding a constant d) All these