MODEL PAPER
FIRST SEMESTER, M. Sc INFORMATION TECHNOLOGY

Paper - VI (MIT - 106): Mathematical Foundations

Note to the examiner: Since most of the students admitted to the course are from Arts/Commerce streams, level of the course is only foundation level and text books used are that of XII class.
1. Question
1. Find the domain and range of the function
   
   OR
   Draw the graph of the absolute value function y = |x|.
2. Find the domain and range of the function y = 15 - 3cosx

   OR
   Evaluate the following limits:

   1. 
   2. 
2. Question
1. For what value of k is the function
   continuous at x = 3.

OR
Find the derivatives of the following functions with respect to x:


1. 
   
2. x³ + y³ = 3axy
2. Evaluate:
1. 
2. 

OR
Evaluate:

1. 
2. 
3. Question.

Solve
1. 
   
   

   OR
   x²dy + y(x + y)dx = 0

2. 
   

   OR
   

4. Question.


1. If
   , find x and y so that A² + AI = yA

   OR
   Find the inverse of the matrix
   

2. Solve the following system of equations using matrix method: -
   

   OR If
   , show that A² - 4A - 5I = 0.

5. Question

Find the value of the determinant


Solve for x the determinant


OR
Prove that


6. Question.
1. Show that the vectors (1, 2, 3), (3, -2, 0) form a linear independent set.
2. Define linear dependence and linear independence of vectors.
7. Question.
1. Define
   1. Proper set
   2. Power
2. Define Cartesian Products and equivalence relation.
3. Define one-one auto mapping and many-one auto mapping.
8. Question.
1. Define tautologies and contradictions.
2. Write the Algebra of propositions.
3. Define negation of a conditional proposition.