MA7158 Applied Mathematics Communication Engineers M.E Question Bank : valliammai.co.in
Name of the College : Valliammai Engineering College
University : Anna University
Department : Electronics and Communication Engineering
Subject Code/Name : MA7158–Applied Mathematics For Communication Engineers
Degree : M.E Communication Systems
Year : I
Semester : I
Document Type : Question Bank
Website : valliammai.co.in
Download : https://www.pdfquestion.in/uploads/va…0Engineers.pdf
Valliammai Applied Mathematics Question Paper
Unit –I( Linear Algebra ) :
Part – A :
1.Write a note on least square solution
Related : Valliammai Engineering College CU7301 Advanced Satellite Based Systems M.E Question Bank : www.pdfquestion.in/2792.html
2.Define singular value matrix
3.If A is a non singular matrix ,then what is A+ ?
4.What is meant by singular value of a matrix?
6.State Singular value decomposition theorem
7.Give an example of a Toeplitz matrix of order 3.
8.Explain least square solution
9.Define Toeplitz matrix with an example
11.Explain singular value decomposition in matrix theory
12. What is the advantage in matrix factorization methods?
14.Define pseudo inverse of a matrix A
15.Give some properties of generalized inverse
16.Define Hermitian matrix
17.Define singular value of a matrix
18.If A is a non singular matrix , then what is ????
19.Define an inner product space
20. Write the general form of the toeplitz matrix of order n. Also write any two applications of it.
Unit – II ( Linear Programming) :
Part –A :
1.What is degeneracy in a transportation model
2.Differentiate between balanced and unbalanced cases in Assignment model
3.List any two basic differences between a transportation and assignment problem
4.What do you mean by degeneracy?
5.Explian optimal solution in L.P.P
6.Solve the following L.P.P by using graphical method
8.What is the difference between feasible solution and basic feasible solution?
9.What is an assignment problem? Give two applications
10.Write down the mathematical formulation of L.P.P.
11.When will you say a transportation problem is said to be unbalanced?
12.What is a travelling sales man problem?
13.Enumerate the methods to find the initial basic feasible solution for transportation problem
14.Define transshipment problem
Unit- III – (Ordinary Differential Equations) :
Part –A :
1. What is a predictor- corrector method?
2. What is the difference between initial and boundary value problems?
3. Write down Adam Bashforth ‘s predictor and corrector method
4. What are the steps involved in shooting method?
5. What is weighting function of collocation method?
6. Explain stiff ordinary differential equations
9. Write down Runge- Kutta method of order four for solving initial value problems in solving ordinary differential equations
10. State the stability region for R-K method of fourth order
11. Differentiate single step and multi step method
13.Mention the methods available to solve boundary value problems
14. Discuss the stability of Euler’s method
15. Discuss the orthogonal collaction method.
16. Discuss the finite element method
Unit –V Queuing Theory :
1. Define traffic intensity of an M/M/1 queuing model .What is the condition for steady state in terms of the traffic intensity?
2. What is the effective arrival rate in an (M/M/1):( K/FIFO) model?
3. What do you mean by steady state and transient state in queuing theory?
4. Write Little’s formula for infinite capacity queuing system
5. There are 3 typists in an office .Each can type an average 6 letters per hour. If the letters arrive for being typed at the rate of 15 letters per hour What fraction of time all the typists will be busy?
6. For an (M/M/S ) (N/FIFO) queuing system write down the formula for 1)Average number of customers in queue 2) Average waiting time of customers in queue.
7. If people arrive to purchase cinema tickets at the average rate of 6 per minute ,it takes an average of 7.5 seconds to purchase a ticket . If a person arrives 2 minutes before the picture starts and it takes exactly 1.5 minutes to reach the correct seat after purchasing the ticket. Can he expect to be seated for the start of the picture?
8. Define M/M/2 queuing model. Why the notation M is used?
9. Consider an M/M/C queuing system .Find the probability that an arriving customer is forced to join the queue.
10. Suppose that customers arrive at a Poisson rate of one per every twelve minutes, and that the service time is exponential at a rate of one service per 8 minutes a) What is the average no. of customers in the system? b) What is the average time of a customers spends in the system?
11. Define the effective arrival rate for M | M | 1/N FCFS queueing system.