Mahatma Gandhi University (MGU) 2007 B.Tech Computer Science and Engineering Mathematics- Question Paper
2007 Mahatma Gandhi University B.Tech Computer Science and Engineering Mathematics january2007 ques. paper
F 3042 (Pages : 3) deg. No...................-...............................
Name........................................................
B.TECH. DEGREE EXAMINATION, JANUARY 2007 Fifth Semester
Branches : Computer Science and Engineeringflnformation Technology
ENGINEERING MATHEMATICSIV (RT)
(Regul ar/S up plementar y)
Time : Three Hours Maximum : 100 Marks
Answer one question from each module.
All questions carry equal marks.
Module I
1. (a) Write notes on queueing theory. . {5 marks J
(b) Cars arrive at a petrol pump with exponential inter arrival timehaving mean minute.
1 , .
The attendant take on an average of "jr minute per car to supply petrol. The service time
being exponentially distributed. Determine
(i) the average number of cars waiting to be served ;
Cii) the average number of cars in the queue ; and
(iii) the proportion of lime'for which attendant is idle.
(15 marks)
2. (a) Arrivals at a telephone booth are considered to be Poisson with an average time of 10 minutes
between one arrival and the next. The length of a phone call is assumed to be distributed exponentially with mean 3 minutes.
(i) What is the probability that a person arriving at the booth will have to wait 7
(ii) What is the average length of queue that forms from time to time ?
(10 marks)
(b) A barber shop has 6 chairs to accomodate people waiting for hair cut. Assume the customers who arrive when all 6 chairs are full leave without entering the barber shop. Customers arrive at the average rate of 3 per hour and spend an average of 15 minutes in the shop then find (i) the probability a customer can get directly into the barber ehair upon arrival ;
(ii) expected number of customers waiting for a hair cut.
(10 marks) Turn over
Module II
3. (a) Find a root of the equation 2 x - log10x = 7 near 3.5 using Regula-Falsi method.
(10 marks)
(b) Using Jacobis method, solve the system of equations :
&x + 2y + 2 = 12
(10 marks)
(10 marks) (10 marks)
* + 4 + 2? = 15 x + 2y + 5z = 20
4. (a) Compute YiT correct to 4 decimal places by Newton-Raphson method.
(b) Using bisection method, find a root of* -x 11 s 0.
n/2
5. (a) Using Trapezoidal rule and Simpson's rule, evaluate Jsinx dx by using 11 ordinates.
0
(10 marks)
Derive Newtons backward interpolation formula. (10 marks)
(b) 6. (a)
Using Lagranges interpolation formula, find/'(4) if/XO) = l,/(2) = 19,/O) = 55,/(5) = 241, f{S) = 415.
dy
dx
