Mahatma Gandhi University (MGU) 2006 B.Tech Computer Science and Engineering Mathematics - Question Paper

2006 Mahatma Gandhi University B.Tech Computer Science and Engineering Mathematics june 2006 ques. paper

G 1636    (Pages i 3)    Keg. No................................

Name..................................

B.TECH. DEGREE EXAMINATION, MAT/JUNE 2006 Fifth Semester

Branches : Computer Science Engineering/Information Technology

ENGINEERING MATHEMATICSIV (RT)

(New Scheme2002 admission onwards)

Time ; Three Hours    Maximum : 100 Marks

Answer one question from each module.

All questions carry equal marks.

Module I

1.    (a) Explain the objects of queueing theory.

(b) A petrol station has two pumps. The service time follows the exponential distribution with mean 4 minutes. Cars arrive for service in a Poisaon process at the rate of 10 cars per hour.

(i)    Find the probability that a customer has to wait for service.

(ii)    What is the proportion of time the pump remains idle ?

2.    (a) The belt shaping for conveyors in open cast mine occur at the rate of 2 per shift. There is only

one hot plate available for vulcanising and it can vulcanise on an average 5 holts snap per shift,

(i)    What is the probability that when a bolt snaps, the hot plate is readily available ?

(ii)    What is the average number in the system ?

(iii)    What is the waiting time of an arrival ?

(iv)    What is the average waiting time plus vulcanising time ?

(b) A TV repairman finds that the time spent on his jobs has an exponential distribution with mean 30 minutes. If he repairs sets in the order in which they came in and if the arrival of s ets is approximately Poisson with ail average rate of 10 per 8 hour daj; what is the repairmans expected idle time each day ? How many jobs are ahead of the average set just brought in ?

Module II

3.    (a) Find a root of 2x - 3 sin i - 5 = 0 correct to four decimal places using Regula Falsi method.

(b) Using Jacobi method solve the system of equations 10ac - 5y - 2z = 3, 4x 10y + 3z = 3. x + 6y 10s = - 3, correct to four places of decimals.

4.    (a) Evaluate Vl2 correct to four places of decimals, by Newton-Raphsan method.

(b) Using Gauss Seidel method, solve correct to four decimal placcs the system of equations :

Module III

5.    (a) Derive Newtons forward interpolation formula.

... ³ (b) Using Trapezoidal rule and Simpsons rule evaluate correct to three decimal places j

2

by dividing (2,3) into 8 equal parts.    

6.    (a) Use Lagranges formula to fit a polynomial to the following data :

x : - 1 0 2 3 y : -8 3 1 12 .

Hence find the value ofy when x - 1,

Module IV

7. (a) Solve graphically the following Linear Programming Problem :    .

Maximize % ~ 22x₁ + 18x% subject to 3*_x + 2%2 < 48, x + x₂- 20, Jtjv x₂ > 0.

(b) Solve the following Linear Programming Problem by Simplex method : Maximize Z = 50i₁ + 6Qx₂ +- 60x₃ such that x₁ + 2*2 + Sx₃< 7, 2 + 3x₂ < 7, *J, x₂, x₃ > 0.

. (a) Using Big M method, solve the following Linear Programming Problem Minimize Z = Sx₁ + 6x₂ subject to

2xj + 5i₂ > 1500, Sac, + x₂ 2 1200, x_v x,₂Z0.

(b) Apply the principle of duality to solve the following Linear Programing Problem Minimize Z = 2x₁ + x₂ such that

Module V

Solve the following transportation problem for minimum cost

Di D2 D3 Dj Dg D6 Supply

1 2 1 4 S 2 3 3 2 1 4 3 4 2 5 9 6 2 3 1 7 3 4 6

Demand 20 40 30 10 50 25

Solve the following assignment problem of six persons and six jobs in which cach jab should bc assigned to one and only one of the six persons so that the total jobs time is the most minimum.

Job (in hours)

1 2 3 4 5 6

126	130	142	160	178	167
132	180	192	200	181	195
135	145-	170	145	128	135
132	142	145	160	135	180
145	173	148	170	141	190
138	137	151	161	160	170

Attachment: mahatma-gandhi-university--mgu--2006-b-tech-computer-science-and-engineering-34487-1.pdf

Earning:   Approval pending.