Analytical Geometry 3D And Vector Calculus B.Sc Model Question Papers : alagappauniversity.ac.in

Name of the University : Alagappa University
Degree : B.Sc
Department : Mathematics
Subject Code/Name : Analytical Geometry 3D And Vector Calculus
Semester : I
Document Type : Model Question Papers
Website : alagappauniversity.ac.in

Download Model/Sample Question Paper : APRIL 2011 : https://www.pdfquestion.in/uploads/alagappauniversity.ac.in/3966.-B.Sc.%20Maths.pdf

Alagappa University B.Sc Mathematics Question Paper

Time : 3 Hours
Maximum : 100 Marks
Part A :

Related / Similar Question Paper : Alagappa University B.Sc Human Physiology Question Paper

Analytical Geometry 3D

1. Find the angle between the planes
2. Write down the equations of the straight lines passing through-
3. Find the point where the line– 2 – 4 6
4. State the conditions for the straight line 1 1 x – x y – y

5. Find the centre and radius of the Sphere
6. Find the tangent plane at – –1, 4, – 2- on.
7. If – – 2xz4 – x2 y , find – – at – 2, –2, –1-
8. Find the value of a such that
10. State the divergence theorem.
11. Find the equation of the plane passing through thepoints – 3
12. Find the equation of the plane through the line o
13. Find the perpendicular distance from – 3, 9, –1- to
14. Prove that the lines 3x – 4y –
15. Find the centre and radius of the circle
16. Find the sphere having the circle
17. Prove :(a) – – u – v – – – u – – v.
18. Show that the vector – y2 – z2 – 3yz – 2x- i
19. If A = 2xy i – yz2 j – xzk and S is the surface of the
20. Use Stoke’ theorem to show that – – – – – .
21. Prove that the equationx2 – y2 – 4z2 – 4yz – 4zx – 2x
22. Prove that the lines1 10 – 1 ; 3 1 –

Operations Research

(Non-CBCS—2004 onwards)
Time : 3 Hours
Maximum : 100 Marks
Section A (10 × 2 = 20)

Answer all questions.
1. Write some applications of OR ?
2. What is Operation Research ?
3. Define : Ordering cost and holding cost.
4. Define : Setup – Cost.
5. Define : Queueing system.
6. Explain (i) E(W) (ii) E(n) (iii) E(v) (iv) E(m).
7. Define critical path.
8. List the three different time estimates used in PERT.
9. State the Rules for determining a saddle point.
10. Define rectangular games.

Section B : (6 × 8 = 48)
Answer any six questions.
11. Explain various models in OR.
12. Derive the Replacement Policy when the value of money changes with time.
13. A manufacturer has to supply 10,000 units/ day. He can produce 25,000 units/day. The cost of holding a unit 20 paise per year and set up cost per run is Rs. 180. How frequently and of what size the production runs to be made.

14. The annual demand for an item is 3,200 units. The units costs is Rs. 12 and inventory carrying charges 30 % per annum. If the cost of one procurement is Rs. 200 determine :
(i) EOQ and
(ii) Minimum average yearly cost.

15. Explain : (M/M/I) : (N/FIFO).
16. Two repairmen are attending five machines in a workshop. Each machine breaks down according to a Poisson distribution with mean 3 per hour. The repair time per machine is exponential with mean 15 minutes. Find the Probability that the two repairmen are idle, that one repairmen is idle.
17. Write the procedure for determining critical path.
18. A Project has the following properties. Find the critical
path and total time for the project.
Activity : 1 – 2 1 – 3 2 – 4 3 – 4 3 – 5 4 – 9 5 – 6 5 – 7
Duration : 4 1 1 1 6 5 4 8
Activity : 6 – 8 7 – 8 8 – 10 9 – 10
Duration : 1 2 5 7
19. Solve the two person game.
20. Solve the following 2×3 game graphically.

Section C : (2 × 16 = 32)
Answer any two questions.
21. Let the value of money be assumed to be 10 % per year. Suppose machine A is replaced after every 3 years, whereas machine B is replaced after every six years. The yearly cost of both the machines are given below. Using that determine which machine should be purchased.
Year : 1 2 3 4 5 6
Machine A : 1,000 200 400 1,000 200 400
Machine B : 1,700 100 200 300 400 500

22. The demand for an item is uniform at a rate of 20 units per month. The first cost in Rs. 10 each time a production run is made. The production cost is Re. 1 per item and the holding cost is Re. 0.25 per item per month. If the shortage cost is Rs. 1.25 per item per month determine how often to make a production run and of what size it should be ?

23. A Television 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 sets is approximately Poisson with an average rate of 10 per 8 hour day, what is repairman’s expected idle time each day ? How many jobs are ahead of the average set just brought in ?

24. The following network shows the completion of project what is the probability of completing the work in 19 days ?