Vinayaka Missions University 2012 B.Sc Mathematics Mathematical methods 1030504 - Question Paper
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COURSE CODE -1030504 UG DEGREE EXAMINATION - FEB 2012 BSC (MATHS)
MATHEMATICAL METHODS (For Candidate Admitted from Calendar 2007 Onwards) Time: 3 Hours Max. Marks: "5
PART -A
Answer All the Questions: 10 X 2 = 20
1. What is mean by Venn diagrams?
2. Define graphs.
3. What is mean by combinations?
4. Given x2 + y2 = a2. find dy/dx
5. Calculate standard deviation of 3.6.8.12,8.6.15,8.9.7
6. Define PDF.
7. Define population.
8. What is mean by hypothesis?
9. Define chi square test?
10. Define standard error?
PART - B
Answer All the Questions: 5 X 5 = 25
11. a. Verify that A fl (BUC) = (AflB) U (ADC)
(Or)
b. Find tie centre and radices of the sphere.
12. a. Find the derivate of the x2 sin x
(Or)
b. Find the equation of the tangent to the circle x2 + y2 = 25 at the point (3.4).
13. a. Define: a. Composite functions b. Trigonometric functions
(Or)
b. State and Prove Bay s theorem.
14. a. What art the merits and dements of cluster sampling?
(Or)
b. What are the differences between Correlation & Regression?
15. a. Find the area of the parallelogram where diagonals are given by 3i + j - 2k and I - 3j -*-4k
(Or)
b. Out of 10 male and 7 female cats, a sample consisting of 2 males and 2 females was chosen for an experiment. In how many ways could this be done?
PART -C
Answer any Two Questions: 2 X 15 = 30
16. Suppose seven coins have been tossed. Calculate the probability of a combination which contains 4 heats and 3 tails.
17. Verify Euler's theorem for the function F(x.y) = x4 y2 sin l(y/x).
18. Evaluate f0n4 tan :x dx.
19. We tossed two identical coins simultaneously for 200 times. We got two heads 55 times, two tails 55 times, and one head and one tail 90 times. Does this result agree with the hypothesis that the tossing is random?
20. If u = 2i + 2j - k, v = i - 3j + 2k. then find Iu X vl and a unit vector perpendicular to both u and v.
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