(Established
under section 3 of UGC Act, 1956)
Course
& Branch: B.E /B.Tech- Common to ALL Branches
Title
of the paper: Engineering Mathematics – I/
Engineering Mathematics - III
Semester:
III Max. Marks: 80
Sub.Code:
20301 (2004/2005)/6C0049/ 6C0032/301Time:
3 Hours
Date: 21-04-2008 Session: AN
PART – A (10
x 2 = 20)
Answer
All the Questions
1. Prove that 
2. State initial value theorem.
3. If y
satisfies the equation y//+ 3y/ 2y = e-1 and
y(0) = 0 and
y/
(0) = 0. find L[y]
4. Solve y(t) = a sin t = 2 
5. Determine whether function 2xy + i(x2 – y2)
is analytic or not.
6. What do you mean by conformal mapping?
7. State Cauchy’s integral theorem.
8. Find the Residue of 
9. What is meant by type I and type II errors?
10. Give the
statistic for testing the significance of mean in small samples.
PART – B (5 x 12 = 60)
Answer All the Questions
11. Find L[te-1 cosh t]
(or)
12. Find using 
convolution theorem.
convolution theorem.
13. Solve: 
(or)
14. Solve: y// - 3y/ + 2y =
et.
15. Find an analytic function whose imaginary
part is 3x2 y – y3.
(or)
16. Find the bilinear transformation that maps
the points
z1 = -i, z2 = 0, z3 =
i in to the points w1 = -1, w2 = i, w3 = 1.
17. Evaluate using Cauchy integral formula 
where C is the circle |z| = 3.
(or)
18. Find the radius pf 
at each of the poles.
at each of the poles.
19. A random
sample of size 16 values from a normal population showed a mean of 53 and a sum
of squares of deviation from the mean equals to 150. Can this sample be
regarded as taken from the population having 56 as mean. Obtain 95% confidence
limits of the mean of the population.
(or)
20. Given the
following contingency table for hair colour and eye colour. Find the value of y2.Is there
good association between the two?
|
|
Hair colour
|
||||
|
|
|
Fair
|
Brown
|
Black
|
Total
|
|
Eye Colour
|
Blue
|
15
|
5
|
20
|
40
|
|
Grey
|
20
|
10
|
20
|
50
|
|
|
Brown
|
25
|
15
|
20
|
60
|
|
|
Total
|
60
|
30
|
60
|
150
|
|
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