Osmania University (OU) 2007 B.E Electronics
Code No.: 4337/N
FACULTY OF ENGINEERING B.E. II/IV Year (ECE/Mech./Prod./CSE) II Semester (Main) Examination, April/May 2008 (New)
MATHEMATICS - IV
Time : 3 Hours] [Max. Marks : 75
Answer all questions of Part A.
Answer any five (Questions from Part B.
Part A - (Marks : 25)
Choose the correct answer from the following :
1. If /(z) is analytic in a domain D and |/(z) | = K (constant) in D then/(z) is-
in D.
(a) Constant (b) 0 (c) None
l + i
2. The value of j (x - y + i x2) dz along the line from z = 0 to z = 1 + i is :
(a) (b) (c) (d) None
r zdz
3. Using Cauchys Integral formula the value of z2+\ where C : \z + i \ = 1 is
(a) - tii (b) 2ni (c) ni (d) None
zsinz
4. Residue of /(z) = _ 3 afz=nis
(a) 1 . (b) 0 (c) - 1 (d) None
5. Using Residue theorem the value of } 5 dz where C is the circle |z| = 2 is
(a) tci (b) - tci (c) 2ni (d) None
6. If A and B are two independent events, P (A/Bc) is-.
(a) P(A) (b) P(BC) (c) P (A) P (Bc) (d) P (Ac/B)
8. If A and B are two mutually exclusive events then P (An B) = P(A)- P[B/A) (TRUE / FALSE)
(b) F ~
(a) Z = sf -
9. If the number of observations (n < 30) then the test known as large sample test. (TRUE / FALSE)
10. A random sample of 10 boys had the IQ's 70, 120, 110, 101, 88, 83, 95, 98, 107 and 100. Do these data support the assumption of a population mean IQ of 160.
Part B - (Marks : 5 x 10 = 50)
11. (a) Verify that the function V{x} y) = e~x [y sin y + xcos y) is harmonic and find the corresponding analytic function f(z) = u (x, y) + iV {x, y).
(b) Find the bilinear transformation that maps z = 1, i, - 1 onto w = 2, i, - 2.
r dz
12. (a) Evaluate J - where Cis |z-3i| = 4 using Cauchy's integral formula.
xsin {mx)dx
m > 0, a > 0 using residue theorem.
13. (a) X is a normal variate with mean 30 and standard deviation is 5. Find the probabilities that (i) 26 < x< 40, (ii) x> 45.
(b) Fit a Poisson distribution to the following data :
No. of mistakes per page ; 0 12 3 4 No. of pages : 109 65 22 3 1
14. (a) Fit a second degree parabola by using least squares approximation for the
following data :
x ; 12 3 4 y : 1.7 1.8 2.3 3.2
(b) Derive rlies between -1 to 1.
15. (a) State and prove Bayes theorem.
(b) The diameter of an electric cable say X is assumed to be continuous Random variable with probability density function is given by /(x) = 6x(l-x);0<x<l. Determine a number b such that P(x < b) = P(x > b).
2z - 3
16. (a) Expand/{z) = 5 in the region 1 < |z| <2.
Z oZ jL
(b) Find the correlation coefficient and equations of regression lines for the following values of x, y.
x : 1 2 3 4 5
y : 2 5 3 8 7
17. (a) State and prove Cauchys integral theorem.
(b) If 2% of the items made by a factory are defective. Find the probability p that there are defective items in a sample of 100 items.
Attachment: |
Earning: Approval pending. |