Osmania University (OU) 2007 B.E Computer Science mathematics - Question Paper

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 :

o

(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 at z = n is

(a) 1 .    (b) 0    (c) - 1    (d) None

g_2

5.    Using Residue theorem the value of } 5 dz where C is the circle |z| = 2 is

c z ~z

(a) tci    (b) - tci    (c) 2ni    (d) None

6. If A and B are two independent events, P (A/B^c) is-.

(a) P(A)    (b) P(B^C)    (c) P (A) P (B^c) (d) P(A^C/B)

[P.T.O.

7. The test statistics for equality of population variances is

(a) Z = sf -

8.    If A and B are two mutually exclusive events then P (An B) = P(A)- P[B/A) (TRUE / FALSE)

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.

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(1-x);0<jc<1. 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: osmania-university--ou--2007-b-e-computer-science-48053-1.pdf

Earning:   Approval pending.