Cochin University of Science and Techology (CUST) 2011-5th Sem B.Tech Computer Science and Engineering IT/CS/EC/CE/ME/SE/EB/EI/EE/FT 501 ENGINEERING MATHEMATICS IV(2006 Scheme) - Quest

B. Tech Degree V Semester exam November 2011

IT/CS/EC/ME/SE/EB/EI/EE/FT 501 ENGINEERING MATHEMATICS IV
(2006 Scheme)

Time: three Hours Maximum Marks: 100

PART A
(Answer All Questions)

(8 x five = 40)

I. (a) Distinguish ranging from discrete and continuous random variable. Also provide examples.

(b) A random variable X has the subsequent probability mass function
values of X=x : -2 -1 0 one two 3
P(x) : 0.1 k 0.2 2k 0.3 k
obtain value of k.

(c) discuss (i) Null and alternate hypothesis (ii) critical region.

(d) Write a note on test of significance for single mean when standard deviation is
known.

(e) obtain (?/E) f(x) where h is the interval of differencing.

(f) Evaluate ? (?+?)?^2 (x² + x) , h=1.

(g) discuss Euler's method in solving an ordinary differential equations.

(f) describe initial and boundary value issue.

PART B

(4 x 15 = 60)

II. (a) obtain mean and variance of binomial distribution . (7)

(b) A sample of 100 dry battery cells tested to obtain the length of life produced the
subsequent results:
? = 12 ; s = 3
Assuming the data to be normally distributed , what percentage of battery cells
are expected to have life (i) more than 15 hours (ii) less than six hours. (8)

OR

III. (a) If X is a Poisson variate such that P(X = 2) = 9P(X = 4) + 90P(X = 6) . obtain
the standard deviation . (7)

(b) From the subsequent data, find the correlation coefficient
N = 12; ? y = 5, ?x² = 670, ?y² = 25, ?xy = 334 (8)

IV. (a) describe (i) significance level (ii) kind I and kind II errors (iii) point estimation
in sampling theory. (6)

(b) A machine is supposed to produce washers of mean thickness of 0.12cm.
A sample of 10 washers obtained to have mean thickness of 0.0128cm and
S.D = 0.008. Test whether the machine is working in proper order at 5% level
of significance . (9)

OR

V. (a) A random sample size is 15 is taken from N(µ,s²) has ? = 3.2 and
s² = 4.24 . find a 90% confident interval for s² . (6)

(b) A random sample of size 18 is taken from a normal distribution N (µ,s²) .Test
the hypothesis H0 : s² = 0.36 against H1 : s² > 0.36 at a=0.05 , provided that
the sample variance s² = 0.68 . (9)

VI. (a) If y(75) = 246, y(80) = 202, y(85) = 118, y(90)=40, obtain y(79) using
Newton's forward interpolation formula. (8)

(b) Apply Stirling's formula to obtain y(25) for the subsequent data.


X 20 24 28 32

Y 2854 3162 3554 3992
(7)

OR

VII. (a) Use Lagrange's interpolation formula to fit a polynomial to the data.


X 0 1 3 4

Y -12 0 6 12

obtain the value of y where x = 2. (8)

(b) Evaluate ?_0^1¦ dx/(1+x²) using Simpson's 3/8 rule testing h = 1/6 . (7)

VIII. calculate y(0.1) and y(0.2) by Runge-Kutta method of 4?? order for the
Differential formula dy/dx=xy+y² , y(0) = 1. (15)

OR

IX. Using Schmidt's method obtain the value of u(x,t) satisfying the parabolic formula
four ?²y/?x²= ?u/?t and the boundary conditions.
u(0,t)=0= (8,t)
u(x,0)= x/2 (8-x)
at the point x=i where i=0,1,2,….,7 and dt=j/8 where
j=0,1,2,·········,5. (15)
***

Earning:   Approval pending.