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Rajiv Gandhi Proudyogiki Vishwavidyalaya 2007-2nd Sem M.C.A Computer Aplications .(ester) ,.-., - Question Paper

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MCA-204
M.C.A.(Second Semester) EXAMINATION,Nov.-Dec.,2007
COMPUTER ORIENTED NUMERICAL ANALYSIS
(MCA-204)
Time : 3 Hours
Maximum Marks : 100
Minimum Pass Marks : 40

Note : All ques. are compulsory. In internal choice, 1 ques. from every Unit.

Unit - I
1.(a) define the errors due to shortage, limitations and safeguards against them.
(b) obtain a real root of the formula xlog10x = 1.2 by Regula-Falsi method, accurate to
3 decimal places.

2.(a) compute the value of (x^2 - y^2)/(x+y) with x= 0.4845 and y= 0.4800 using normalized
floating point arithmetic. Compare the outcome with the value of (x-y).
(b) Show that Newton's meethod has a quadratic convergence.

Unit - II
3.(a) Derive Newton's forward interpolation formula and use it to estimate the value of
f(1.25) from the subsequent table :

(b) Evaluate :
?1 to 0 v(sin x + cos x ) dx
Using Simpson's 1/3 rule, accurate to 3 decimal places using 7 ordinates.

4.(a) obtain F(9) from the subsequent table:

(b) Write short notes on the subsequent :
(i) Gauss-Legendre integration method
(ii) Inverse interpolation

Unit - III
5.(a) Write short notes on the subsequent :
(i) Partial and complete pivoting
(ii) Ill-conditioned equations
(b) Apply Runge-Kutta 4th order method to obtain an approximate value of y when x = 0.2
in step of 0.1. provided that dy/dx = x +y and y=1 when x=0.

6.(a) obtain the solution of the system of equations :
83x + 11y - 4z = 95
7x + 52y + 13z = 104
3x + 8y + 29z = 71
using Gaussian-elimination method.
(b) Using Runge-kutta 4th order method obtain y when x =1.2 in steps of 0.1 provided that :
dy/dx = x^2 + y^2 and y(1) = 1.5

Unit - IV
7.(a) The subsequent data are the number of seeds germinating out of 10 on damp filter for
80 sets of seeds. Fit a binomial distribution to these data :
(b) obtain the point of inflexion of the normal curve :

y = (1/sv2?) e^-1/2(x-m/s)^2

8.(a) From records of Army Corps kept over 20 years, the subsequent data was obtained, showing
the number of deaths caused by the kicks of a horse. compute the theoretical Poisson
Frequencies :
[given e^-0.61 = 0.5436]
(b) 5 dice were thrown 192 times and the number of times 4,5 or six were as follows :
compute ?^2

Unit - V
9.(a) For a random sample of 10 pigs fed on diet A, the increases in weight in pounds in
certain period were :
10, 6, 16, 17, 13, 12, eight 14, 15, nine lbs.
For a different random sample of 12 pigs fed on diet B, the increases in weight in the
identical period were :
7, 13, 22, 15, 12, 14, 18, 8, 21, 23, 10, 17 lbs.
Show that the estimate of population variance in the 2 samples was not significantly
various ( for v1= 11, v2=9, the 5% value of F= 3.112).
(b) Ten individuals chosen at random from a population of their heights are obtained to be
in inches 63,63,64,65,66,69,69,70,70,71. explain the suggestion that the mean height
in the universe is 65 inches. provided that for nine degress of freedom, the value of
Student's t at 5% level of significance is 2.262.

10.(a) Show that in two ? two contingency table wherein the frequencies are
?^2 = (a++c+d)(ad-bc^2)/(a+b)(c+d)(b+d)(a+c)

(b) Write short notes on the subsequent :
(i) Normal distribution
(ii) Comparison of large samples

18.25 44.00

54.25