Rajiv Gandhi Proudyogiki Vishwavidyalaya 2007-2nd Sem M.C.A Computer Aplications .(ester) , e, -university exam paper

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

Note : Attempt all ques. by selecting 2 parts from every ques.. All ques. carry equal
marks.

1.(a) discuss arithmetic operations for normalized floating point numbers giving examples.
(b) obtain a real root of the formula xlog10x = 1.2 by method of false position accurate to
4 decimal places.
(c) obtain the iterative formulae for finding vN,3vN where N is a real
number, using Newton's method. Hence evaluate v32 and 3v41 accurate to
4 decimal places.

2.(a) Derive Newton's backward interpolation formula and use it to obtain the value of f(0.7) from the
ahead table :
x f(x)
0.1 2.68
0.2 3.04
0.3 3.38
0.4 3.68
0.5 3.96
0.6 4.21

(b) The subsequent table provide the values of x and y :
x f(x)
1.2 4.2
2.1 6.8
2.8 9.8
4.1 13.4
4.9 15.5
6.2 19.6
obtain the value of x corresponding to y=12 Language's technique.
(c) Evaluate integration 0 to one dx/ 1+x by kjusing :
(i) Simpson's 3/8 rule.
(ii) 3 point Gausssian quadrature formula.

3.(a) Write an algorithm for solution of a system of equations by Gauss-seidel method and use it to
solve the system of equations :
27x+6y-z = 85
6x+15y+2z=72
x+y+54z=110
(b) Using Runge-Kutta 4th order method obtain the value of y where x=0.1 and x=0.2, provided that
dy/dx = x+y, y(0) = 1
(c) Solve :
10x-7y+3z+5u = 6
-6x+8y-z-4u = 5
3x+y+4z+11u = 2
5x-9y-2z+4u = 7
by gauss elimination method.
4.(a) describe binomial distribution and obtain its mean and variance.
(b) obtain the probability that at most five defiective fuses will be obtained in a box of 200 fuses,
if experience indicates that 2 percent of such fuses are defective.
(c) If 2 normal universes have the identical total frequency but the standard deviation of 1 is k
times that of other, show that the maximum frequency of the 1st is (1/k) times that of
other.

5.(a) Ten individuals are chosen at random from a population and their heights obtained to be in
inches 63,63,64,65,66,69,69,70,7,71. explain the proposal that the mean weight in the
universe is 65 inches provided that for nine d.f. the value of learner t at 5% level of
significance is 2.262.
(b) 200 digits were chosen at random from a set of tables. The frequencies of the digits were :
Digit Frequencies
0 18
one 19
two 23
three 21
four 16
five 25
six 22
seven 20
eight 21
nine 15

Use the x2 test to assess the correctness of the hypothesis that the digits were distributed
in equal numbers in the tables from which these were choosen. The 5% value of x2, for nine d.f.
is 16.919.
(c) Write notes on the subsequent :
(i) Null hypothesis
(ii) F-test
(iii) Critical region
(iv) Composite hypothesis

Earning:   Approval pending.