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Posted Date: 07 Jul 2009 Posted By:: rajesh kale Member Level: Silver Points: 5 (₹ 1)
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2007 Rajiv Gandhi Proudyogiki Vishwavidyalaya(Technical University) Computer M.C.A M.C.A.(Second Semester) EXAMINATION, June,2007 Question paper
MCA-204
M.C.A.(Second Semester) EXAMINATION, June,2007
COMPUTER ORIENTED NUMERICAL ANALYSIS
(MCA-204)
Time : Three Hours
Maximum Marks : 100
Minimum Pass Marks : 40
Note : Attempt all questions by selecting two parts from each question. All questions carry equal
marks.
1.(a) Explain arithmetic operations for normalized floating point numbers giving examples.
(b) Find a real root of the equation xlog10x = 1.2 by method of false position correct to
four decimal places.
(c) Find the iterative formulae for finding vN,3vN where N is a real
number, using Newton's method. Hence evaluate v32 and 3v41 correct to
four decimal places.
2.(a) Derive Newton's backward interpolation formula and use it to find 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 following table gives 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
Find the value of x corresponding to y=12 Language's technique.
(c) Evaluate integration 0 to 1 dx/ 1+x by kjusing :
(i) Simpson's 3/8 rule.
(ii) Three 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 fourth order method find the value of y where x=0.1 and x=0.2, given 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) Define binomial distribution and find its mean and variance.
(b) Find the probability that at most 5 defiective fuses will be found in a box of 200 fuses,
if experience shows that two percent of such fuses are defective.
(c) If two normal universes have the same total frequency but the standard deviation of one is k
times that of other, show that the maximum frequency of the first is (1/k) times that of
other.
5.(a) Ten individuals are chosen at random from a population and their heights found to be in
inches 63,63,64,65,66,69,69,70,7,71. Discuss the proposal that the mean weight in the
universe is 65 inches given that for 9 d.f. the value of Student 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
1 19
2 23
3 21
4 16
5 25
6 22
7 20
8 21
9 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 9 d.f.
is 16.919.
(c) Write notes on the following :
(i) Null hypothesis
(ii) F-test
(iii) Critical region
(iv) Composite hypothesis
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