Rajiv Gandhi Proudyogiki Vishwavidyalaya(Technical University) Computer M.C.A.(Second Semester) EXAMINATION,Nov.-Dec.,2007 model question papers

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2007 Rajiv Gandhi Proudyogiki Vishwavidyalaya(Technical University) Computer M.C.A M.C.A.(Second Semester) EXAMINATION,Nov.-Dec.,2007 Question paper

Course: M.C.A   University/board: Rajiv Gandhi Proudyogiki Vishwavidyalaya(Technical University)

M.C.A.(Second Semester) EXAMINATION,Nov.-Dec.,2007
Time : Three Hours
Maximum Marks : 100
Minimum Pass Marks : 40

Note : All questions are compulsory. In internal choice, one question from each Unit.

Unit - I
1.(a) Describe the errors due to shortage, limitations and safeguards against them.
(b) Find a real root of the equation xlog10x = 1.2 by Regula-Falsi method, correct to
three decimal places.

2.(a) Calculate the value of (x^2 - y^2)/(x+y) with x= 0.4845 and y= 0.4800 using normalized
floating point arithmetic. Compare the result 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 following table :

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

4.(a) Find F(9) from the following table:

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

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

6.(a) Find 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 fourth order method find y when x =1.2 in steps of 0.1 given that :
dy/dx = x^2 + y^2 and y(1) = 1.5

Unit - IV
7.(a) The following 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) Find 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 following data was obtained, showing
the number of deaths caused by the kicks of a horse. Calculate the theoretical Poisson
Frequencies :
[given e^-0.61 = 0.5436]
(b) Five dice were thrown 192 times and the number of times 4,5 or 6 were as follows :
calculate ?^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, 8 14, 15, 9 lbs.
For another random sample of 12 pigs fed on diet B, the increases in weight in the
same period were :
7, 13, 22, 15, 12, 14, 18, 8, 21, 23, 10, 17 lbs.
Show that the estimate of population variance in the two samples was not significantly
different ( 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 found to be
in inches 63,63,64,65,66,69,69,70,70,71. Discuss the suggestion that the mean height
in the universe is 65 inches. Given that for 9 degress of freedom, the value of
Student's t at 5% level of significance is 2.262.

10.(a) Show that in 2 ? 2 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 following :
(i) Normal distribution
(ii) Comparison of large samples


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