Madras University (UnOM) 2009 B.C.A Computer Application NumericalMethods, , - Question Paper
Numerical Methods BCA Semester3 Madras University
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21. Evaluate I - -- by Trapezoidal rule with
o1 + x
Aj = 0.5 and h2 = 0.25 and then use Romberg procedure for a better estimate of I. Compare the result with exact value.
22. Calculate mean deviation from the following data :
x: 10 11 12 13 14 f: 3 12 18 12 3
23. Explain about Poisson Distribution.
24. From the following data, state which series is more consistent:
Variable: 10-20 20-30 30-40 40-50 50-60 60-70
Series A: 20 18 32 40 22 18
Series B: 13 22 40 32 18 10
Time : Three hours Maximum : 75 marks
SECTION A (10 x 2 = 20 marks)
Answer any TEN questions.
All questions carry equal marks.
Each answer should not exceed 30 words.
1. Define Truncation Error.
2. Write the formula for Regular-Falsi method.
3. Write a note on Matrix inversion method.
4. What is Numerical differentiation?
5. Write the formula for Trapezoidal Rule for Numerical Integration.
6. Write the formula for fourth order Runge-Kutta method.
7. Define Frequency Distribution.
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8. What is meant by Median?
9. Define Standard Deviation.
10. Write a note on Binomial Distribution.
11. What is correlation coefficient?
12. Write a note on Chi-square Test.
SECTION B (5 x 5 = 25 marks)
Answer any FIVE questions.
All questions carry equal marks.
Each answer should not exceed 200 words.
13. Write an algorithm for computation of a root of f(x) = 0 by Newton-Raphson method.
14. Solve the following system by Gauss elimination method :
Xj + 2x2 + x3 = 0 2xx + 2x2 + 3x3 = 3 -x1 -3x2 = 2.
b
t5. Write an algorithm for the evaluation of J" f(x) dx
a
by Simpsons one-third rule.
16. Using Eulers method, compute y(0.l) and y(0.2) for the initial value problem,
y" + y = 0, y(0)=0, y'(0) = 1.
17. Find the Arithmetic mean of the following frequency distribution :
X: 5 10 15 20 25 30 35 40 45 50
Y: 20 43 75 67 72 45 39 9 8 6
18. Given that P(A) = 0.35, P(B) = 0.73 and P(AnB) = 0.14, find
(a) P(AuB)
(b) p(AnB)
(c) pjAufi).
19. Calculate Rank Correlation coefficient for the following data :
Roll Nos : 1 2 3 4,5
Mathematics Marks : 85 60 73 40 90 Accounts Marks93 75 65 50 80
SECTION C (3 x 10 = 30 marks)
Answer any THREE questions.
All questions carry equal marks.
Each answer should not exceed 500 words.
20. Solve the following system by Gauss-Seidal Iteration method :
20!+22+3 = 30 x1 - 40x2 + 3x3 = -75 2x1 ~x2 +10x3 =30
Give the solution correct to three significant figures.
3 51303/SAZ3C
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