University of Mumbai 2009-3rd Sem B.E Electrical and Electronics Engineering Numerical Techniques - Question Paper
Numerical Techniques Sem III May 2009
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(REVISED COURSE)
VR3273
[Total Macks : 100
Con. 2640-09. *
(1) Question No. 1 is compulsory.
(2) Attempt any four questions out of remaining six questions.
(3) Make suitable assumptions if required and justify the same.
(4) Write programs in C/C++.
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1. (a) Find absolute, relative and percentage error in following numbers. Determine
5
5
5
5
10
10
10
number of significant digits :
(i) a = 123-41769543 a = 123-41
(ii) b b 0-0053102500 b = 0-0051
t (fii) c = 450550 C = 450552.
(b) Define the operators A, V, 5, n and E. Prove that -
(i) 25 = A + V (ii) E = 1 *- A.
(c) Using Picards method solve
dy .
= 1 + xy such that y = 0 when x = 0. dx 7
(d) Derive the equation for Regula-falsi method using geometrical interpretation.
2. (a) List the bracketing methods and open methods and find the real root of the
equation x sin x 4 cos x = 0 using Newton-Raphson method correct to three decimal places.
(b) Solve the following equations by Gauss-Seidel method.
27x + 6y - z = 85, 6x + 15y + 2z = 72, x + y + 54z = 110.
3. (a)
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From the following table find the number of students who obtained marks less than 45. | ||||||||||
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Using Newton's divided difference formula, find the value of f(9) from the following table. | ||||||||||||
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10
(b)
Write a program for Lagranges interpolation method and using this formula, find the value of y when x = 10 from the following table.
10
4. (a)
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x |
5 |
6 |
9 |
11 |
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y |
12 |
13 |
14 |
16 |
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The result of measurement of electric resistance R of a copper bar at various temperatures tC are listed below : | ||||||||||||||||
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10
(b)
Con. 2640-VR-3273-09. 2
(a) The velocity of the train which starts from rest is given by the following table, 10 the time being reckoned in minutes from the start and speed in km/hour.
5.
vt
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Estimate approximately the distance covered in 18 minutes by Simpson's 3/8th rule. |
Solve = x + y2 wilh x0 = 0, y0 = 1 by Eulers modified formula find the 10 value of y when x = 0-5 taking h = 0*25.
(b)
dy
10
10
5
10
6. (a) Solve = x + y with initial conditions y(1) = 2 and find y at x = 1 -2,
x = 1-4 by Runge-Kutta Method of Fourth Order taking h = 0-2.
(b) Write a algorithm and c/c++ program for Gauss Elimination method and also solve the following set of equations using Gauss Elimination method.
2x + y + z 10, 3x + 2y + 3z = 18, x + 4y + 9z = 16.
7, (a) Explain the propagation of errors.
(b) Derive Newton Cotes integration formula and also write a program Simpsons 1/3rd rule.
(c) Write a short note on Golden section search.
i
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Attachment: |
| Earning: Approval pending. |
