MCSE-004
1. (a) If 0.333 is the approximate value of 1/3, then find absolute,
relative and percentage errors.
(6 Marks)
(b) For
x = 0.4845 and y = 0.4800, calculate the value of (x2 – y2) / (x +y) using normalized floating point arithmetic compare value with
the value of (x – y). (4 Marks)
2. (a) Find the real root of equation f(x) = x3 – x – 1 = 0 using Bisection method. (5 Marks)
(b) How many
iterations of Bisection method are required to be performed, to obtain smallest
positive root of x3 – 2x – 5 = 0, correct upto 2 decimal
places. (3 Marks)
(c) Use Newton’s method to find root of the
equation x3 – 2x – 5 = 0 (5 Marks)
3. (a) Use Gauss
Elimination to solve
10x1
– 7x2 = 7;
-3x1
+ 2.099x2 + 6x3 = 3.901;
5x1
– x2 + 5x3 = 6.
Correct to six decimal places of significant digit.
(b) Solve Ax = B, where
LU decomposition method.
(c) Solve the
following system of equations using (i) Jacobi Method (ii) Gauss – seidel
method
x + y – z = 0;
- x + 3y = Z,
x – 2z = 3,
assume the initial solution vector as [ 0.8 0.8
2.1]T (10 Marks)
4. (a) For the
given discrete data find the interpolating polynomial using
(i) Lagrange’s interpolation
(ii) Newton Divided difference interfdation
|
xi
|
0
|
1
|
3
|
|
|
Fi
|
1
|
3
|
55
|
|
(b) Evaluate
by using (i) Simpson’s 1/3 rule (ii) Simpson’s 3/8 rule (iii)
Weddle’s rule
(c) Solve the
difference equation
(where y(0) = 2) find y(0.1) and y(0.3) correct to four
decimal places using
(i) Runge-kutta second order formula
(ii) Runge-Kutta Fourth order formula
5. Find the two
regression lines from the following data
|
X
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
|
Y
|
10
|
12
|
16
|
28
|
25
|
36
|
41
|
49
|
40
|
50
|
|
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Note: Answer with Dotcom Books
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(Last 5 year solved question
paper with Assignment solutions)
9825183881
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