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Chapter Test-EC/EE/IN Engineering Mathematics
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Numerical Methods
Answer Keys and Explanations
1. [Ans. *] Range: 2.30 to 2.35
Let ( )
( )
( )
( )
( )
( )
( )
( )
2. [Ans. *] Range: 3.375 to 3.375
( )
( )
( )
( )
( )
( )
Root lies in [3.25, 3.5]
3. [Ans. A]
Given ( )
Now, For initial value
( )
( )
( )
|
First approximation is much near to
Option (A) is correct.
Chapter Test-EC/EE/IN Engineering Mathematics
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4. [Ans. *] Range: 1.916 to 1.917
√
; ;
( )
( )
( )
( )
( )
5. [Ans. *] Range: 4 to 4
( )
Maximum number if positive real roots for f(x) are number of sign changes in the coefficients
of x for f(x)
There is no sign change.
Maximum number of negative real roots of f(x) is number of sign changes in the coefficients of
x for ( )
Total real roots = Positive real roots+ Negative real roots
=4
6. [Ans. C]
From graphs, there would be exactly one point where
( )
( )
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7. [Ans. *] Range: 2.080 to 2.084
For ( ) , for which approximated root has to be found in (a, b) using results false method is
( ) ( )
( ) ( )
( )
( )
( ) ( )
( ) ( )
( )
( )
( ) ( )
( ) ( )
8. [Ans. A]
9. [Ans. D]
For regular – ‘ ’ ( ) in (a, b) is given by
( ) ( )
( ) ( )
10. [Ans. *] Range : 14 to 14
For a cubic polynomial
11. [Ans. *] Range: 0.10033 to 0.10033
Using Runge-kutta method of fourth order
( )
(
)
(
)
( )
( )
( )
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( (
)
)
( (
)
)
( )
12. [Ans. A]
Let ( )
Iterative equation using N-R method is
( )
( )
( )
( )
(
)
Option (A) is correct.
13. [Ans. *] Range: 100 to 100
x y
Third
term 3 2.7
3.7
4 6.4 2.4
6.1 0.6
5 12.5 3.0
9.1 0.6
6 21.6 3.6
12.7 0.6
7 34.3 4.2
16.9 0.6
8 51.2 4.8
21.7 0.6
9 72.4 5.4
27.1
10 100
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14. [Ans. *] Range: 1.70 to 1.72
As ( )
For iterative equation
15. [Ans. *] Range: 1.22-1.23
Using Forward Euler method
( )
( )
( )
( )
( )
( )
( )
( )
16. [Ans. C]
For convergence of N-R method iteration
*
+
√
17. [Ans. *] Range: 0.97372-0.97373
The Differential equation
( )
( )
Forward-Euler method (Predictor)
( )
( )
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( )
( ) ( )
Predictor corrector: ( )
* ( ) (
( ))+
( )
( ( ) )
( )
( )( ) ( )
( )
( )( ) ( )
18. [Ans. *] Range: 0.66 to 0.67
Error in three equations is
( )
( ) ( ) ( )
For minimum value of sum of squares
( )
( )
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( )
19. [Ans. B]
First approximation using second order R-K method
( )
( )
( )
(
)
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( ( )
)
20. [Ans. B]
For bisection method
Option (C) is correct answer.