Practical Examination April-2015

Subject: Numerical Methods and Optimization

Time: 2.00 Hrs

Marks: 50

Examination Seat No:

Class: T.E. (Mechanical)

__________________________________________________________________________________
Instructions:

1
2
3
4

Draw the flowcharts of all methods.

Solve any one question from 1 & 2 , 3 & 4.
Submit attached (a) Question paper (b) printout pages to the supervisor.
Write Examination seat number in printout page as well

___________________________________________________________________________________

SET-A
Q1. Write a program to solve root of equation f(x)=cosx-1.3x with accuracy of
0.01 using bi-section method.

[20]
OR
4

2.

Solve

the

integral

using

trapezoidal

rule

4 x+ 2dx
1

[20]
Q 3. Using Langranges interpolation formula for given set of values find
y(1.5)

[30]

X
0
Y=f(x) 2

1
3

2
12

5
147

OR
Q4 Solve following set of equation using Gauss elimination method
X+3y+z=10

X+2y+5z=12

4X+y+2z=16

[30]

Practical Examination April-2015

Subject: Numerical Methods and Optimization

Time: 2.00 Hrs

Marks: 50

Examination Seat No:

Class: T.E. (Mechanical)

__________________________________________________________________________________
Instructions:

1
2
3
4

Draw the flowcharts of all methods.

Solve any one question from 1 & 2 , 3 & 4.
Submit attached (a) Question paper (b) printout pages to the supervisor.
Write Examination seat number in printout page as well

___________________________________________________________________________________

SET-B
Q1. Write a program to solve root of equation f(x)=-0.9x 2+1.7x+2.5. With
initial guesses x1= 2.8 and x2 =3, using three iteration of bi-section method.
[20]
OR
1

Q2. Solve the integral using simpsons 1/3rd rule

(cosxx )/(1+ x)dx

0

[20]
Q3. Q1. Write the program on Gauss-Elimination Method with Solver. Also draw the
Flowchart for the same. Given: Solve 1) 10x+y+z=12;

2)2 x+10y+z=13;

3)

[30]

2x+2y+10z=14.

OR
Que 4. Using newtons forward interpolation formula for given set of values
find y (3.5)

[30]

Y=F(x)

19

48

99

178

291

444

643

894

Practical Examination April-2015

Subject: Numerical Methods and Optimization

Time: 2.00 Hrs

Marks: 50

Examination Seat No:

Class: T.E. (Mechanical)

__________________________________________________________________________________
Instructions:

1
2
3
4

Draw the flowcharts of all methods.

Solve any one question from 1 & 2 , 3 & 4.
Submit attached (a) Question paper (b) printout pages to the supervisor.
Write Examination seat number in printout page as well

___________________________________________________________________________________

SET-C
Q1. Write a program to solve root equation f(x)=xe xcos3x-0.5 between the
limits of x1=0 and x2=1 with accuracy of 0.01 using false position method.
[20]
OR
1

Q2. Solve the integral using simpsons 3/8th rule

sinx/( 2+ 3 sinx)dx
0

[20]

Que 3. Solve following set of equation using Gauss Seidal

Method.
4x+y+2z=16

x+3y+z=10

x+2y+5z=12

[30]
OR

Practical Examination April-2015

Subject: Numerical Methods and Optimization

Time: 2.00 Hrs

Marks: 50

Examination Seat No:

Class: T.E. (Mechanical)

__________________________________________________________________________________
Instructions:

1
2
3
4

Draw the flowcharts of all methods.

Solve any one question from 1 & 2 , 3 & 4.
Submit attached (a) Question paper (b) printout pages to the supervisor.
Write Examination seat number in printout page as well

___________________________________________________________________________________

Q2. Write the program on Lagranges interpolation with Solver. Also draw the
Flowchart for the same. Given: Find y at x=1.5 for the following data.
[30]
x
y

0
2

1
3

2
12

5
47

SET-D
Que 1. Write a program to solve root equation f(x)= e xcosx-1.2sinx-0.5. With
initial guesses x1= 0 and x2 =1, using three iteration of regula falsi method [20]
OR
Q2. Write the program on Newton-Raphson Method with Solver.

Given: Find root of

[20]

f(x)=0.51x-sin(x)=0; do 3 iterations.

Que 3.

Find dy/dx at x=0.1 using Newtons Forwards

Differentiation
X

0.1

[30]
0.2

0.3

0.4

0.5

Practical Examination April-2015

Subject: Numerical Methods and Optimization

Time: 2.00 Hrs

Marks: 50

Examination Seat No:

Class: T.E. (Mechanical)

__________________________________________________________________________________
Instructions:

1
2
3
4

Draw the flowcharts of all methods.

Solve any one question from 1 & 2 , 3 & 4.
Submit attached (a) Question paper (b) printout pages to the supervisor.
Write Examination seat number in printout page as well

___________________________________________________________________________________

-2.3

-1.6

-1.2

-0.91

-0.69

OR
Que-4 . Write the program on Gauss-Elimination Method Given: 1) 10x+y+z=12; 2)2
x+10y+z=13; 3) 2x+2y+10z=14.
[30]

SET-E
Q1. Write the program on Newton-Raphson Method with Solver. Also draw the Flowchart
for the same. Given: Find root of f(x)=cos(x)-xex =0; accuracy=0.0001.

[20]

OR

x + y dxdy

Que 2. Solve the double integral using trapezoidal rule.

for x =

1 to 3 and y= 0 to 2. With step size for both x and y is 1

[20]
Que 3. Using Langranges interpolation formula for given set of values find
y(1.5)
[30]
X
Y=f(x)

0
2

1
3

2
12

5
147

Practical Examination April-2015

Subject: Numerical Methods and Optimization

Time: 2.00 Hrs

Marks: 50

Examination Seat No:

Class: T.E. (Mechanical)

__________________________________________________________________________________
Instructions:

1
2
3
4

Draw the flowcharts of all methods.

Solve any one question from 1 & 2 , 3 & 4.
Submit attached (a) Question paper (b) printout pages to the supervisor.
Write Examination seat number in printout page as well

___________________________________________________________________________________

OR
Que-4 .Solve following set of equation using Gauss elimination method with
partial pivoting
X+3y+z=10
X+2y+5z=12
4X+y+2z=16
[30]

SET-F
Que-1. Write a program to solve root of equation
accuracy of 0.001 using newton raphson method.

f(x)=excosx-1.4 with
[20]

OR
Que 2. Solve the integral using Guass Legender 2 point formula
4

x 3 + x1 dx
1

[20]

Practical Examination April-2015

Subject: Numerical Methods and Optimization

Time: 2.00 Hrs

Marks: 50

Examination Seat No:

Class: T.E. (Mechanical)

__________________________________________________________________________________
Instructions:

1
2
3
4

Draw the flowcharts of all methods.

Solve any one question from 1 & 2 , 3 & 4.
Submit attached (a) Question paper (b) printout pages to the supervisor.
Write Examination seat number in printout page as well

___________________________________________________________________________________

Que 3. Solve following set of equation using Tridigonal matrix algoritham

(Thomas method) method
X+2y=3
2x+3y+z=4
2y-z=1
[30]
OR
Que 4. Using newtons forward interpolation formula for given set of values
find y (3.5)
[30]
X
Y=F(x)

2
19

3
48

4
99

5
178

6
291

7
444

8
643

9
894

SET-G
Que-1. Write a program to solve root of
Successive Iteration Method
OR

equation x 3 -15x+8=0 using

[20]

Que 2. . Write the program on Simpsons 1/3rd rule with Solver. Given: Find integration of
f(x)=ex-x3-2x+1; with limits 1 to 4. n=6
[20]

Practical Examination April-2015

Subject: Numerical Methods and Optimization

Time: 2.00 Hrs

Marks: 50

Examination Seat No:

Class: T.E. (Mechanical)

__________________________________________________________________________________
Instructions:

1
2
3
4

Draw the flowcharts of all methods.

Solve any one question from 1 & 2 , 3 & 4.
Submit attached (a) Question paper (b) printout pages to the supervisor.
Write Examination seat number in printout page as well

___________________________________________________________________________________

Que-3. Solve the following equations by Gauass Seidal Method.

x1+20x2+9x3= -23 , 2x1-7x2-20x3= -57 and 20x1+2x2+6x3=28 . Write a
Computer program .Also solve it by MATLAB .Assume Acc=0.001
OR

[30]

Que-4. Solve Elliptic Laplace equation w.r.t. grid shown in fig. with specified
BCs. Find Temp.,T1, T2, T3, T4 H=K=250.Write a Computer program
[30]

SET-H
Que 1. Write a program to solve root of equation x 3 -15x+8=0 using successive
iteration method
[20]
OR
Que-2. Solve dy/dx = x+2y for given boundary condition that
x=1,y=1 find y(1.4) take h=0.1. using Eulers Method
[20]

Practical Examination April-2015

Subject: Numerical Methods and Optimization

Time: 2.00 Hrs

Marks: 50

Examination Seat No:

Class: T.E. (Mechanical)

__________________________________________________________________________________
Instructions:

1
2
3
4

Draw the flowcharts of all methods.

Solve any one question from 1 & 2 , 3 & 4.
Submit attached (a) Question paper (b) printout pages to the supervisor.
Write Examination seat number in printout page as well

___________________________________________________________________________________

Que 3. Using newtons forward interpolation formula for given set of values
find y (3.5)
[30]
X
2
3
4
5
6
7
8
9
Y=F(x)
19
48
99
178
291
444
643
894
OR
Que-4 . Solve the parabolic equation for the following condition using explicit
finite difference method at t=0 U= sin x (0<x<1) at x=0 and x=1, u=0 for all
values of t. taking increment in t as 0.02 and increment in x as 0.2. tabulate
values of u for t=0 to 0.006 and x=0 to 1.
[20]

SET-I
Que-1 . Fit a straight line using following data. Find values of a and b.
X
Y

1
0.5

2
2.5

3
2

4
4
OR

5
3.5

6
6

7
5.5

[20]

Practical Examination April-2015

Subject: Numerical Methods and Optimization

Time: 2.00 Hrs

Marks: 50

Examination Seat No:

Class: T.E. (Mechanical)

__________________________________________________________________________________
Instructions:

1
2
3
4

Draw the flowcharts of all methods.

Solve any one question from 1 & 2 , 3 & 4.
Submit attached (a) Question paper (b) printout pages to the supervisor.
Write Examination seat number in printout page as well

___________________________________________________________________________________

Que-2 . Write the program on Simpsons 1/3rd rule with Solver. Given: Find integration of
f(x)=ex-x3-2x+1; with limits 1 to 4. n=6
[20]

Que 3. Find dy/dx at x=0.1 using newtons forwards differentiation

X
Y

0.1
-2.3

0.2
-1.6

0.3
-1.2

0.4
-0.91

[30]

0.5
-0.69

OR
Que4. Write the program on Gauss-Elimination Method Given: 1) 10x+y+z=12;
[20]

2)2 x+10y+z=13; 3) 2x+2y+10z=14.

SET-K
Que-1. Fit a exponential equation y=aebx . find value of a and b.
X
0.1
0.2
0.3
0.4
Y
1.8
2.238
2.733
3.338

[20]

OR
Que-2. Solve dy/dx = x+y for given boundary condition that
x=0,y=1 find y(0.2) take h=0.1. using RK2 method.
[20]

Practical Examination April-2015

Subject: Numerical Methods and Optimization

Time: 2.00 Hrs

Marks: 50

Examination Seat No:

Class: T.E. (Mechanical)

__________________________________________________________________________________
Instructions:

1
2
3
4

Draw the flowcharts of all methods.

Solve any one question from 1 & 2 , 3 & 4.
Submit attached (a) Question paper (b) printout pages to the supervisor.
Write Examination seat number in printout page as well

___________________________________________________________________________________

Que-3. Solve the following equations by Gauass Seidal Method.

x1+20x2+9x3= -23 , 2x1-7x2-20x3= -57 and 20x1+2x2+6x3=28 . Write a
Computer program .Also solve it by MATLAB .Assume Acc=0.001
[30]
OR
Que-4. Solve Elliptic Laplace equation w.r.t. grid shown in fig. with specified
BCs. Find Temp.,T1, T2, T3, T4. H=K=250.Write a Computer program
[30]

SET-L
Que-1. For given data fit a Power equation y=axb . find value of a and b. [20]
X
Y

1
0.5

2
2

3
4.5

4
8

5
12.5

OR
Que 2. Solve the simultaneous method using RK2 method
Y=x+y, y(0)=1, Find y(0.2). Take h=0.1

[20]

Practical Examination April-2015

Subject: Numerical Methods and Optimization

Time: 2.00 Hrs

Marks: 50

Examination Seat No:

Class: T.E. (Mechanical)

__________________________________________________________________________________
Instructions:

1
2
3
4

Draw the flowcharts of all methods.

Solve any one question from 1 & 2 , 3 & 4.
Submit attached (a) Question paper (b) printout pages to the supervisor.
Write Examination seat number in printout page as well

___________________________________________________________________________________

Que 3. Using Langranges interpolation formula for given set of values find
y(1.5)
[30]
X
0
1
2
5
Y=f(x) 2
3
12
147
OR
Que-4. Write the program on Gauss-Elimination Method with Solver. Also draw the
Flowchart for the same. Given: Solve 1) 10x+y+z=12;
2x+2y+10z=14.

2)2 x+10y+z=13;

3)

[30]