Exam Details
| Subject | computer-oriented numerical methods (conm) | |
| Paper | ||
| Exam / Course | mca | |
| Department | ||
| Organization | Gujarat Technological University | |
| Position | ||
| Exam Date | June, 2017 | |
| City, State | gujarat, ahmedabad |
Question Paper
1
Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MCA SEMESTER- II EXAMINATION SUMMER 2017
Subject Code:2620004 Date:05/06/2017
Subject Name: Computer Oriented Numerical Methods
Time: 10.30 am to 01.00 pm Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1
Explain the following terms: Blunders, Formulation Errors, Data Uncertainty. Explain Total Numerical Error. How can one control numerical errors
07
Explain the concept of successive approximation method used to find root of equation. Discuss the convergence of the method using graphical techniques.
07
Q.2
Find a real root of −x 1 between 1 and 2 by bisection method. Compute five iterations.
07
Solve for a positive root of −4x+1= 0 by false position method.
07
OR
Using Newton-Raphson method find root of =4x by taking =2.
07
Q.3
Find Newton's forward difference interpolating polynomial for the following data and then obtain f(0.6).
x
0.1
0.2
0.3
0.4
0.5
1.40
1.56
1.76
2.00
2.28
07
If P is the pull required to lift a load W by means of a pulley block, find a linear law of the form P=mW c which connect P and W. Using the following data
12
15
21
25
50
70
100
120
Also Compute P when W=150kg.
07
OR
Q.3
Find function from following data using Langrange's interpolation formula.
x
0
1
2
5
2
3
12
147
07
Using least square method to obtain normal equations of parabola on data set
07
Q.4
Apply Newton's forward difference formula of interpolation to find at x=1 for following data.
x
1
1.05
1.10
1.15
1.20
1.25
1.30
1.0000
1.02470
1.04881
1.07238
1.09544
1.11803
1.14017
07
Derive Newton cotes' general quadrature formula. Using it obtain Trapazodial formula for numerical integration.
07
OR
Q.4
Derive Newton's Backward Difference interpolation formula of first order differentiation.
07
Compute the value of definite integral dx using simpson's 1/3 rule of numerical integration by taking h=0.2.
07
Q.5
Solve by Gauss-Seidel method, the following system of equations,
28x+4y-z=32, x+3y+10z=24, 2x+17y+4z=35
07
2
Apply Runge-Kutta method of fourth order to find approximate value of y when x=0.4 given that by taking h=0.2
07
OR
Q.5
Solve the system of equations using Gauss Elimination method.
x-2y+9z=8
07
Given 3x+ and 1. Find the values of y(0.1) and y(0. using the Taylor series method.
07
Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MCA SEMESTER- II EXAMINATION SUMMER 2017
Subject Code:2620004 Date:05/06/2017
Subject Name: Computer Oriented Numerical Methods
Time: 10.30 am to 01.00 pm Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1
Explain the following terms: Blunders, Formulation Errors, Data Uncertainty. Explain Total Numerical Error. How can one control numerical errors
07
Explain the concept of successive approximation method used to find root of equation. Discuss the convergence of the method using graphical techniques.
07
Q.2
Find a real root of −x 1 between 1 and 2 by bisection method. Compute five iterations.
07
Solve for a positive root of −4x+1= 0 by false position method.
07
OR
Using Newton-Raphson method find root of =4x by taking =2.
07
Q.3
Find Newton's forward difference interpolating polynomial for the following data and then obtain f(0.6).
x
0.1
0.2
0.3
0.4
0.5
1.40
1.56
1.76
2.00
2.28
07
If P is the pull required to lift a load W by means of a pulley block, find a linear law of the form P=mW c which connect P and W. Using the following data
12
15
21
25
50
70
100
120
Also Compute P when W=150kg.
07
OR
Q.3
Find function from following data using Langrange's interpolation formula.
x
0
1
2
5
2
3
12
147
07
Using least square method to obtain normal equations of parabola on data set
07
Q.4
Apply Newton's forward difference formula of interpolation to find at x=1 for following data.
x
1
1.05
1.10
1.15
1.20
1.25
1.30
1.0000
1.02470
1.04881
1.07238
1.09544
1.11803
1.14017
07
Derive Newton cotes' general quadrature formula. Using it obtain Trapazodial formula for numerical integration.
07
OR
Q.4
Derive Newton's Backward Difference interpolation formula of first order differentiation.
07
Compute the value of definite integral dx using simpson's 1/3 rule of numerical integration by taking h=0.2.
07
Q.5
Solve by Gauss-Seidel method, the following system of equations,
28x+4y-z=32, x+3y+10z=24, 2x+17y+4z=35
07
2
Apply Runge-Kutta method of fourth order to find approximate value of y when x=0.4 given that by taking h=0.2
07
OR
Q.5
Solve the system of equations using Gauss Elimination method.
x-2y+9z=8
07
Given 3x+ and 1. Find the values of y(0.1) and y(0. using the Taylor series method.
07
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