Exam Details
| Subject | computer-oriented numerical methods (conm) | |
| Paper | ||
| Exam / Course | mca | |
| Department | ||
| Organization | Gujarat Technological University | |
| Position | ||
| Exam Date | January, 2019 | |
| City, State | gujarat, ahmedabad |
Question Paper
1
Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MCA SEMESTER- 1 EXAMINATION WINTER 2018
Subject Code: 2620004 Date: 05-01-2019
Subject Name: Computer-Oriented Numerical Methods
Time: 02.30 pm to 5.00 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
1. List two bracketing and open methods.
2. Use Descartes' rule of signs to the following equation to determine positive
and negative roots.
2x4 3x3 -6x2 +6x 0
3. What is inverse interpolation? List methods of inverse interpolation.
4. When Newton's forward difference interpolation method is used?
02
02
02
01
Define error. Explain the types of errors with example.
07
Q.2
Find a root of the equation x3 x -11 using bisection method up to fourth approximation.
07
Find the root of x3 2x2 +10x 20 0 correct up to three significant digits using Birge Vieta Method. (Hint: Take
07
OR
What are the similarities and differences between Secant Method False Position method of finding a root of a given equation
07
Q.3
Apply Lagrange's inverse interpolation formula to obtain the value of x when
y 6 from the given table.
168
120
72
63
3
7
9
10
07
For the following data, interpolate at x 21 and x 28 by suitable Newton's interpolation formula.
20
23
26
29
0.3420
0.3907
0.4384
0.4848
07
OR
Q.3
By the method of least squares, find the best fitting straight line to the data given below.
5
10
15
20
25
16
19
23
26
30
07
Express Maclaurin series expansion of e-x in terms of chebyshev polynomials.
07
Q.4
Given that,
1
1.1
1.2
1.3
1.4
1.5
1.6
7.989
8.403
8.781
9.129
9.451
9.750
10.031
Find dy/dx and d2y/d2x at x=1.1
07
Dividing the range into 10 equal parts, find the approximate value of
by trapezoidal rule.
07
OR
Q.4
Find from the following table using Newton's Divided Difference formula.
0
2
3
4
7
9
4
26
58
112
466
922
07
2
Find the value from using Simpson's 1/3 rule with 0.25
07
Q.5
Solve the system using gauss elimination method.
3X Y Z 3
2X 8Y Z
X 2Y 9Z 8
07
Find Eigen value, Eigen vector of the matrix
07
OR
Q.5
Given dy/dx= y y 2. Find y y(0.2) correct to four decimal places using R.K. 2nd order method.
07
Given y y 2.0933, y 2.1755, y 2.2493. Find y by Milne's Predictor Corrector method.
07
Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MCA SEMESTER- 1 EXAMINATION WINTER 2018
Subject Code: 2620004 Date: 05-01-2019
Subject Name: Computer-Oriented Numerical Methods
Time: 02.30 pm to 5.00 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
1. List two bracketing and open methods.
2. Use Descartes' rule of signs to the following equation to determine positive
and negative roots.
2x4 3x3 -6x2 +6x 0
3. What is inverse interpolation? List methods of inverse interpolation.
4. When Newton's forward difference interpolation method is used?
02
02
02
01
Define error. Explain the types of errors with example.
07
Q.2
Find a root of the equation x3 x -11 using bisection method up to fourth approximation.
07
Find the root of x3 2x2 +10x 20 0 correct up to three significant digits using Birge Vieta Method. (Hint: Take
07
OR
What are the similarities and differences between Secant Method False Position method of finding a root of a given equation
07
Q.3
Apply Lagrange's inverse interpolation formula to obtain the value of x when
y 6 from the given table.
168
120
72
63
3
7
9
10
07
For the following data, interpolate at x 21 and x 28 by suitable Newton's interpolation formula.
20
23
26
29
0.3420
0.3907
0.4384
0.4848
07
OR
Q.3
By the method of least squares, find the best fitting straight line to the data given below.
5
10
15
20
25
16
19
23
26
30
07
Express Maclaurin series expansion of e-x in terms of chebyshev polynomials.
07
Q.4
Given that,
1
1.1
1.2
1.3
1.4
1.5
1.6
7.989
8.403
8.781
9.129
9.451
9.750
10.031
Find dy/dx and d2y/d2x at x=1.1
07
Dividing the range into 10 equal parts, find the approximate value of
by trapezoidal rule.
07
OR
Q.4
Find from the following table using Newton's Divided Difference formula.
0
2
3
4
7
9
4
26
58
112
466
922
07
2
Find the value from using Simpson's 1/3 rule with 0.25
07
Q.5
Solve the system using gauss elimination method.
3X Y Z 3
2X 8Y Z
X 2Y 9Z 8
07
Find Eigen value, Eigen vector of the matrix
07
OR
Q.5
Given dy/dx= y y 2. Find y y(0.2) correct to four decimal places using R.K. 2nd order method.
07
Given y y 2.0933, y 2.1755, y 2.2493. Find y by Milne's Predictor Corrector method.
07
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