Download SGBAU BCA 2019 Summer 2nd Sem Numerial Methods Question Paper

Download SGBAU (Sant Gadge Baba Amravati university) BCA 2019 Summer (Bachelor of Computer Applications) 2nd Sem Numerial Methods Previous Question Paper

AW?l 796
B.C.A. (Part?l) Scmcstcr?II Examination
ZST4 : NUMERICAL METHODS
Time : Three Hours] [Maximum Marks : 60
Note :? (1) All questions are compulsory.
1 . (a)
(b)
(C)
k)
(a)
(b)
(C)
(a)
b)
(b)
(C)
(b)
(C)
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(2) All questions carry equal marks.
What do you mean by Multiple Regression ? 4
Fit a straight line to the following data :
X : 1 2 3 4 5
Y : 3 4 5 6 8 4
Show that regression coef?cients are independent of change oforigin but not of scale. 4
OR
Derive normal equation for ?tting of straight line.
Explain regression.
Fit 3 multiple linear regression to the data given below :
X1 : 0 2 2.5 l 4 7
X2 : 0 1 2 3 6 2
Y : 5 10 9 0 3 27 4
Fit :1 power equation y = ax? to the following given data :
x : 1 2 3 4 5
y : 0.5 1.7 3.4 5.7 8.4
Explain how you will reduce nonlinear equations in linear form.
Explain linear least square.
OR
What do you mean by transcendental equation ?
Explain non-linear regression.
The population of a State at ten year interval is given below :
Years : 1925 1935 1945 1955 1965 1975 1985 1995
Population in
millions : 12.9 14.1 19.7 25.3 33.6 41.5 51.3 63.2
F it a curve of the form y = abX and estimate the population for the year 2005. 4
State Newton Gregory forward interpolation formula. In which case is it useful ? 6
Using Lagrange?s interpolation formula compute [(5) from the given data :
x : 2 4 7 9
f(x) : 10 26 65 101 6
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6 (a) What do you mean by intelpolm ion and extrapolation ?? Explain with example. 6
0)) By means of Nemon divided 11: 1"?erence interpolation formula ?nd the values of f(2) and f(8)
from the following table. :
x : 4 5 7 10 11 13
?x) : 48 100 294 900 1210 2028
7 (a) Explain the inverse interpolatior technique.
(b) Explain the spline interpolation 1echnique.
(c) Using Lagrangc's inverse interpolation formula compute the value ofx for y = 0.6742 :
x : 3.5 4 C 4.8 5.6
y : 0.5441 (1.6010 0.6812 0.7482 4
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8 (a) What are assumptions ofimcrsc interpolation '.? 4
(b) Explain the Chebyshev interpolation polynomial. 4
(c) Using Lagrange?s interpolation formula estimate value of e1 ? using the following data :
x : 0 l 2 3
e??? : 0 1.7183 6.3891 19.0855 4
9 (a) State and provc trapcmidal ml: of numerical integration.
dx
(b) Evaluate J11? X7 by using S'mpson?s 1/3 rule. 6
OR
10. (a) State and prove Simpmn?s F 7H rule. 6
5.7.
(b) Solve using trapezoidal rulc :i'ld the value ofintegral I = [log x d.\' . 6
4
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