M.Sc. (Electronics) (Semester III) (CBCS) Examination, 2017
NUMERICAL METHODS
Day Date: Tuesday, 18-04-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
N.B. Q.1 and Q.2 are compulsory.
Attempt any three questions from Q. 3 and 7.
Figures to the right indicate full marks.
Answer five questions.
Q.1 Choose correct answer: 08
R-2R Ladder network results in to matrix.
Lower triangular Upper triangular
Tridiagonal None of these
Laplace Transform of tn is given by
1/S
Newton`s -Cotes integration formula for four points reduce to

Simpson 1/3 rule Trapezoidal rule
Simpson 3/8 rule All of these
For RK-4 order method Taylors Series can be truncated from

Oh5 Oh2 Oh4 All of these
Laplace Transform converts the function of
Frequency domain into time domain
Time domain into frequency domain
Time domain into continuous time domain
None of these
Interpolation of set of four points results into polynomial of
the order
One Two Zero Three
For Newton's forward difference Δ2 Y0
E2 All of these
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The least squares method of curve fitting is developed by
considering
Minimization of data points Minimization of error
Maximization of data points Maximization of errors
State True or False: 06
For triangular factorization method of solution of linear
system of equations, the system may be expressed as
LUX=B.
Numerical integration for two variable is called quadrature.
Laplace transformation of
Lagrangian method is used for interpolation of unequal
spacing.
RK- III order method of solution of ODE has 3 constants.
For Newton's forward method of interpolation the u is given
by xn)/h.
Q.2 Attempt any two: 10
Derive expression for Laplace transformation of eat.
What do you mean by pivoting?
Solve
4x1 x2 2x3 12
2x1 3x2 8x3 20
-x1 11x2 4x3= 33
Using least squares fitting process, fit following data to straight
line.
04
X=0 2 4 6
Y=0 8 16 24
Q.3 What do you mean by Newton's Cotes Integration formula?
Derive expression for Simpson`s mid- point and one third rule
for numerical integration.
08


Evaluate by using Simpson one third method. 06
Q.4 What do you mean by Laplace Transformation of the given
function? Describe in detail the analysis of RL circuit by using
Laplace Transformation.
08
Find first and second order derivatives at x=1.0 for following
data points.
06
1 1.1 1..2 1.3 1.4
43.1 47.7 52.1 56.4 60.8
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SLR-RI 392
Q.5 Describe formation of system of linear equations? Describe
Gaussian elimination Method for solution of system of linear
equations.
08


Evaluate by using composite trapezoidal rule for 10 intervals. 06
Q.6 What do you mean by numerical differentiation? Derive
expression for Newton's forward difference formula for
numerical differentiation.
08
Using Newton's forward difference interpolation method find
for following data points.
06
X=10 20 30 40 50
Y=12 16 20 25 35
Q.7 Describe Euler`s method of finding solution of first order ordinary
differential equation.
08
Using RK-II order method find value of y(0.2).