M.Sc. (Semester (CBCS) Examination Nov/Dec-2018
Electronics
NUMERICAL METHODS
Time: 2½ hrs Max. Marks: 70
Instructions: All questions are compulsory.
Use of log table and calculators are allowed.
Figures to the right indicate full marks.
Draw neat and labeled diagram wherever necessary.
Q.1 Choose the correct answer. 14
Laplace transformation of
sF

In Gauss-Jordon elimination method of solving system of linear equation, the
coefficient matrix should be reduced to matrix.
L I
U T
For finite difference, ordered forward difference is=
Always zero Always infinity
Undetermined Always one
R-2R ladder network of digital to analog converter produces the coefficient
matrix of type.
singular upper triangular
tridiagonal lower triangular
R-K method of finding solution of first order differential equation is based on

Initial value theorem Boundary value theorem
Mid-Value Theorem Final value theorem
Interpolation polynomial for three points is order polynomial.
third fourth
second All of these
For Euler method the Taylors Series can be truncated from
Oh5 Oh3
Oh4 Oh2
If E is shift operator, then which of the following is correct?
Δ2y0 E − 1 y0 Δ2y0 E2y0
Δ2y0 − 1)2y0 Ey2 y2 − y1
If the set of points consists of point of unequal interval, then which of the
following is correct?
Newton's forward difference interpolation formula is suitable for
interpolation.
Lagrangian method is suitable for interpolation.
Newton's backward difference interpolation formula is suitable for
interpolation
R-K Method is suitable for interpolation
10) Newton-Cotes integration formula for three points reduces to
Simpson 1/3 rule Trapezoidal rule
Simpson 3/8 rule All of these
11) For implementation of forward substitution, the coefficient matrix should be
reduced to Matrix.
Square L
U Sparse
12) Laplace Transformation of the function f t 2t2 9t 4 is
4/S 4
4/S
13) For Newton's Forward difference interpolation formula the u is given

u u

14) In least square fitting process, the basic principle is to minimize of
the errors.
sum squares
data points sum of the squares
Q.2 Answer any four of the following. 08
Define Laplace Transformation of given function.
Give composite formula for numerical integration by Simpson's mid point
rule.
What is initial value theorem?
List Laplace Transformation of any four standard functions.
Give Newton's interpolation formula for forward differences.
Solve any two of the following 06
Derive expression for Laplace transformation of eα t
What do you mean by system of linear equations?
Write a note on Piecewise Linear Interpolation.
Q.3 Answer any two of the following. 08
Describe Gauss-Jordan elimination method for solutions of system of
linear equations.
Using Guassian elimination method solve
10x1 x2 x3 12
x1 10x2 x3 12
x1 x2 10x3 12
Obtain forward and Backward difference for following data points.
X 10 20 30 40 50
Y 9.21 17.54 31.82 55.32 92.51
Solve any one of the following. 06
With suitable example describe Least Squares method of curve fitting.
Write a note on Lagrangian method for interpolation
Q.4 Answer any two of the following. 10
Describe in detail the analysis of RL circuit for DC input by using Laplace
Transformation.
With suitable example Euler's method of getting solution of ordinary
differential equation.
Evaluate by using Simpon's Trapezoidal method.
Solve any one of the following 04
What do you mean by Laplace Inverse Transformation? Discuss Partial
Fraction Rule.
Using Newton's forward interpolation formula find
X 4 6 8 10
Y 1 3 8 16
Q.5 Answer any two of the following. 14
What do you mean by numerical integration? Using Newton's Cotes
integration formula, derive expression for numerical integration by
trapezoidal rule and Simpson's one third rule.
Using RK II order method find value of y(0.2) Given that
dy/dx= x − y 2 and y 0 1
With suitable example explain Least Squares fitting process for straight line.