M.Sc. (Semester (CBCS) Examination Oct/Nov-2017
Electronics
NUMERICAL METHODS
Day Date: Thursday, 16-11-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
Instructions: Q. and are compulsory.
Answer any three questions from Q.3 to Q.7.
Answer five questions.
Figures to the right indicate full marks.
Q.1 Choose the alternatives given below. 08
On Laplace transformation, the function converts from
Time domain to frequency domain
Frequency domain to time domain
Time domain to amplitude domain
Amplitude domain to time domain
If data consist n number of points, then Newton's forward interpolation
method generates the polynomial of order.
nth
Second
For set of points of unequal interval method of interpolation is
suitable.
Cubic splines Newton's forward difference
Lagrangian All of these
In Gauss Jordon Elimination method, the coefficient matrix is reduced to
Matrix.
Lower Triangular Identity
Tridiagonal Upper Triangular
Laplace Transform of t4 is given by
1/S

The R-2R ladder network can be solved by using matrix system
of equations.
Tridiagonal U-matrix
L-matrix All of these
For Newtons forward difference
E2
All of these
The Least squares method of curve fitting is developed by considering

Minimization of data points
Minimization of sum of squares of errors
Maximization of data points
Maximization of errors
Page 2 of 2
SLR-MJ-347
State True or false. 06
Forward substitution method is adopted for U-matrix.
On Laplace Transformation, an expression for current response through
RL circuit consists of two parts DC and transient.
Newton-Cotes integration formula for three points reduces to Sompson's
one third rule.
For solving ODE by Eulers method, final value of the function is
considered.
For cubic splines only two points are considered.
The matrix of single column is called vector.
Q.2 Attempt any two. 10
Derive expression for Laplace transformation of coswt
What do you mean by forward and backward substitution method for
solution of system of equation?
Solve
x1 x2 2x3 4
2x1 4x2 x3 6
x1 x2 5x3
Write a note on Piece-wise linear analysis. 04
Q.3 Describe formation of system of linear equations? Describe Gaussian
Jordon elimination method for solution of system of linear equations.
08
Evaluate by using Simpson's one third rule for 10 points. 06
Q.4 What do you mean by Laplace Transformation and Inverse Transformation?
With suitable example describe partial fraction rule.
08
Obtain Laplace Inverse Transformation of the function 06
Q.5 Using Newton's forward interpolation formula derives the expression for first
order and second order numerical differentiation.
08
Find first and second order derivative for following data x 6. 06
X 2 4 6 8 10
Y 1.583 1.797 2.044 2.325 2.651
Q.6 What do you mean by quadrature? Describe in detail the Newton Cote
formal for numerical integration. Obtain expression for Simpson mid-point
and one third rule.
08
Evaluate by using trapezoidal rule for 10 points. 06
Q.7 Using Taylers series derive the expression for solution of ODE for RK-II
order method.
08
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