M.Sc. (Computer Science) (Sem
(CBCS) Examination, 2017
NUMERICAL ANALYSIS
Day Date: Tuesday, 25-04-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
Instruction: Question no. 1 and 2 are compulsory.
Attempt any 3 questions from Q. no. 3 to Q. no. 7.
Figures to the right indicate full marks.
Use of simple or scientific calculator is allowed.
Q.1 Choose correct alternatives. 10
A computer that represents only 4 significant digits with
rounding would calculate 66.666 x 33.333 as
2220 2221 2221.17778 2222
The truncation error in calculating for by


with h 0.1 is
0.1 -0.1 -0.31 -0.13
An equation such as tan( has h
Zero one two infinite
The goal of forward elimination steps in the Gauss elimination
method is to reduce the coefficient matrix to matrix.
a diagonal an identity
a lower triangular none of these
The next iterative value of the root of x2-4=0 using secant
method, if the initial guesses are 3 and4, is
2.2857 2.5000 5.5000 5.7143
In if is real and continues in the interval a x
then there is at least one real root in the interval between a
and b iff

or
The following functions(s) can be used for interpolation:
Polynomial Exponential
Trigonometric All of the above
A square matrix A is lower triangular if


Page 2 of 2
In composite Simpson's
rule the number of segments n must
be
any positive integar a multiple of 2 and 3
multiple of 3 an odd number
10) When the differentiate equation contains only first derivative,
it is called a
first-order differentiate equation
second-order differentiate equation
first-degree differentiate equation
none of these
State True or False. 04
If and then
The general solution of the differentiate equation is
If and then the first divided
difference
Let be the first approximation to the root of the
equation The next approximation to the
root of the equation by using Newton-Raphson method is
.
Q.2 Define an absolute error.
Given x=10.00 0.05 and y=0.055 0.002
Find the maximum value of the absolute error in .
04
ii) Define the operators . Show that . 04
State Mean-value theorem for derivatives. 03
ii) State the theorem which states about the convergence of the
root obtained by the iteration method.
03
Q.3 Explain Regula Falsi method. 07
Given the following information
1 3 7 8
0 1.0986 1.9459 2.0794
Find by using Langrange's interpolation formula.
07
Q.4 Explain Newton's forward difference interpolation formula. 07
Find a root of the equation using secant method
with initial estimates . Use at least three iterations.
07
Q.5 Explain Simpson's 1/3 rule. 07
Solve the system
by using Dolittle LU decomposition method.
07
Q.6 Explain Gaussian elimination method. 07
Give the equation
with
Estimate by Euler's method using h=0.25.
07
Q.7 Write a note on Euler's modified method. 07
Evaluate the integral
by using Trapezoidal rule with
h=1.
Verify your results by actual integration.