M.Sc. (Semester III) (CBCS) Examination Oct/Nov-2017
Mathematics
NUMERICAL TECHNIQUES
Day Date: Saturday, 25-11-2017 Max. Marks: 70
Time: 02.30 PM to 05.00 PM
Instructions: Question No.1 and 2 is compulsory.
Attempt any three questions from Question No.3 and Question No.7.
Figures to the right indicate full marks.
Use of calculator is allowed.
Q.1. Fill in the blanks:- (one mark each) 10
The best approximation for 1/3 is
If A is upper triangular then A-1 is
Householders method is used to obtain eigenvalues of matrices.
The relation between ∇ and E is given by
Error in Trapezoidal rule is
The third forward difference is given by
The process of computing the value of the function inside the given
range is called
Divided difference of is
The method of false position is also known as
10) In Newton Raphson method the iterative formula to find
1

is given by

Q.1. Choose the correct alternative:- (one mark each) 04
Simpsons 3/8 rule for integration gives exact result when is a
polynomial of degree
3 At least 3
At most 3 None
An approximate value of is x1 3.1428571 and its true value is x
3.1415926, then the absolute error EA is
0.0012645 0.0012645
-0.000402 -0.00012645
If 1 and 3 then the unique polynomial of degree one is

3-2x x-3
2x+1 2x-1
Which of the following is correct
∇ − Δ∇ ∇ − −Δ∇
∇ −Δ∇ ∇ Δ∇
Q.2 If 0.333 is the approximate value of
1
3
find absolute, relative and
percentage error.
03
Prove that Newton Raphson method converges quadratically. 04
Prove that Lagranges interpolation is unique. 04
Prove that − −1)
2
−2+. … … 03

Q.3 Derive Newton's general interpolation formula with divide differences. 07
Find real root of 1 0 using bisection method. 07
Q.4 Reduce the matrix:-
A
1 3 4
2 2 −1
4 −1 1
To tridiagonal form using Householder's method.
07
Solve I 1

1
0 correct to three decimal places by Simpsons 1/3 rule
with h 0.125.
07
Q.5 Derive Lagrange interpolating formula. 07
Using Euler method solve 2y take h 0.1 and obtain
y(0.1).
07
Q.6 Derive Newton's backward difference interpolation formula. 07
Solve the system 3x+2y+3z=18, x+4y+9z=16 using Gauss
elimination method.
07
Q.7 Find the cubic polynomial which takes the values
and hence find
07
Given
x2 determine y(0.02) Using Euler's modified
method.