Master of computer application I (Science) Examination: Oct/Nov
2016 Semester II (New CBCS)
SLR No. Day
Date Time Subject Name Paper
No. Seat No.
SLR U
08
Tuesday
22/11/2016
10.30 AM
To
01.00 PM
Numerical Analysis
C

Instructions: Question no. 1 2 are compulsory
Attempt any three questions from Q. No. 3 to Q. No. 7
Figures to the right indicate full marks.
Use of calculator is allowed
Total Marks: 70
Q.1 Fill in the blanks [one mark each] 07
First divided difference of relative to x0 and x1 is
In false position method, we choose two points x0 x1 such that
are of
The central difference operator δyr is defined by the relation
The effect of the error with the order of the differences.
The algebraic sum of the error in any difference column is
The Newton Raphson method fails when is
Error in trapezoidal rule is
State whether true or false one mark each] 07
Δ∇ δ2
Newton Raphson method is also called method of tangent
The second phase of Gauss elimination method is forward substitution phase.
If there is two or more independent variables, then the differential equation is
called partial differential equation.
In Gauss elimination method the coefficient matrix is reduced to an upper
triangular matrix.
Newton's backward difference Interpolation formula is used for interpolation
near the beginning of the tabular values
Δ∇ Δ ∇
Q.2 What is an degree of Differential equation?
If y0 y1 2 y2 4 then Δ2y0
03
03
with usual notations prove that E 1 Δ
Evaluate the sum to significant digits find its absolute
relative error
04
04
Q.3 Derive Newton forward difference Interpolation formula.
Find root the equation x3 2x 5 0 using Newton Raphson method
07
07
Q.4 Write a note on absolute, relative and percentage error.
Find the cubic polynomial for the values 24, 120, 336
720 also find the values of
06
08
Page 1 of 2
Q.5 08
Q.6
Use simsons Rule to find by taking 6 subintervals
Solve the following system
3x1 6x2 x3 16
2x1 4x2 3x3 13
x1 3x2 2x3 09
using Gauss elimination method
07
07
Q.7 Values of x in degrees) sin x are given in the following table
x 15 20 25 30 35 40
sin x 0.2588190 0.3420201 0.4226183 0.5 0.5735764 0.642787
6
Find the value of sin 380
Find the area bounded by the curve and the x -axis from x 7.47 to x 7.52
using following table.
x 7.47 7.48 7.49 7.50 7.51 7.52
1.93 1.95 1.98 2.01 2.03 2.06