paper - iv - Acharya Nagarjuna University

III B.A./B.Sc. Mathematics
10
Paper IV (Elective -1) - Curriculum
AACHARYA NAGARJUNA UNIVERSITY
B.A / B.Sc. DEGREE EXAMINATION, PRACTICAL MODEL PAPER
(Practical examination at the end of third year, for 2010 - 2011 and onwards)
MATHEMATICS PAPER - IV (ELECTIVE - 1)
NUMERICAL ANALYSIS
Time : 3 Hours Max. Marks : 30
1
Answer ALL questions. Each question carries 7
2
marks. 4× 7 1
2
= 30 M
1 (a) Find a positive root of the equation xe x = 1, which lies between 0 and 1 by bisection method.
OR
(b) Using Newton-Raphson method, establish the iterative formula x = 1 ⎛ N
n+ x + ⎞
1
⎜
n
⎟ to calculate the
2 ⎝ x ⎠
square root of N. Hence find the square root of 8.
2 (a) Find the missing term in the following data.
(b)
x : 0 1 2 3 4
y: 1 3 9 81
OR
If l x
represents the number of persons living at age x in a life table, find as accurately as the data will
permit the value of l 47
. Given that l = 512, l = 439, l = 346, l = 243 .
20 30 40 50
3 (a) Find f ′( 06and ⋅ ) f ′′( 06from ⋅ ) the following table :
x 04 ⋅ 05 ⋅ 06 ⋅ 07 ⋅ 08 ⋅
f ( x) 15836 ⋅ 1⋅ 7974 20442 ⋅ 23275 ⋅ 26510 ⋅
1
OR
(b)
dx
Find the value of the integral ∫ 2
1+
x
0
by using Simpson’s 1 3 and 3 rule. Hence obtain the approximate
8
value of π in each case.
4 (a) Solve the system of equations 2x+ y+ z = 10, 3x+ 2y+ 3z = 18, x+ 4y+ 9z
= 16by Gauss
elimination method.
OR
(b)
dy y − x
Given = with y = 1, when x = 0 . Find approximately the value of y for x = 01by ⋅
dx y + x
Picard’s method.
n
Written exam : 30 Marks
For record : 10 Marks
For viva-voce : 10 Marks
Total marks : 50 Marks