Exam.
Code 107202
Subject Code : 2103
nd
Bachelor of Computer Application (B.C.A.) 2 Semester
NUMERICAL METHODS & STATISTICAL
TECHNIQUES
Paper—Ill
Time Allowed Three Hours] [ Maximum Marks-75
o m
Note :—(1) Students will attempt any FIVE questions.
All questions carry 15 marks each.
. c
(2) Students can only use Non-programmable
r
and Non-storage type Calculator.
1.
p e
(a) Solve x 3 — 9x + 1 = 0 for the root between
m
a
x = 2 and x = 4 by the bisection method.
p c o
(b) Find a real root of the equation x 3 — x — 1 = 0
r r .
b using Newton-Raphson method, correct to four
decimal places.
p e
2.
a
(a) Solve by Gaussian elimination method with partial
p
0x + 4x
1 2
2x + 8x = 24
3 b r
pivoting, the following system of equations
4
4x 1 + 10x + 5x + 4x = 32
2 3 2
4x 1 + 5x 2 + 6.5x 3 + 2x 4 = 26
9x 1+ 4x + 4X + OX = 21
2 3 4
3083(2518)/CTE-37367 1
(b) Solve the system of equations :
x + 2y + z = 8
2x + 3y + 4z = 20
4x + 3y + 2z= 16
by Gauss-Jordon elimination method.
3. By using the method of least squares, find a relation
of the form y = ax b that fits the data :
,
x 2 3 4 5
y 27.8 62.1 110
m
161
o
.r c
4. Evaluate f(15), given the following table of values :
X
Y = f(x)
p e
10
46
20
66
30
81
40
93
50
101
m
a o
p
by Newton's forward difference interpolation method.
r .r c
b
5. (a) Find Lagrange's interpolation polynomial fitting
the point y(1) = —3, y(3) = 0, y(4) = 30,
p e
y(6) = 132. Hence find y(5).
p a
(b) Find the approximate value of
π
b r
∫ sin x dx
0
using trapezoidal rule.
3083(2518)/CTT-37367 2 (Contd.)
6. A function y = f(x) is given at the sample points
x = x 0 , x and x 2 . Show that the Newton's divided
1
difference interpolation formula and the corresponding
Lagrange's interpolation formula are identical.
7. (a) Find out the correlation coefficient to the following
data :
X 65 66 67 67 68 69 71 73
Y 67 68 64 68 72 70 69 70
o m
(b) Calculate the rank correlation coefficient from
the following after assigning ranks to them.
X 73.2 85.8
.r c 78.9 75.8 77.2 81.2 83.8
Y 97.8
p e
99.2 98.8 98.3 98.3 96.7 97.1
m
a
8. (a) If in a moderately asymmetrical distribution the
o
r p
values of median and mean are 72 and 78
.r c
b respectively. Estimate the value of mode.
p
(b) Calculate the mean and standard deviation from e
the following data :
p a
Y 170 110 80 45 40 30
b
25
r
X 20-25 25-30 30-35 35-40 40-45 45-50 50-55
3083(2518)/CTT-37367 3 7700
