 May Jun 2018.pdf-Q1) Moment at a point i...
May_Jun_2018.pdf-Q1) Moment at a point in
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May Jun 2018.pdf-Q1) Moment at a po...
May_Jun_2018.pdf-Q1) Moment at a point in
##### Page 1
Q1)
Moment at a point in a cantilever carrying a uniformly distributed load is,
2
2
Pl
M
, where P is the intensity of UDL and
l
is the distance. If the error in
the calculation of P is 0.0 1 kN/m and
l
is 0.02 m, find the error in calculation
of M at
l
= 3.5 and P = 2 kN/m.

OR
Q2)
Using five iteration of bi-section method determine root of the following
equation

f (x) = x
3
 x
2
 x  1 = 0
Take initial guess
x
1
=
1.7
and
x
2
=
1.9.
Q3)
Draw the flowchart for Gauss elimination method.

OR
Q4)
Using Gauss - Seidal method solve the following set to simultaneous equations.
Solve upto four iterations.

x
1
+
20
x
2
+
9
x
3
=
 23
2
x
1
 7
x
2
 20
x
3
=  57
20
x
1
+ 2
x
2
+ 6
x
3
= 28
Total No. of Questions : 12]
[Total No. of Pages : 3
 - 116
T.E. (Mechanical / Automobile) (Semester - II)
NUMERICAL METHODS AND OPTIMIZATION
(2012 Pattern)
Time :2½ Hours]
[Max. Marks :70
Instructions to the candidates:
1)
Solve Q.1 or Q.2, Q.3 or Q.4, Q.5 or Q.6, Q.7 or Q.8, Q.9 or Q.10, Q.11 or Q.12.
2)
Neat diagrams must be drawn wherever necessary.
3)
Figures to the right indicate full marks.
4)
Use of programmable calculator is not permitted.
5)
Assume suitable data, if necessary.
P3253
SEAT No. :
P.T.O.
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CEGP013091
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##### Page 2
2
 - 116
Q5)
a)
Minimize
Subject to
(Use graphical method)
b)
Write a short note on Simulated Annealing.

OR
Q6)
Maximize
Z= 50,000
x
1
+ 12, 000
x
2
Subject to
75
x
1
+ 15
x
2
£
1000
100
x
1
+ 30
x
2
£
1500
45
x
1
+ 10
x
2
£
750
And
x
1
,
x
2
³
0
(Use simplex method)

Q7)
a)
Using the following points, fit a polynomial using Lagrange's method
and find the value of
y
at
x
= 2.7

(2.10,5.14) (2.50,6.78) (3.10,10.29) (3.50,13.58)
b)
Determine the values of
a
and
b
so that the equation
y
=
ax
b
best fits the
following data by the method of least squares.

x
25
20
12
9
7
5
y
0.22
0.2
0.15
0.13
0.12
0.1
OR
Q8)
a)
Using the method of least square, fit the curve
y
=
ax
2
+
b
x
to the following
data.

x
1
2
3
4
y
1.51
0.99
8.88
7.66
b)
Draw the flowchart for Newton's forward difference interpolation.


1
2
1
2
1
2
1
2
1
2
80
120
9
2
3
20
50
300
,
0
Z
x
x
x
x
x
x
x
x
xx
b
p
p
b
p
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##### Page 3
3
 - 116
Q9)
a)
Use Simpson's 1/3
rd
rule to find
0.8
0
(log (
1)
sin (2 )).
e
x
x
dx
¨
where
x
is in radians. Divide the entire interval in 8 strips.

b)
Find
1
1
(
2
)
0
0
.
,
x
y
e
dx dy
¨¨
using Simpson's 1/3
rd
rule. Take
h
=
k
= 0.5.

OR
Q10)
a)
Draw flowchart for Gauss Legendre 2 point and 3 point method.

b)
Use Trapezoidal rule with four steps to estimate the rule of integral
2
2
0
2
x
dx
x
¨

Q11)
a)
Solve the differential equation
(
)
dy
x
y
dx
using Euler's method
under the boundary conditions
x
= 2 and
y
= 4 find
y
at
x
= 2.5 in 10
steps.

b)
Solve the equation
2
2
2
2
1
u
u
x
y
xy
s
s
s
s
corresponding to grid shown in
following fig

OR
Q12)
a)
Write down step by step procedure for solution of PDE of Laplace
equation and develop a flowchart to write a program.

b)
Initial temperature within an insulated cylindrical metal rod of 4 cm length
is given by, T = 50 (4 -
x
), 0
£
x
£
4, where
x
is distance from one end in
cm. Both the ends
are maintained at 0°C. Find the temperature as a
function of
x
and
t
(0
£
t
£
1.5) if the heat flow is governed by
2
2
2
.
1,
0.25
T
T
x
t
y
x
s
s
%
%
s
s

M
M
M
CEGP013091
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CEGP013091
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CEGP013091
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