


May Jun 2018.pdf
May_Jun_2018.pdf
Showing 13 out of 3
May Jun 2018.pdfQ1) Moment at a point in
May_Jun_2018.pdfQ1) Moment at a point in
May Jun 2018.pdfQ1) Moment at a po...
May_Jun_2018.pdfQ1) 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.
[6]
OR
Q2)
Using five iteration of bisection method determine root of the following
equation
[6]
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.
[6]
OR
Q4)
Using Gauss  Seidal method solve the following set to simultaneous equations.
Solve upto four iterations.
[6]
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
[5353]  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.
CEGP013091
49.248.216.238 23/05/2018 13:57:26
CEGP013091
49.248.216.238 23/05/2018 13:57:26
CEGP013091
49.248.216.238 23/05/2018 13:57:26
Page 2
2
[5353]  116
Q5)
a)
Minimize
Subject to
(Use graphical method)
b)
Write a short note on Simulated Annealing.
[3]
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)
[8]
Q7)
a)
Using the following points, fit a polynomial using Lagrange's method
and find the value of
y
at
x
= 2.7
[8]
(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.
[8]
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.
[8]
x
1
2
3
4
y
1.51
0.99
8.88
7.66
b)
Draw the flowchart for Newton's forward difference interpolation.
[8]
[5]
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
CEGP013091
49.248.216.238 23/05/2018 13:57:26
CEGP013091
49.248.216.238 23/05/2018 13:57:26
CEGP013091
49.248.216.238 23/05/2018 13:57:26
Page 3
3
[5353]  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.
[8]
b)
Find
1
1
(
2
)
0
0
.
,
x
y
e
dx dy
¨¨
using Simpson's 1/3
rd
rule. Take
h
=
k
= 0.5.
[8]
OR
Q10)
a)
Draw flowchart for Gauss Legendre 2 point and 3 point method.
[8]
b)
Use Trapezoidal rule with four steps to estimate the rule of integral
2
2
0
2
x
dx
x
¨
[8]
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.
[8]
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
[10]
OR
Q12)
a)
Write down step by step procedure for solution of PDE of Laplace
equation and develop a flowchart to write a program.
[8]
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
[10]
M
M
M
CEGP013091
49.248.216.238 23/05/2018 13:57:26
CEGP013091
49.248.216.238 23/05/2018 13:57:26
CEGP013091
49.248.216.238 23/05/2018 13:57:26
Ace your assessments! Get Better Grades
Browse thousands of Study Materials & Solutions from your Favorite Schools
University of Pune
University_of_Pune
School:
Numerical_Methods_and_Optimization
Course:
Introducing Study Plan
Using AI Tools to Help you understand and remember your course concepts better and faster than any other resource.
Find the best videos to learn every concept in that course from Youtube and Tiktok without searching.
Save All Relavent Videos & Materials and access anytime and anywhere
Prepare Smart and Guarantee better grades
Students also viewed documents
lab 18.docx
lab_18.docx
Course
Course
3
Module5QuizSTA2023.d...
Module5QuizSTA2023.docx.docx
Course
Course
10
Week 7 Test Math302....
Week_7_Test_Math302.docx.docx
Course
Course
30
Chapter 1 Assigment ...
Chapter_1_Assigment_Questions.docx.docx
Course
Course
5
Week 4 tests.docx.do...
Week_4_tests.docx.docx
Course
Course
23
Week 6 tests.docx.do...
Week_6_tests.docx.docx
Course
Course
106