Download GTU BE/B.Tech 2019 Summer 3rd Sem New 2130002 Advanced Engineering Mathematics Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 3rd Sem New 2130002 Advanced Engineering Mathematics Previous Question Paper

1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ?III (NEW) EXAMINATION ? SUMMER 2019
Subject Code: 2130002 Date: 30/05/2019

Subject Name:Advanced Engineering Mathematics

Time: 02:30 PM TO 05:30 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

MARKS

Q.1 (a)
Solve
( 2) ( 4) 0 x y dx x y dy ? ? ? ? ? ?

03

(b) Solve
1
2 tan
(1 ) ( ) 0
y
dx
y x e
dy
?
?
? ? ? ?


04
(c)
Expand
( ) cos f x x ?
as a Fourier series in the interval
x ? ? ? ?

07
Q.2 (a) Define unit step function and unit impulse function. Also sketch
the graphs.
03

(b)
Solve
2
2
2 4sin 2
d y dy
yx
dx dx
?
? ? ?
?
?


04
(c)
Find the series solution of
0 y xy y ? ? ? ? ? ?
about the ordinary
point 0 x ? .

07
OR
(c)
Find the Fourier series expansion for () fx , if
,0
()
,0
x
fx
xx
?
?
? ? ? ? ?
?
?
?
?
, Also deduce that
2
22
11
1 ......
3 5 8
?
? ? ? ?
07
Q.3 (a) Using Fourier integral representation, show that
0
,0 1 cos
sin
2
0,
x
xd
x
?
? ?
?
?
?
?
?
? ? ?
?
?
?
?
?
?

03

(b)
Solve
2
2
2
sin 2
dy
y x x
dx
?
?
?
?


04
(c) Solve by method of variation of parameters
2
2
1
9
1 sin3
dy
y
dx x
?
?
?
?
?



07
OR
Q.3 (a)
Find Laplace transform of sin
at
te at
03

(b)
Solve
2
2
5 sin 2
x
d y dy
ex
dx dx
? ? ?


04
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1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ?III (NEW) EXAMINATION ? SUMMER 2019
Subject Code: 2130002 Date: 30/05/2019

Subject Name:Advanced Engineering Mathematics

Time: 02:30 PM TO 05:30 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

MARKS

Q.1 (a)
Solve
( 2) ( 4) 0 x y dx x y dy ? ? ? ? ? ?

03

(b) Solve
1
2 tan
(1 ) ( ) 0
y
dx
y x e
dy
?
?
? ? ? ?


04
(c)
Expand
( ) cos f x x ?
as a Fourier series in the interval
x ? ? ? ?

07
Q.2 (a) Define unit step function and unit impulse function. Also sketch
the graphs.
03

(b)
Solve
2
2
2 4sin 2
d y dy
yx
dx dx
?
? ? ?
?
?


04
(c)
Find the series solution of
0 y xy y ? ? ? ? ? ?
about the ordinary
point 0 x ? .

07
OR
(c)
Find the Fourier series expansion for () fx , if
,0
()
,0
x
fx
xx
?
?
? ? ? ? ?
?
?
?
?
, Also deduce that
2
22
11
1 ......
3 5 8
?
? ? ? ?
07
Q.3 (a) Using Fourier integral representation, show that
0
,0 1 cos
sin
2
0,
x
xd
x
?
? ?
?
?
?
?
?
? ? ?
?
?
?
?
?
?

03

(b)
Solve
2
2
2
sin 2
dy
y x x
dx
?
?
?
?


04
(c) Solve by method of variation of parameters
2
2
1
9
1 sin3
dy
y
dx x
?
?
?
?
?



07
OR
Q.3 (a)
Find Laplace transform of sin
at
te at
03

(b)
Solve
2
2
5 sin 2
x
d y dy
ex
dx dx
? ? ?


04
2
(c) Solve
2
2
2
4 cos(log ) sin(log )
d y dy
x x y x x x
dx dx
? ? ? ?



07
Q.4 (a)
Find the orthogonal trajectories of the curve
2
y x c ?
03
(b)
Find the Laplace transform of (i) cos( ) at b ?
(ii)
2
sin 3t
04
(c) State convolution theorem and apply it to evaluate
? ?
2
1
2
2
4
s
L
s
?
?
?
?
?
?

07
OR
Q.4
(a)
Solve
32
32
3 4 0
d y d y
y
dx dx
? ? ?


03
(b)
Find Half range cosine series for ? ?
2
( ) 1 f x x ? in the interval
01 x ?

04
(c)
Solve 4 3 , (0) (0) 1
t
y y y e y y
?
? ? ? ? ? ? ? ? ? using
Laplace transform.

07
Q.5 (a) Form the partial differential equation by eliminating the arbitrary
constants from
22
z ax by a b ? ? ? ?
03
(b)
Solve
( ) ( ) y z p x y q z x ? ? ? ? ?

04
(c)
Solve
3 2 0,
uu
xy
?
?
?
where ( ,0) 4
x
u x e
?
? using the
method of separation of variables.

07
OR

Q.5 (a) Form the partial differential equation by eliminating the arbitrary
function from
22
( , ) 0 f x y z xy ? ? ?

03
(b)
Solve
2
log .
z
xy
xy
? ?
?
?
?
?


04
(c)
A bar with insulated sides is initially at temperature
0
0 C
,
throughout. The end 0 x ? is kept at
0
0 C
and heat is suddenly
applied at the end xl ? so that
u
A
x
?
?
?
for xl ? , where A
is a constant. Find the temperature function.

07

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