Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 3rd Sem Old 130002 Advanced Engineering Mathematics Previous Question Paper
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?III (OLD) EXAMINATION ? WINTER 2018
Subject Code:130002 Date:17/11/2018
Subject Name:Advanced Engineering Mathematics
Time:10:30 AM TO 01:30 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a)
(i) Solve:
22
tan sec sec 0
y y y
x y dx x dy
x x x
??
? ? ?
??
??
04
(ii) Find Laplace transform of
? ? cos cos at bt
t
?
03
(b)
(i) Solve:
2
.
1
dy x
y x y
dx x
??
?
04
(ii) Find Inverse Laplace transform of
? ?
2
2
5
31 s
s
?
03
Q.2 (a)
(i) Find Half-Range cosine series for ? ? 1; 0 1. f x x ? ? ?
= ; 1 2. xx ??
04
(ii) Solve: 03
(b)
Obtain Fourier series for ? ?
2
; 1 1 f x x x x ? ? ? ? ?
07
OR
(b)
Find series solution of
2
2
2
0.
d y dy
x
dx dx
??
07
Q.3 (a) (i) Solve 04
(ii) Solve:
? ? ? ?
2 2 2
2 tan tan sec 0. xy y y dx x x y y dy ? ? ? ? ? ?
03
(b)
Obtain Fourier series for ? ? sin ; . f x x x ?? ? ? ? ?
07
OR
Q.3 (a)
(i) Define periodic function. Find Laplace transform of
? ? ? ? ? ?
2
; 0 2 2 . f t t t f t f t ? ? ? ? ?
04
(ii) Solve:
? ?
2
1 2 1.
dy
x xy
dx
? ? ?
03
(b)
State Convolution theorem. Use it find Inverse Laplace transform of
? ? ? ?
2 2 2 2
s
s a s b ??
07
Q.4 (a)
(i) Solve:
4
4
4 0.
dx
x
dt
??
04
(ii) Evaluate: Prove that
0
ln .
at bt
e e b
dt
ta
???
? ??
?
??
??
?
03
(b)
(i) Solve
2
2
2
.
uu
c
tx
??
?
??
using method of separable variable method.
04
(ii) Solve 03
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?III (OLD) EXAMINATION ? WINTER 2018
Subject Code:130002 Date:17/11/2018
Subject Name:Advanced Engineering Mathematics
Time:10:30 AM TO 01:30 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a)
(i) Solve:
22
tan sec sec 0
y y y
x y dx x dy
x x x
??
? ? ?
??
??
04
(ii) Find Laplace transform of
? ? cos cos at bt
t
?
03
(b)
(i) Solve:
2
.
1
dy x
y x y
dx x
??
?
04
(ii) Find Inverse Laplace transform of
? ?
2
2
5
31 s
s
?
03
Q.2 (a)
(i) Find Half-Range cosine series for ? ? 1; 0 1. f x x ? ? ?
= ; 1 2. xx ??
04
(ii) Solve: 03
(b)
Obtain Fourier series for ? ?
2
; 1 1 f x x x x ? ? ? ? ?
07
OR
(b)
Find series solution of
2
2
2
0.
d y dy
x
dx dx
??
07
Q.3 (a) (i) Solve 04
(ii) Solve:
? ? ? ?
2 2 2
2 tan tan sec 0. xy y y dx x x y y dy ? ? ? ? ? ?
03
(b)
Obtain Fourier series for ? ? sin ; . f x x x ?? ? ? ? ?
07
OR
Q.3 (a)
(i) Define periodic function. Find Laplace transform of
? ? ? ? ? ?
2
; 0 2 2 . f t t t f t f t ? ? ? ? ?
04
(ii) Solve:
? ?
2
1 2 1.
dy
x xy
dx
? ? ?
03
(b)
State Convolution theorem. Use it find Inverse Laplace transform of
? ? ? ?
2 2 2 2
s
s a s b ??
07
Q.4 (a)
(i) Solve:
4
4
4 0.
dx
x
dt
??
04
(ii) Evaluate: Prove that
0
ln .
at bt
e e b
dt
ta
???
? ??
?
??
??
?
03
(b)
(i) Solve
2
2
2
.
uu
c
tx
??
?
??
using method of separable variable method.
04
(ii) Solve 03
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2
OR
Q.4 (a)
(i) Solve:
32
32
6 11 6 0.
d y d y dy
y
dt dt dt
? ? ? ?
04
(ii) Find Inverse Laplace transform of
? ? ? ?
2
2
5 2 19
31
ss
ss
??
??
03
(b)
Find series solution of
? ?
2 '' '
1 0. x y xy y ? ? ? ?
07
Q.5 (a) (i) Express the function as Fourier integral.
= 0; Otherwise
05
(ii) Define Dirac-Delta function
02
(b)
Find solution of
'
'' 2 2 tan
x
y y y e x ? ? ? using method of variation of parameter.
07
OR
Q.5 (a)
(i) Solve:
? ?
22
4 2 log . x D xD y x x ? ? ? ?
05
(ii) Define Gamma function and find its value for 3/2.
02
(b)
Find solution of
? ?
22
2 4. D D y x x ? ? ? ? using method of undetermined coefficient
07
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This post was last modified on 20 February 2020