Download GTU BE/B.Tech 2019 Winter 3rd Sem Old 130002 Advanced Engineering Mathematics Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 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 2019
Subject Code: 130002 Date: 22/11/2019

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.

Q.1 (a) (i) Solve ?? ?? ?? ???? + (2?? + ?? ?? ) ???? = 0
(ii) Solve (?? + 1)
????
????
? ?? = ?? 3?? (?? + 1)
2

03
04

(b) Obtain Fourier series of ?? (?? ) = ?? 2
in the interval(0, 4). 07

Q.2 (a) (i) Use method of Undetermined coefficients and find general solution of
?? ??
+ 10?? ?
+ 25?? = ?? ?5??
07


(b) Find general solution of (?? 2
+ 2?? ? 35)?? = 37 sin 5?? 07
OR
(b) Solve by Variation of parameter method (?? 2
+ 9)?? = ?????? 3?? 07

Q.3 (a) Find Fourier series of ?? (?? ) = ?? ????
in (0, 2?? ), ?? > 0 07
(b)
Find Fourier series of ?? (?? ) = {
?? , 0 ? ?? ? 2
4 ? ?? , 2 ? ?? ? 4

07
OR
Q.3 (a) Find the Series solution of ?? ??
? 2?? ?
= 0 07
(b)
Express the function ?? (?? ) = {
sin ?? , 0 ? ?? ? ?? 0 , ?? > ?? as a Fourier sine integral and
show that
?
sin ???? sin ????
1 ? ?? 2
?
0
???? =
?? 2
sin ?? , 0 ? ?? ? ??


07

Q.4 (a)
(i) Find Laplace transform of ?? ?? (1 + ??? )
4

(ii) Find the inverse Laplace transform of
2?? +2
?? 2
+2?? +10

03
04

(b) State Convolution theorem and using it find inverse Laplace transform of
1
(?? ?2)(?? +2)
2

07
OR
Q.4 (a) (i) Find Laplace transform of ?? ?3?? ?? (?? ? 2)
(ii) Find inverse Laplace transform of
?? ?2?? (?? +4)
3

03
04

(b) Solve initial value problem using Laplace transform method
?? ??
? 3?? ?
+ 2?? = 12?? ?2?? , ?? (0) = 2, ?? ?
(0) = 6
07

Q.5 (a) (i) Form Partial differential equation for the equation
?? = ???? + ???? + ????
(ii) Find Laplace transform of ?? (?? ) = {
?????? ?? , 0 < ?? < 2??
0 , ?? > 2??

03

04
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1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ?III (Old) EXAMINATION ? WINTER 2019
Subject Code: 130002 Date: 22/11/2019

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.

Q.1 (a) (i) Solve ?? ?? ?? ???? + (2?? + ?? ?? ) ???? = 0
(ii) Solve (?? + 1)
????
????
? ?? = ?? 3?? (?? + 1)
2

03
04

(b) Obtain Fourier series of ?? (?? ) = ?? 2
in the interval(0, 4). 07

Q.2 (a) (i) Use method of Undetermined coefficients and find general solution of
?? ??
+ 10?? ?
+ 25?? = ?? ?5??
07


(b) Find general solution of (?? 2
+ 2?? ? 35)?? = 37 sin 5?? 07
OR
(b) Solve by Variation of parameter method (?? 2
+ 9)?? = ?????? 3?? 07

Q.3 (a) Find Fourier series of ?? (?? ) = ?? ????
in (0, 2?? ), ?? > 0 07
(b)
Find Fourier series of ?? (?? ) = {
?? , 0 ? ?? ? 2
4 ? ?? , 2 ? ?? ? 4

07
OR
Q.3 (a) Find the Series solution of ?? ??
? 2?? ?
= 0 07
(b)
Express the function ?? (?? ) = {
sin ?? , 0 ? ?? ? ?? 0 , ?? > ?? as a Fourier sine integral and
show that
?
sin ???? sin ????
1 ? ?? 2
?
0
???? =
?? 2
sin ?? , 0 ? ?? ? ??


07

Q.4 (a)
(i) Find Laplace transform of ?? ?? (1 + ??? )
4

(ii) Find the inverse Laplace transform of
2?? +2
?? 2
+2?? +10

03
04

(b) State Convolution theorem and using it find inverse Laplace transform of
1
(?? ?2)(?? +2)
2

07
OR
Q.4 (a) (i) Find Laplace transform of ?? ?3?? ?? (?? ? 2)
(ii) Find inverse Laplace transform of
?? ?2?? (?? +4)
3

03
04

(b) Solve initial value problem using Laplace transform method
?? ??
? 3?? ?
+ 2?? = 12?? ?2?? , ?? (0) = 2, ?? ?
(0) = 6
07

Q.5 (a) (i) Form Partial differential equation for the equation
?? = ???? + ???? + ????
(ii) Find Laplace transform of ?? (?? ) = {
?????? ?? , 0 < ?? < 2??
0 , ?? > 2??

03

04
2
(b)
Solve
?? 2
?? ????
2
+ 3
?? 2
?? ???? ????
+ 2
?? 2
?? ????
2
= ?? + ??
07
OR

Q.5 (a) Find the Series solution of 4????
??
+ 2?? ?
+ ?? = 0 07

(b)
Using method of Separation of variables solve
????
????
= 4
????
????
given that
?? (0, ?? ) = 8 ?? ?3??
07

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