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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