Download PTU B.Tech 2020 March Aero 3rd Sem AM 201 Mathematics Iii Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech Aero (Aerospace-Engg) 2020 March 3rd Sem AM 201 Mathematics Iii Previous Question Paper

1 | M ? 60537 (S2)-481
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech. (Aerospace Engg.) (2012 Onwards)/(ANE) (Sem.?3)
MATHEMATICS ? III
Subject Code : AM-201
M.Code : 60537
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.

SECTION-A
1. Attempt the following :
a. Find L{e
?2t
sin2t}.
b. Find L
?1

2
2
s
e
s
?
? ?
? ?
?
? ?

c. What is the value of J
n?1
(x) + J
n+1
(x) in terms of J
n
(x)?
d. Write the complete solution of a differential equation when the roots of the
indicial equation are distinct and differ by an integer.
e. Form the partial differential equation from, z = xf
1
(x + t) + f
2
(x + t).
f. Solve pq = p + q.
g. Write any one property of analytic functions.
h. Give an example of a harmonic function.
i. What are Dirichlets conditions?
j. Find the sine series of x in (0, 2).
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1 | M ? 60537 (S2)-481
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech. (Aerospace Engg.) (2012 Onwards)/(ANE) (Sem.?3)
MATHEMATICS ? III
Subject Code : AM-201
M.Code : 60537
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.

SECTION-A
1. Attempt the following :
a. Find L{e
?2t
sin2t}.
b. Find L
?1

2
2
s
e
s
?
? ?
? ?
?
? ?

c. What is the value of J
n?1
(x) + J
n+1
(x) in terms of J
n
(x)?
d. Write the complete solution of a differential equation when the roots of the
indicial equation are distinct and differ by an integer.
e. Form the partial differential equation from, z = xf
1
(x + t) + f
2
(x + t).
f. Solve pq = p + q.
g. Write any one property of analytic functions.
h. Give an example of a harmonic function.
i. What are Dirichlets conditions?
j. Find the sine series of x in (0, 2).
2 | M ? 60537 (S2)-481
SECTION-B
2. Find the Fourier series of e
?x
in the interval (0, 2 ?).
3. Using the concept of Laplace equations, solve
x" + 2x' + 5x = e
? t
sin t, where x(0) = 0, x' (0) = 1.
4. Show that J
n
(x) =
0
1
cos( sin ) n x d
?
? ? ?
?
?
?

5. Solve, (x
2
? y
2
? z
2
)p + 2xyq = 2xz.
6. Determine the analytic function whose imaginary part is cosx cosh y.

SECTION-C
7 . Solve in series, x y" + y' ? y = 0.
8. A string is stretched and fastened to two points I apart. Motion is started by displacing the
string in the form y = a sin
x
l
?
from which it is released at time t = 0. Show that the
displacement of any point at a distance x from one end at time t is given by,
( , ) sin cos
x ct
y x t a
l l
? ?
?
9. Evaluate by contour integration
2
0
cos2
5 4cos
d
?
?
?
? ?
?
.




NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.

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