Download PTU B.Tech 2020 March ICE 3rd Sem Applied Mathematics III Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech ICE (Instrumentation And Control Engineering) 2020 March 3rd Sem Applied Mathematics III Previous Question Paper

1 | M-54501 (S2)-181
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.(Instrumentation & Control Engg.) (Sem.?3)
APPLIED MATHEMATICS ? III
Subject Code : AM-201
M.Code : 54501
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. Write briefly :
a) Evaluate,
cos ?
? ?
z
C
e
dz
z
along the circle C : | z | = 1.
b) Find L (sin
2
3t).
c) Solve (x
2
? yz) p + (y
2
? zx) q = z
2
? xy.
d) Show that an analytic function with constant modulus is constant.
e) Write half range sine series of the function f (x) = x in the interval 0 < x < 2.
f) Write the sufficient conditions for the existence of Laplace transform.
g) Find solution of homogeneous partial differential equation 4r ? 12s + 9t = 0.
h) Show that nP
n
(x) =
1
( ) ( )
n n
xP x P x
?
? ?
? .
i) If f (x) is an odd function in (? l, l), then what are the values of a
0
and a
n
?
j) Find the bilinear transformation that map the points z = 1, i, ?1 into the points
w = i, 0, ? i.
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1 | M-54501 (S2)-181
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.(Instrumentation & Control Engg.) (Sem.?3)
APPLIED MATHEMATICS ? III
Subject Code : AM-201
M.Code : 54501
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. Write briefly :
a) Evaluate,
cos ?
? ?
z
C
e
dz
z
along the circle C : | z | = 1.
b) Find L (sin
2
3t).
c) Solve (x
2
? yz) p + (y
2
? zx) q = z
2
? xy.
d) Show that an analytic function with constant modulus is constant.
e) Write half range sine series of the function f (x) = x in the interval 0 < x < 2.
f) Write the sufficient conditions for the existence of Laplace transform.
g) Find solution of homogeneous partial differential equation 4r ? 12s + 9t = 0.
h) Show that nP
n
(x) =
1
( ) ( )
n n
xP x P x
?
? ?
? .
i) If f (x) is an odd function in (? l, l), then what are the values of a
0
and a
n
?
j) Find the bilinear transformation that map the points z = 1, i, ?1 into the points
w = i, 0, ? i.
2 | M-54501 (S2)-181
SECTION?B
2. Find a Fourier series to represent e
?x
from x = ? l to x = l.
3. A tightly stretched string with fixed end points x = 0 and x = 1 is initially in a position
given by y = y
0
sin
3
( ?x). If it is released from rest from this position, find the
displacement y (x, t).
4. Show that function f (z) defined by f (z) =
2 3
6 10
( )
,
x y x iy
x y
?
?
z ? 0, f (0) = 0, is not analytic at
the origin even though it satisfies Cauchy-Riemann equations.
5. Evaluate
2
2 sin
0
t t
e
dt
t
?
?
?
.
6. Show that
5
2
2
2
2 1 3
( ) (3 )sin cos J x x x x
x x x
? ?
? ? ?
? ?
?
? ?
.

SECTION?C
7. Use the concept of residues to evaluate
2
0
(5 4sin )
x
dx
x ?
?
.
8. Solve the equation using Laplace transformation :
2
2
2 5 sin ,
?
? ? ?
t
d x dx
x e t
dt dt
x (0) = 0, x ? (0) = 1
9. Find the power series solution about the origin of the equation :
(1 ? x
2
) y ? ? ? 2xy ? + 6y = 0.



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page of Answer Sheet will lead to UMC against the Student.
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