Download PTU B.Tech 2020 March Automation-And-Robotics Question Paper 3rd Sem BTAR 301 Mathematics Iii

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech Automation-And-Robotics 3rd Sem BTAR 301 Mathematics Iii 2020 March Previous Question Paper

1 | M-63001 (S2)-483
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.(Automation & Robotics) (2012 & Onwards) (Sem.?3)
MATHEMATICS ? III
Subject Code : BTAR-301
M.Code : 63001
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) Find Laplace Transform of e
?t
(t + 2)
2

b) Find Inverse Laplace Transform of
2
2 18
s
e s
s
?
?

c) Define a singular point and regular singular point.
d) Express f (x) = 2x
2
? x + 1 in terms of Lagendre function.
e) Show that | z |
2
is not analytic at any point.
f) Define error function.
g) Define a conformal mapping.
h) Evaluate , :| | 1
2
z
C
e
dz C z
z
?
?
?
.
i) Define poles and find the same for
2
1
( 2)
z
z z
?
?

j) Show that sinh z is analytic function.
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1 | M-63001 (S2)-483
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.(Automation & Robotics) (2012 & Onwards) (Sem.?3)
MATHEMATICS ? III
Subject Code : BTAR-301
M.Code : 63001
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) Find Laplace Transform of e
?t
(t + 2)
2

b) Find Inverse Laplace Transform of
2
2 18
s
e s
s
?
?

c) Define a singular point and regular singular point.
d) Express f (x) = 2x
2
? x + 1 in terms of Lagendre function.
e) Show that | z |
2
is not analytic at any point.
f) Define error function.
g) Define a conformal mapping.
h) Evaluate , :| | 1
2
z
C
e
dz C z
z
?
?
?
.
i) Define poles and find the same for
2
1
( 2)
z
z z
?
?

j) Show that sinh z is analytic function.
2 | M-63001 (S2)-483
SECTION-B
2. Solve the differential equation using Method of Laplace transform
2
3
2
4 3 ,
t
d y dy
y e
dt dt
?
? ? ? y(0) = 1, y ?(0) = 1
3. Prove that P
n
? (x) = xP ?
n?1
(x) + nP
n?1
(x)
4. Find the real part of the analytic function whose imaginary part is tan
?1
(y/x). Also find
the analytic function.
5. Expand
1
( )
( 1)( 3)
f z
z z
?
? ?
in Laurent?s series, valid for | z |> 3
6. Find the image of
1
w
z
? under the mapping | z ? 3 | = 5

SECTION-C
7. a) Define unit impulse function and find its Laplace transform
b) Prove that
1/2
2
( ) sin J x x
x
?
?
?

8. Solve in series :
2
2
(1 ) 2 0
d y dy
x x y
dx dx
? ? ? ?
9. Evaluate
2
2
0
1 2 cos
d
a a
?
?
? ? ?
?
, 0 < a < 1 using Contour integration.



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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