Download PTU B.Tech 2020 March Automation-And-Robotics Question Paper 3rd Sem BTAR 303 18 Mathematics Iii

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech Automation-And-Robotics 3rd Sem BTAR 303 18 Mathematics Iii 2020 March Previous Question Paper

1 | M-76502 (S2)- 383
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.(Automation & Robotics) (2018 Batch) (Sem.?3)
MATHEMATICS-III
Subject Code : BTAR-303-18
M.Code : 76502
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) Explain the Dirichlet conditions for a function to be expressed in terms of Fourier
series.
b) Find Laplace Transform of e
?t
cos
2
t
c) Find Laplace Inverse Laplace transform of
2
1
.
1 s s ? ?

d) Define ordinary point and regular singular point.
e) Express f (x) = x
2
+ 2x + 1 in terms of Lagendre function.
f) Form a partial differential equation from f (x
2
+ y
2
, z ? xy) = 0.
g) Solve the partial differential equation .
z z
yz xz xy
x y
? ?
? ?
? ?

h) Evaluate
2
3
,, :| | 2.
2 5
C
z
C z
z z
?
?
? ?
?

i) Show that sin z is analytic function
j) Define even function and write fourier series for an even function in the interval
(?c, c), provided it satisfies all the conditions.
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1 | M-76502 (S2)- 383
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.(Automation & Robotics) (2018 Batch) (Sem.?3)
MATHEMATICS-III
Subject Code : BTAR-303-18
M.Code : 76502
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) Explain the Dirichlet conditions for a function to be expressed in terms of Fourier
series.
b) Find Laplace Transform of e
?t
cos
2
t
c) Find Laplace Inverse Laplace transform of
2
1
.
1 s s ? ?

d) Define ordinary point and regular singular point.
e) Express f (x) = x
2
+ 2x + 1 in terms of Lagendre function.
f) Form a partial differential equation from f (x
2
+ y
2
, z ? xy) = 0.
g) Solve the partial differential equation .
z z
yz xz xy
x y
? ?
? ?
? ?

h) Evaluate
2
3
,, :| | 2.
2 5
C
z
C z
z z
?
?
? ?
?

i) Show that sin z is analytic function
j) Define even function and write fourier series for an even function in the interval
(?c, c), provided it satisfies all the conditions.
2 | M-76502 (S2)- 383
SECTION-B
2. Find the Fourier series for f (x) in the interval (? ?, ?) when f (x) =
, 0
.
, 0
x x
x x
? ? ? ? ? ? ?
?
? ? ? ? ?
?

3. Solve the differential equation using Method of Laplace transform
2
2
4 5
d y dy
y
dt dt
? ? = sin 5t, y (0) = 0, y ?(0) = 0
4. Prove that
1
[ ( )] ( )
n n
n n
d
x J x x J x
dx
?
?
5. Expand
1
( )
( 1)( 3)
f z
z z
?
? ?
in Laurents series, valid for (i) 1 < | z | < 3
6. Solve the Partial differential equation
2 2 2
2 2
6
z z z
x y
x x y y
? ? ?
? ? ? ?
? ? ? ?


SECTION-C
7. a) Find half-range cosine series for f (x) = x in the interval [0, ?]
b) Define Unit step function and find its Laplace transform.
8. Evaluate
0
cos x
dx
x
?
?
by contour integration.
9. A homogeneous conducting rod of length 100 cm has its ends kept at zero temperature
and temperature initially is
0 50
( ,0)
100 , 50 100
x x
u x
x x
? ? ?
?
?
? ? ?
?

Find the temperature u (x, t) at any time t.

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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