Download PTU B.Tech 2021 Jan Automation-And-Robotics 3rd Sem 76502 Mathematics Iii Question Paper

Download PTU (Punjab Technical University) B.Tech (Bachelor of Technology) / BE (Bachelor of Engineering) 2021 January Automation-And-Robotics 3rd Sem 76502 Mathematics Iii Previous Question Paper

Roll No.
Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (Automation & Robotics) (2018 Batch) (Sem.?3)
MATHEMATICS-III
Subject Code : BTAR-303-18
M.Code : 76502
Time : 3 Hrs. Max. Marks : 60
INST RUCT IONS T O CANDIDAT ES :
1 .
SECT ION-A is COMPULSORY cons is ting of TEN questions carrying TWO marks
each.
2 .
SECT ION-B c ontains F IVE questions c arrying FIVE marks eac h and s tud ents
have to atte mpt any FOUR q ues tions.
3 .
SECT ION-C contains THREE questions carrying T EN marks e ach and s tudents
have to atte mpt any T WO questio ns.
SECTION-A
Write briefly :
1.
Define odd function and write Fourier series for an odd function satisfying Dirichlet
conditions in the interval (?c,c).
2.
Find Laplace inverse transform of
1
.
2
s 3s 2
3.
Find Laplace Transform of t sin 2t.
4.
Write down the Bessel's equation.
5.
Express f (x) = 2x2 ? x + 1 in terms of Lagendre function.
y
6.
Form a partial differential equation by eliminating arbitrary functions from z = f .
x
7.
Solve the partial differential equation p tan x + q tan y = tan z, where p
z
z
, q
.
x
y
8.
Evaluate
z 3
, C :| z | 2.
C
2
z 2 z 5
9.
Write down the necessary and sufficient conditions for a function to be analytic.
10. Write down the mathematical function for Triangular wave form.
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SECTION-B
11. Obtain the Fourier series for f (x) = x cos x in the interval (? , ).
12. Solve the differential equation using Method of Laplace transform
2
d y
dy
2
2
t
y e
, y(0) = 0, y (0) = 1
2
dt
dt
13. If and are the roots of the equation Jn (x) = 0, then prove that
1
xJ ( x ) J (x ) dx 0, if
n
n
0
14. Expand
1
f ( z )
in Laurents series for 1 < | z | < 3.
2
z 4 z 3
15. Solve the Partial differential equation
2
2
2
z
z
z
2
6
9
12 x xy
2
x y
2
x
y
SECTION-C
16. a) Find half-range cosine series for f (x) = x + x2 in the interval [0, ].
b) Find the Bilnear transformation which maps z = 1, i, ?1 onto the points w = i, 0 ? i.
17. A string is stretched between the fixed points (0, 0) and (l, 0) and released at rest from the
initial deflection given by
2 k x,
0 x l / 2
l
f ( x )
2 k
( l x ),
l / 2 x l
l
Find the deflection in the string at anytime t.
18. Solve in series using Frobenius method :
2
d y
dy
2
2
2 x
x
( x 1) y 0
2
dx
dx
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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