Download PTU B-Tech AR-Automation-And-Robotics 2020 Dec 3rd Sem 63001 Mathematics Iii Question Paper

Download PTU (I.K.Gujral Punjab Technical University (IKGPTU)) B-Tech (Bachelor of Technology) (AR)- Automation-And-Robotics 2020 December 3rd Sem 63001 Mathematics Iii Previous Question Paper

Roll No.
Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (Automation & Robotics) (2012 & Onward) (Sem.?3)
MATHEMATICS-III
Subject Code : BTAR-301
M.Code : 63001
Time : 3 Hrs. Max. Marks : 60
INST RUCT IONS T O CAND IDAT 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
t
1.
If Laplace transform of f(t) is F(s) then find Laplace Transform L
f t
dt ,
if it exists.
0
2s 6
2.
Find Inverse Laplace Transform of
.
2
s 4
3.
Write down the Bessel's differential equation of order `n'.
4.
Define error function.
5.
Express the following in terms of Lagendre polynomials 1 ? x + x2
6.
Show that cosz is an analytic function.
7.
Define a conformal mapping.
2
1 z
8.
Evaluate
dz,,C : z 3
C z 2
3i
9.
Evaluate the integral
2
z dz
along the line y = x/3
0
10. Expand log(1 + z) about z = 0.
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SECTION-B
11. Solve the differential equation using Method of Laplace transform
2
d y
dy
2
5 y sin 2t, given that y (0) = 2, y(0) = ? 4
2
dt
dt
12. Prove that (2n + 1) xPn (x) = (n + 1) Pn+1 (x) + nPn?1 (x)
2 3
x y (x iy)
z 0
13. Show that the function defined by
6
10
f (z) x y
, is analytic at origin, even
0,
z 0
though f (0) does not exist.
14. If the potential function is log (x2 + y2), find the flux function and complex potential
function.
z i
15. Show that the transformation w
maps the real axis in the z-plane onto the circle
z i
| w | = 1.
SECTION-C
16. (a) Define unit step function and find its Laplace transform.
d
(b) Prove that
[ n
x
J (x)]
n
n
x
Jn 1(x)
dx
2
d y
dy
17. Solve by applying Frobenius method : 9x (1 x)
12
4 y 0
2
dx
dx
dx
18. Using Contour integration, evaluate the integral
4
x 1
0
NOTE : Disclosure of Identity by writing Mobile No. or Marking of passing request on any
paper of Answer Sheet will lead to UMC against the Student.
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