Download PTU B-Tech CE 2020 Dec 3rd Sem 76373 Mathematics Iii (Transform And Discrete Mathematics) Question Paper

Download PTU (I.K.Gujral Punjab Technical University (IKGPTU)) B-Tech (Bachelor of Technology) (CE)- Civil Engineering 2020 December 3rd Sem 76373 Mathematics Iii (Transform And Discrete Mathematics) Previous Question Paper

Roll No.
Total No. of Pages : 02
Total No. of Questions : 18
B.Tech. (CE) (2018 Batch) (Sem.?3)
MATHEMATICS-III (TRANSFORM & DISCRETE MATHEMATICS)
Subject Code : BTAM-301-18
M.Code : 76373
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.
Prove that r .dr 0,
where r has its usual meaning.
2
2.
If
2
^
^
^
A 2zi yj x k,
2
3
2
^
^
^
B x yzi 2xz j xz k then find
( A B) at (1, 1, 1).
x
y
3.
Show that
2
curl curl v grad div v v where v is any vector.
4.
If f is solenoid vector then show that curl curl curl curl f = 4f.
5.
Define Gradiant and state its physical significance.
6.
State and prove Second shifting property of Laplace transform.
7.
Evaluate L (cos2 t sin t).
8.
Find finite Fourier sine transform of f (t) = 1.
9.
Define Euler formulae.
10. State and prove change of scale property of laplace transform.
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SECTION-B
11. Find directional derivative of = 3y2 + yz3 at a point (2, ?1, 1) in the direction normal to
the surface x log z ? y2 + 4 = 0 at a point (?1, 2, 1).
12.
2
2 ^
^
f (2x y )i (3y 4 )
x j, evaluate
f d r
around the triangle ABC whose vertices
C
are A (0, 0), B (2, 0) and C (2, 1).
13. Using Laplace evaluate
3 t
t e sin t dt
.
0
2
s
14. Find inverse laplace of
.
2
2 2
(s )
1
15. Use convolution theorem to find
1
F
.
2
12 s
7is
SECTION-C
16. Verify Green's theorem in the XY-plane for
2
2
(xy 2xy) dx (x y 3) dy
around
C
boundary C of the region enclosed y2 = 8x and x = 2.
17. The string is stretched between the points (0, 0) and (l, 0). If it is displaced along the
x
curve y = K sin
and released from rest in that position at time t = 0. Find the
l
displacement y (x, t) at any time t > 0 and at any point, x, 0 < x < l.

x, when 0 x
2
4
sin 3x
sin 5x
18. If f (x)
show that f (x)
sin x
.....

2
2

3
5

2, when
x
2
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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