Download PTU B.Tech 2021 Jan CE 3rd Sem 76373 Mathematics Iii Transform And Discrete Mathematics Question Paper

Download PTU (Punjab Technical University) B.Tech (Bachelor of Technology) / BE (Bachelor of Engineering) 2021 January CE 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.
Define gradient of a scalar point function.
2.
If F = (x + y + 1) i + j ? (x + y) k. Show that F. curl F = 0
3.
Define Laplace transform.
4.
Write the relation between Laplace and Fourier transform.
5.
Represent f (t) = sin 2t, 2 < t < 4 and 0 otherwise, in terms of unit step function.
6.
Define Solenoidal and irrotational fields.
7.
State convolution theorem of Fourier transform.
8.
State Stokes theorem.
9.
Write Euler's formula of Fourier series.
10. Write Gibbs phenomenon.
1 | M-76373
(S2)- 640

---

SECTION-B
11. Find the values of a and b such that the surfaces ax2 ? byz = (a + 2) x and 4x2 y + z3 = 4
cut orthogonally at (1, ?1, 2).
12. Apply Convolution theorem to evaluate the inverse Laplace transform of :
2
s
2
2
2
2
( s
a ) ( s b )
13. Find the Fourier sine transform of e?|x|. Hence show that
sin
m
x
mx
e
dx
, m 0
0
2
2
1 x
14. Apply Green's theorem to evaluate C [(2x2 ? y2)dx + (x2 + y2)dy], where C is the
boundary of the area enclosed by the x-axis and the upper-half of the circle x2 + y2 = a2.
15. If A and B are irrotational, prove that A ? B is solenoidal.
SECTION-C
16. Verify Gauss divergence theorem for F = (x2 ? yz)i + (y2 ? zx)j + (z2 ? xy)k taken over the
parallelepiped 0 x a, 0 y b, 0 x c.
17. Find the Fourier cosine series of the function f (x) = ? x in 0 < x < . Hence show that
2
1
2
8
r 0 ( 2 r 1)
18. a) Use Laplace transform method to solve :
2
d x
2dx
t
x e
2
dt
dt
With x = 2, dx 1
at t = 0.
dt
b) Find the directional derivative of f = x2 ? y2 + 2z2 at the point P (1, 2, 3) in the
direction of the line PQ where Q is the point (5, 0, 4). Also calculate the magnitude of
the maximum directional derivatives.
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.
2 | M-76373
(S2)- 640

---