Download PTU B.Tech 2020 March Civil 3rd Sem BTAM 301 18 Mathematics Iii Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech Civil Engineering (CE) 2020 March 3rd Sem BTAM 301 18 Mathematics Iii Previous Question Paper

1 | M-76373 (S2)- 746
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.(CE) (2018 Batch)/(ECE) (Sem.?3)
MATHEMATICS-III (TRANSFORM & DISCRETE MATHEMATICS)
Subject Code : BTAM-301-18
M.Code : 76373
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) Define gradient of a scalar point function.
b) Define Solenoidal and irritational fields.
c) State Gauss divergence theorem.
d) Define Laplace transform.
e) Write the relation between Laplace and Fourier transform.
f) State Convolution theorem.
g) Write Gibbs phenomenon.
h) Define dirac-delta function and impulse function.
i) Write the Laplace transform of t
2
e
?t
.
j) If u = x
2
y i + yz j + z
2
x k. Find the divergence of u.


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1 | M-76373 (S2)- 746
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.(CE) (2018 Batch)/(ECE) (Sem.?3)
MATHEMATICS-III (TRANSFORM & DISCRETE MATHEMATICS)
Subject Code : BTAM-301-18
M.Code : 76373
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) Define gradient of a scalar point function.
b) Define Solenoidal and irritational fields.
c) State Gauss divergence theorem.
d) Define Laplace transform.
e) Write the relation between Laplace and Fourier transform.
f) State Convolution theorem.
g) Write Gibbs phenomenon.
h) Define dirac-delta function and impulse function.
i) Write the Laplace transform of t
2
e
?t
.
j) If u = x
2
y i + yz j + z
2
x k. Find the divergence of u.



2 | M-76373 (S2)- 746
SECTION-B
2. Find the directional derivative of ? = 5x
2
y ? 5y
2
z + 2.5z
2
x at the point P (1, 1, 1) in the
direction of the line
1 3
2 2
x y
z
? ?
? ?
?
.
3. If f = (x
2
+ y
2
+ z
2
)
?n
. Find n if div grad f = 0.
4. Solve the equation
2
2
2 3 sin
d y dy
y t
dt dt
? ? ? , 0
dy
y
dt
? ? , when t = 0, by the Laplace
transform method.
5. Express f (x) = x sin x, 0 < x < 2 ? as a Fourier series.
6. Find the inverse Laplace transform of
/2
2 2
s s
se e
s
? ?
? ?
? ?


SECTION-C
7. Verify Stoke?s theorem for the vector field F = (x
2
+ y
2
) i ? 2xy j taken around the
rectangle bounded by the lines x = ? a, y = 0, y = b.
8. If f (x) = sin x, 0 ? x ? ? and f (x) = 0, ? ? ? x ? 0, Prove that
2
1
1 sin 2 cos 2
( )
2 4 1
n
x nx
f x
n
?
?
? ? ?
? ? ?
?

Hence show that
1 1 1 2
...
1.3 3.5 5.7 4
? ?
? ? ? ? ? ? .
9. a) Evaluate :
0
sin
t
t
t
L e dt
t
?
? ?
? ?
? ?
?

b) Show that ?
2
(r
n
) = n (n + 1) r
n?2
, where r
2
= x
2
+ y
2
+ z
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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