Download DBATU B-Tech 3rd Sem and 4th Sem 2019 May Engineering Mathematics III 1 Question Paper

Download DBATU (Dr. Babasaheb Ambedkar Technological University) B.Tech 3rd Sem and 4th Sem 2019 May Engineering Mathematics III 1 Question Paper

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DR. BABASAHEB AMBEDKAR TECHNOLOGICAL UNIVERSITY, LONERE
' End Scmcstcr Examination ? May 2019
Course: B. Tech
Subject Name: Engineering Mathematics?III
Max Marks: 60 Date: 28-05-2019
Sem: III
Subject Code: BTBSC301
Duration: 3 Hr.
Instructions to the Students:
1. Solve ANY FIVE questions out of the following.
2. The level question/expecled answer as per OBE or the Course Outcome (CO) on
which the question is based is mentioned in () in front of the question.
3. Use ofnon-programmable scienti?c calculators is allowed.
4. Assume suitable data wherever necessary and mention it clearly.
Q. 1
A)
B)
C)
D)
A)
B)
C)
A)
B)
(Level/CO)
Attempt any three.
F ind L{f(t)}, where f (t) = t2 e?3tsinhat Understand
Express f (t) in terms of Heaviside's unit step function and hence ?nd its Understand
cost, 0 < t < n '
Laplace transform where f (t) ? {sinm t > 11
Find L{f(t)}, where f(t) = 2? 1:? du Understand
By using Laplace transform evaluate [00? 8?: (g) dt Evaluation
Attempt the following.
- . ?1 52 Application
Usmg convolutlon theorem ?nd L {(574492}
Find L'1{f (5)}, where f (s) = cot?1 (?) Application
Using Laplace transform solve y? ? 3y? + 2y = 12e?2t; y(0) = 2, Application
y?(0) = 6
Attempt any three.
< < ?
Express f (t) = 1' O ? x " n: as a F ourier sine integral and hence Evaluatlon
0, x > 1:
deduce that [0? 1"? sin ml d1 = g.
Using Parseval?s identity for cosine transform, prove that Application
I00 sinat dt?n 1?K?:
0 t(a2+t2) _2 a2
. 15F8A8CAEE76137CDEFD5C570EO0F2B9
Marks
12
4
4
12

C)
D)
A)
B)
C)
A)
B)
C)
D)
A)
B)
C)
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_ 2 ' <
Findthe'Fouriertransform of f (x) = {1 x0, i;]?I,ICTI>?11
co xcosx?sinx x 3n
thatf ? cos? dx= ?-
0 x3 2 16
. Hence prove
Find Fourier sine transfonn of 53?" + Ze?sx
Attempt the following.
F orm the partial differential equation by eliminating arbitrary function f
fromf(x+y+z,x2 +y2 +22) = 0
Solve xz(z2 + xy)p ? yZCZ2 + xy)q = x4
F ind the temperature in a bar of length two units whose ends are kept at zero
temperature and lateral surface insulated if the initial temperature is
. n'x . 511x
5m? + 3 sm 7?
Attempt Any three.
If the function f (z) = (x2 + axy + byz) + i(cx2 + dxy + yz) is analytic,
?nd the values of the constants a, b, c and d.
If f (z) is an analytic function with constant modulus, show that f (z) is
constant.
Find the bilinear transformation which maps the points z = 0, ?i, -?1 into
the points w = i, 1,0.
Prove that the ?mction u = ex(xcosy ? ysiny) satis?es the Laplace's
equation. Also ?nd the coresponding analytic function.
Attempt ANY TWO of the following.
Evaluate #5 i dz, where C is the circle Iz + 1 ? 1'] = 2.
C 22+22+5
sinz
Find the residues of f (Z) =
at its poles inside the circle Izl = 2.
Z COSZ
' 2 2
Slntrz +COSTIZ
Evaluate f
Cm dz, where C 15 the Clrcle |z| = 3.
*1? End 22:29:
15F8A8CAEE76137CDEFD5C570EO0F2B9
Understand
Understand
Synthesis
Analysis
Application
Understand
Understand
Understand
Synthesis
Evaluation
Understand
Evaluation
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