Download SGBAU (Sant Gadge Baba Amravati university) B-Tech/BE (Bachelor of Technology) 4th Sem Applied Mathematics III Previous Question Paper
Time : Three llours
B.Tech. Fourth Semester (Chem. / Poly / Food / Pulp / Oil / Petro) (Old)
Applied Mathematics ? III : 4 SCE 1
AW - 3554
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Notes :
b)
2 a)
b)
3 a)
b)
C)
4 a)
1 Answer three question from Section A and three question from Section B.
2 Due credit will be given to neatness and adequate dimensions.
3. Assmne suitable data wherever necessary.
4. - Illustrate your answer necessary with the help of neat sketches.
5 Use of calculator is permitted.
6 Use of pen Blue/Black ink/re?ll only for writing the answer book.
SECTION ? A
2 l 6
Solve d__:r_+2g_y_+y = x2 cosx
dx dx
7 ex . . . 7
Solve (D? + 3D+2)y = e by usmg vanatxon of parameter.
OR ?
3 . 2 X 6
Solve (D +1)y = 5111 3x ?cos ?2? .
2 7
Solve x2 51?2, ? xd?y+4y = cos (log x) + x sin (logx)
dx? dx
t sint 5
Evaluate Laplace transform of et ?? t
0
t 4
Prove that L?I {11041 +?l-)} = I mdu
S 52 0 U
Express f(t) in lenns unit step function and hence ?nd its Laplace transform 5
f(t)=t2 , 0
OR
F ind the Laplace transform of 7
f(t)=asinpt . 0
= 0 , E < t < 2??
P P
where f(t+2?nj=f(t)
P
AW - 3554 1 ' P.T.O
b) '
Use convolution theorem to ?nd L?1 i ??-1?2??}
.(s + l)(s +1)
a) Solve the differential equation using Laplace transform
dzy 7T
_, +9y =cos?lt if y(0) = l, y(?] = ?1
dt? 2
b) e?ax
Find the Fourier sine transform of ?
x
OR
a) Using Foun'er integral show that
00 . . . .
IWdAzisinx . O
0
r 0 . x > 1:
b) d , t
Use Laplace trans?mu to solve the differential equation :11 + 2y +J' y dt = sin t
t I 0
when y (0) = 1.
SECTION - B
a) Solve the following difference equation -
0 3m +391 4x = X?
ii) ."n+2 ?4yn :: n2 + 11?]
b) Find the inverse z-transfnrm of 1 Z 1
(2 -?) (2")
4 5
OR
a) Solve the difference equation Yn+2 ?? ZoosaynH + yn = O with y(0) = 1, y(]) = cosa
using method of z-transfomm.
b) Find the z-transform of
i) -??l
n +1
ii) (cosO + sin 0)n
a) Find the tangential & normal component of acceleration at any time t of a particle whose
position (x, y) at any time t is given by x = log (t2 +1), y = t ?2tan?l t .
AW - 3554 2
10.
ll.
12.
b)
a)
b)
b)
b)
Find the directional derivative of 4? = e2x cos yz at the origin in the direction of the
. n
tangent to the curve x=asmt, y=acost, z=at at t=2
OK
If pi = VP , where p, P and F are point functions, prove that F- curl? = o.
Prove that ?~V(h-Vl)
r
_3(?-T) (B-n?-B?)
r5 r3
A vector ?eld is given by F = sin y ; + x(1+ cos y)3 . Evaluate the line integral over the
2
circular path given by x2 +y2 = a , z = 0.
Apply Stokes theorem to evaluate I (x + y) dx + (2x ? z)dy + (y + z)dz where C is the
C
boundary of the triangle with vertices (2, O, 0), (0, 3, O), (0, 0, 6).
OR
Use Divergence theorem to evaluate U(yzzzi + 22x2} + xzyzh)-d? where s is the upper
S
pan ofthe sphere x2 +y2 +22 :1.
Prove that F = (x2 - yz)i? + (y2 -'7J()] + (x2 ? yz)f< is irrotational and ?nd (1) if i? = V4).
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AW - 3554 3
This post was last modified on 10 February 2020