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Total No of Pages:
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484L76
B.Tech. IV-Sem (Main & Back) Examl June-July 2016
Electrical & Electronics Bngineering
4EX6A Advanced Engg. Mathematics-Il
Common with EE,EX
Time: 3 Hours
Maximum Marks: 80
Min. Passing Marks (Main & Back): 26
Min. Passing Marks (OId Back): 24
Instructions to Candi.date
s:
-
Attempt any
five questions, selecting one question from each unit. All
Questions carry equal marks. Schematic diagrams must be shown
wherever necessary. Any data you feel missing suitably be assumed and
stated clearly.
(Jnits of quantities used,l calculated must be stated crearry.
'
Use of following supporting material is permitted during examination.
(M entioned in form No.205 )
UNIT.I
Q.1
(a) Use Newton - Raphson method to find arealroot of f(x) = x3 - 3x - 5 = 0.
(b) Given the following dak:
x: 0.0
0.2
0.4
0.6
0.8
y: 0.3989 0.3910 0.3683 0.3332 O.Z8g7
Evaluate the value of y(0.25), y(O.62) and y(0.43).
tgl
tgl
OR
Q.l (a)
Fit a straight line for the following
x:12345
y: 35 65
[4841761
100 138
data:
tgl
170
Page
tof4
[1zo00l
(b)
Using Lagrange's interpolation formula, find the value
of
from
y(5)
following table:
the
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x: I2347
y:24816128
Q.2
(a)
Evaluate the value of
x:0
+
dx
for x = 0.1 and 0.5 from the following
0.2
0.1
0.3
y: 30.28 31.43 32.98 33.54
(b)
0.4
33.97
rable:
0.5
33.48
tgl
0.6
32.t3
i]
Use Runge -:Kutta method to find y(1.1), given that:
dv.,)*'+ y';Y(1)
fr
=
=
Q
t8l
OR
Q.2 (a)
_
Use Simpson's
t?l--z
integralj-x-dx.
]3 and ]8 rules to evaluate the ___._o__-i
_...
r*rE
Hence obtain
the hpproximate value of log"2.
(b)
Use Milne's Predictor- Corrector method to find y(O.g), given that:
dv
#
Q
3 (a)
O)
t8l
=*
.'
-y';y
(0) = 0, y (0.2) =0.02,y (0.4) = 0.0795, y (0.6)
=0.1762.
Show that xJn*1 *xJn-1
Prove that
t8l
"_J
=Jfln
t8l
r
fo ; m+n
-r
l2n+1
2
IPm(x)P(x)dx={
'_
n
l-lln=n
t8l
AB
Q.3 (a)
(b)
Show that J-, (x) =
Show that
(-l)n ln(x), neZ
Pn(x)= I
dn
(n!) 2n dxn
l4E4r76l
t8l
1*2-1;,
PageZ of 4
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[120001
e.4 (a) A newly constructed house may fall down either due to wrong
designing or by
inferior material used in the construction. Chance that the designing is faulty
is
l07o andthe probability of,its collapse, if design is faulty is 957o and that due to
bad materi al is 45Vo.If the house collapses, find the chance that
it
was due to
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wrong designing.
(b) If rhe height of 300 students are normally distributed with mean 64.5 inches and
standard deviation 3.3 inches. how many students have heights
(i)
(ii)
Less than 5 feet,
Between 5 feet and
99Vo
5
feet 9 inches. Also find the height between which
of the student lie.
[(Given P (0 <
Z<
1.36) =0.4t31, P (0 <
Z<2.57) = 0.495)]
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OR
Q.4
(a)
Razor blades are supplied UV
a probability
.
of 1 in
calculate the number
1
manufacturing company in packets of 10. There is
100 blades to be defective. Using Poisson distribution,
of packets containing one defective blade, no
blade and all defective blades in a consignment of 10,000 packets.
(b)
defective
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The distribution of weekly wages for 500 workers in factory is approximately
normal with the mean and standard deviation of
t
75 and
{
15 respectively. Find
the number of workers who receive weekly wages
(i)
(ii)
More than
Less than
{ 90,
{
45.
t(Grven P (0 < Z < 1) = 0.3413] P fO <Z < 2) = 0.4772)l
l4}4t76l
Page 3
of4
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[12000]
\
UNIT.V
Q'5 (a)
In a partially destroyed laboratory on record
of an analysis of correlation data, the
following results only are legible:
var(x) = 9, Regression equations: gx
(i)
(ii)
(iii)
(b)
-
10y + 66
The mean values of x and y,
- 0, 40x -
lgy
= 2r4. Find
The standard deviation of y,
The correlation coefficient of x and y.
Find the inverse Z
F(z) =
-
t8l
transform cif fo,owing function:
^. , if RoC is
--+
(z-t)(z-2)'--
(i)
(ii)
l<lzl <2,
(iii)
tzt> Z.
lzl
< I,
t8l
OR
Q.5
(a)
Calculate the coefficient
of cbrrelation
between
x
and y.using the following
data:
x:1
2
345678
.., yt 9
8
10 t2 ; L.t t3 14 16
(b) Find lhe Z - transform of un cn cosh an, n >
=
[4E41V6]
Page
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9
15
0.
4 of4
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[12o00J
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