RTU 2016 Question Paper Semester IV Electrical and Electronics Engineering Advanced Engineering Mathematics II

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t{ B.Tech. IV-Sem (Main & Back) Examl
!t June-July 2016
Electrical & Electronics Engine"e"rrrg
EI
+ 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 Candidate s : -

Attempt any five questions, selecting one question
Jrom each unit. All
Questions carry equal marks. schematic diagrams must be
shown
wherever necessary- Any data you missing
feel suitably be assumed and
stated clearly.
units of quantities used/ carcurated must be stated
clearry.
use offollowing supporting material is permitted
during examination.
(Mentioned in form No.205 )

UNIT.I
Q' 1 (a) Use Newton - Raphson method to find a real root of f(x)
(b) Given the following dara:
= a3 -3x-5=0. tSl
x: 0.0 0.2 0.4 0.6 0.g
y: 0.3989 0.3910 0.3683 0.3332 0.2897
Evaluate the value of y(0.25), y(0.62) and y(0.43).
t8l
OR
Q.l (a) Fit a straight line for the following data:
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x:12345
y: 35 65 100 138 tTo
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(b) Using Lagrange,s interpolation formula, find the value of y(5)
from the
following table:
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x:123 47
y:248 t6 128
UNIT.II
Q.2 (a) Evaluate rhe varue for x = 0.r and 0.5 from the following tabre:
"f * t8l
x:0 0.1 0.2 0.3 0.4 0.5 0.6
y: 30.28 31.43 32.98 33.54 33.97 33.48 32.13
(b) Use Runge - Kutta merhod to find y(l.l), given that:
dv)1
f=*-+Y';Y(t)=o t8l

OR

Q.2 (a) Use Simpson', 1 uno
i _I1d-. Hence obtain
f rules to evaluate rhe integral 6l+xJ
the approximate value of log"2.
tgl
(b) use Milne's predictor - Corrector method to find y(0.g), given
that:

ff = ^ -y': v(0) = 0. y (0.2) = 0.02,y (0.4) = 0.0795, y (0.6) = o.fi62. tsl
UNIT.III
Q.3 (a) Show that xJr*1 * xJn-1 = lnJ,
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, ,o : m+n
(b) Provethat Ip (x)p (x)dx=j 2
" m l -:m=n
-l l2n+t ""
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OR
Q.3 (a) Show that J-" (x) = (-l)n Jn (x), neZ
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(b) Show rhar pn(x) = _,,"
#$,*, t8l

I4E4L76) Page? of4

UNIT.IV
due to wrong designing or by
Q.4 (a) A newly constructed house may fall down either
is faulty is
inferior material used in the consffuction. Chance that the designing
due to
lYbo andthe probability of its collapse, if design is faulty is 95Vo and that
bad materialis 45Vo.If the house collapses, find the chance that
it was due to

wrong designing. t8l

(b) If the height of 300 students are normally distributed with mean 64.5 inches and
standard deviation 3.3 inches, how many students have heights

(i) Less than 5 feet,
(ii) Between 5 feet and 5 feet 9 inches. Also find the height between which
997o of the student lie.

[(GivenP (0< Z<l'36)=0'4131' P (0< Z<2'57) =0'495)] t8l

OR
in packets of 10' There is
Q.4 (a) Razor blades are supplied by a manufacturing company
a probability of 1 in 100 blades to be defective. Using Poisson distribution,
calculate the number of packets containing one defective blade.
no defective

blade and all defective blades in a consignment of 10,000 packets' t8l

(b) 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) More than { 90,
(ii) Less than { 45.
(0 < Z < 2) = 0'4772)] t8l
[(Given P (0 < Z < l) = O'3413'P

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UNIT-V
of an analysis of correlation data' the
Q.s (a) In a partially destroyed laboratory on record
following results only are legible:
+ 66 = 0' 40x - 18y =Zt{'Firrd
Var(x) = 9, Regression equations: 8x - 10y
(i) The mean values of x and Y'
(iD The standard deviation of Y,
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(iii) The correlation coefficient of x and y'
(b-) Find the inverse Z - transform of following function:
F(z) =
'\"/ -=, if RoC is
(z-l)(z-2)
(i) lzl < l,
(ii) l<lzl<2,
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(iii) lzl>2.
OR
between x and y using the following
e.5 (a) Calculate the coefficient of c6rrelation
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data:

x:12 3456789
y:98 10 12 11 13 14 16 15
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(b) Find,the Z - transform of un = cn cosh an' n 2 0'

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