RTU 2016 Question Paper Semester IV Applied Electronics and Instrumentation Engineering Mathematics IV

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H B.Tech. rv-Sem (Main & Back) Examl June-July 2016
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Applied Electronics & Inst. Engineering
!t 4AI1 Mathematics-IV
Common with AI, BM, EI, CRE, BC, PE, PC
Time: 3 Hours Maximum Marks: 80
Min. Passing Marks (Main & Back): 26
Min. Passing Marks (Old Back): 24
I nstructions to Candi.dste s :'

Attempt any fi.ve 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.
Units of quantities used./ calculated must be stated clearly'

Use of following supporting material is permitted during examination.

( Mentioned in form No.205 )
I. NIL 2. NIL

Q.1 (a) Prove the following relations, where symbols have their usual meaning: t8l
t f-"- o
(i) E-l =r-[+4./t+!1-
2\4
-')lr
(ii) I =[+4"/t+!1
2\I4
(b) Find interpolation polynomial, which passed through the points (1, -l), (2, 1),
-

(3, 1) and (4, 5). t8l

[4E413s] Page 1 of4 [s36ol

(b) Using Runge - Kutta method, solve the following initial problem for
x= 1.2 & 1.4 t8l
dvvl
,Y(1) = 1.
dxxx' 1

Q.3 (a) State and prove orthogonal property for Legendre polynomial. t8l

(b) Prove that t8l

o f:_nrrll 2sinnr
a1L-l= 4
OR
Q.3 (a) Show that t8l

(i) xJ', (x) = nJn (x) - xJn-1 (x)

(ii) 1312(x) =

(b) Show that t8l

(l - Zxz + z2)'1t2 =
, rn p, (x),
,Eo
l*l < t, lrl . r.

,NIT.IV
Q.4 (a) There are three similar coins, one of which is ideal and other two are biased. The
chances of head are respectively ll3 and 213. A coin is selected at random and

tossed twice. If head occurs both times, then find the probability that the ideal

coin was selected. t8l
(b) Derive moment generating function for Binomial distribution. Hence, find mean
and variance for the same. t8l

[4E413s] Page 3 of4 [s360l

OR
Q.1 (a) By making use of the following table, find the value of x for which f(x) is
maximum or minimum I8l

x 1 2 7 8

f(x) 4 5 5 4

Also find the value of f(x) at x = 6.

(b) Use Sterling formula to find y25. given that
Yzo= 24, Yzq= 32,Yzs = 35, Yy= 4t0 t8l

UNIT-II
I
Q 2 (a) Find the value of log"2 u"* using simpson's ;J rule, by dividing
l*dx,
into four equal parts. t8l
(b) Using Euler's modified method, obtain a solution y(l) = 1, for
"f *=2+Utl,
the range 1( x < 1.6 in three steps. t8l
OR
Q.2 (a) Below given table shows the values of ln,* for various x. Find approximation to
the derivatives of 1r,* at x = 2.4 by using the central interpolation formula: t8]

x 2.0 2.2 2.4 2.6 2.8

ln,, 0.69315 0.78846 0.87547 0.955s1 1.02962

[4E413s] Page? of4 [s360]

OR
Q.4 (a) Prove that Poisson distribution is a limiting case of Binomial distribution. t8l
(b) Calculate the rank correlation coefficient for the tbllowing data: t8l

X: 8l 78 73 73 69 68 62 58

Y: 10 r2 r8 18 18 22 20 24

Q.s (a) Find the curve joining the points (xr, yr) and (x2, y2) that yields a surface of
revolution of minimum area when revolved about the axis. t8l

(b) Find a function y(x) for which i[.' - (v')2-l dx--- ----- -----r given thar
is starionary, t8]
6L
l.)
I y" d*= 2. y(0) =0, y(l )=0.
0

OR

Q.5 (a) State and prove Euler's equation. t8l
v
(b) Find the extremals of the functional t8l

v[y (x), z(x)] = "'{lfr' *(,')2 +zv,fa*

Where y(0) = 0, y(r I 2) = -1, z(0)= 0 and z(n I 2) = l.

[4E413s] Page 4 of4 Is3601