Kurukshetra University 2008 B.Tech Electronics and Communications Engineering MATHEMATICS-3(Supplimentry) - Question Paper
Mathematics-3(Supplimentry)
Paper-201E
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IIT-4AI08 8752MjiihiiutilcsTIT [*&piLr: Math'2(H E OptionTl
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L (iix'Find the Fourier serin, 10 repi*enMhc function x) given by TOO = \ . 0 l x s w
= 2n-xT it 5 \ In.
| | j j Deduct [hnj -*-+-r+,'+*.....J =
10
lJ 3J 5
Obtain 4 Ha3 f-ftangt: tnhtcw scriu far j
frx) = k\ , Ositi -
i
0 = s ii f. 10
* ()) finj the Ftmrwr Transform frf
kmJ1-*1 ; '*'
r * UttK-smx
Ik'nee iMjiluqlt- f---- cosxdx
10
*
M thtJ milinl [t m (ic rat Line ol'an infinite tvat1 I* givtn by
f (L for ;xt<a
- -\; i.t>.
riclcrmillL' 1 fit lem pc nature af any pO iilt Ii and w fl nv Enmanl I.
10
SEC'fTONB
j |L' tan (A t ift) = \ t iy, P-ve thaL
(i) x1 - v2 i- 2k cot 2A - L.
(> k! + y1 = 2y cnt h 2B +?1 = 0. 3+S
(b>Dclermicie the Analytic function who Real pan Ii / c* (x cos y - y -hiti y). IQ-'
4 (3 Srt3:> isji Holomoillic fiinctiim of Z, itow rfqgT
y
i i
10
(1'xSH<jw ihal ihe transformation
W = z 4 f LraClst'ormH (he circle uf radius
1 . w .(a +b)F centre at the origin, in die /.-jilune into ellipse of
_ 5cnji-.ax.eFi a, b in the w-plane, IA
; SECTIONC
/
5 (3) There art three baj-s : Fir?t containing | whitt, i red, 3 gjieecL j/ ballfii second 2 while, 1 red, I green bulla and Lhird 3 white,
1 redH 2 green bails, i,
'jOuniil.,1
ballsJnn lrQmbagchoi<ii jj lamtan Tin* iTc found td hr um and me ml. find iht (Withobi lit)
ihrtT (he half* w ftaup cbIYic Trvm Ihtf Sffiond 10
fti'ji X a conlLnuuu* fflnddlH variable with pmhuh i tiljf density lumJLHiii ivticL by
[ t (lx<2 2\ 2sx<4 -U+*k 4?tG
hlltl the tmean vtlEu{ of \ and vlliK of It. 10
&J "{H,) lTii ThtPorasall DI Jtfl bllH rtrl 1 rt the JuElowLLlfc l
1 r
U
i i*
2 22
3 y
4 I 10
(llil 'Shcsw that Lhe SHudflK) 1>cViiLon fr Distribution
k upproviuiaTcly 2fl% mntc ihjin Lbt mean dcvimimi. 10
StniON-D Tr 4a> - Cnphtcalf) solve tkc I PF
* Mbs / = 6*t-
suhjed lo t- 3,lj Iff
3s, Oxj fe24;
Xj 1 * 13, x(. itjill 10
*
r1,
the following Ll1!3 by Simplex Meihud : / Mjin. Z = 5*. 4 3ki
I *
subject lu Jtj + ji2 i 2+ 2*., LO + Kjtj'S 13;
s:
A. s?\ Usinj; DuaJ Simp]
ex Method :
Minimize Z - *L \ 2x 1 3aiL subjt to Z* - 3(2 -f Ji >4
Xj + Xj - 2x Si *2 *3 2;
K|, Xji o,
(h-"ficfine :
(i) Basic KeasibJc Solutions.
tii) Optimum linhi-L- Feaaibit! Solution.
(LiiJ SliitWSdrptus Variable. y-
ai t
(iv) Artificial Variable.
(v) 1 tejseneracy in LPP,
S752(UL> 4
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