Kurukshetra University 2009 B.Tech Electronics and Communications Engineering Mathematics-3 - Question Paper
Mathematics
Paper-201E
Roll No..........................................................Total No. of Piiyo t I
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Mathematics111 Paper ; Mnlb-20lK
(imc: IhrtfcIIouni] (Maximum Marks - 1IX)
Note : Allcmpl any FIN E quehlUtr.s, selecting al least ONK from each scction
SECTIONI 1. (a) Find a Tourier series for die function defined by:
1 i'oi w<x<0 flx> <0 (oi x-0 i (or 0 < x < ji.
I Ietice prove lluil
I - + - - + n/A. in
3 5 7 1U
(b) Write erudition* for <i Fourier expansion. Hcncc obtnio the Fourier series for ibe liiucliou:
f jix iKxSl *](2-x) 15X52 10
(a) Solve the mlciral equation J f(x)cosaxdx r**.
u
(b) Using Kffiincnranstonuauou, solve ihe differential equation:
rnj S:u
, , Riven rhat: et Ok
u {x, 0) - 2x; 0 < x < u. t > 0. 20
il
}. (ah Ef \i = Log tan H Oft), prove thsl
U- ilou Liin K
|xy: (* +iy)V aj -!-jf\ ?.#t) th) Showtbtf f(z)- L
ls Hft auljlir jI /: 0, j|ltunili CJR_ cuIhhii iff dl tffiOll 91 ibe origin. I?
30
ftMlKINIJ]
fl. (h) CiLvcn' that P(A) - L/Z HIU) = 1/J, F<A n B) 1/4. FithI P(A|B).P(Au BJJIA' I EV). 10
Adtcisirasccl [Kikv- A iwq impeding I nr om moth, Find the mom iikt vyjmtc of lhe number of mKicW lf>
6. (4) Pind lhe innfticm jtcncihnp function of I be! cipunenLi-fl
= -- <r"\ 0 S * 5 , t > 0
C
JEcnte [inti its Tticjin And S I)- HI
ICi
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lb) Fit a Poi&un dLmribuliun lli Lhe f<il kiwin: | ||||||||||||
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7i [a) UilUti GraphitnJ Method, Milvc, iHin, -2(1+ }[>k jub. Iu K
3xt + jtj a m
JyxCJ JO
[hi FUm! Lhe wlininr *p*cc nfihe J P.P.;
Mil*, /-a + 3y- 1/ lnfaHO \ i >y-i J/-J
2* + 3y + ir * 7
Jt&if
Whki Hjf [hoc ore the (S) Hiuic, (J>) Dtndiuenlc haac fcotiblc, (c) opUnuM basic feaMc 7 10
6, {a) Ulrin Simple* Mtlliod, solve ,i
Mm Z-i-3y
nib. la 1 t 2y 10
0<x 5
0iys4, 10
lit) t ting I>ii Stmp<tnMcLlMx1, jolvc:
Min. 7< "2 - 2y-+l raib. to 2x + Jiy -t 5aE2 I* t y +- 72 J
* + 4y m* S 5
= *,yn?2fl. to
3
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Attachment: |
| Earning: Approval pending. |
