Kurukshetra University 2008 B.Tech Electronics and Communications Engineering Mathematics-3 - Question Paper
Mathematics-3
Paper-201-E
Rnll No, VaUiln Puiies; 3
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tjpH: AnrmtK,/iiAr (luesiians in uliH itoktiine at ksiti ww question from cach Uflii- AU quttiiMii cany ctpji nwfa.
I, |a| Ofomin (he Fourier jbtIm for ihc function
> fix) * 1U, U j I aiidjtJ n(2 - x), I Xi 2. b) Ftnd lhe1 hBlf-flMtsc comiw series for /10 * .t2 in the range 0 S Jr x-
2* ,{*} Fitkl the Fuuriei truufonn of = i - jr if (jr[ < I ( / tnd fix) - D if f i j > L And hcncc cvylmic
UMTWI
3* (a) If vim (0 + cot a + Uin a, prove thui
(i) sin1 * i sin1 fif
(ii) cor 28 + ttidi 2 _ 1
<10 Uk-knnnf +j+ then prove lhai (ff Uinh ti/2 = i;mi 6/2.
(ii) C<jh1i k3Ki;B.
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4. (a| Determine The? vnkJyi ic function fchose real' ipari is u=-e* f.i cos y - y sin v>.
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rcion |r| S I inio ihe upper half of plaiv mdLicLmg [he reiJ mis. |
5. (i) A survey was ctrfiducicd to find ihe supplier of ihc ctMi?gincr durable* for the murkcl. It fiwjid thal ihe ihrce major timpanics A. B and C h*ve nuirtei steue of 35%, 25Tt indfHt mp3iv?]y tjgc of wtiicfr 2**h I** and 3% ire nol ttfnu ihe saTisfctinji. A Ccrt.sumcr buys u prodtxtf and isdijisniijified with it. Wtai is the pnobnbiJiiy ihat it mighl he frum the company C?
(b) Obtain [hcro.g.f. aTibe random vjtriithle X huvinji p.d.f,
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A-r) - Jr for 0 5 x < I, /(*) 2 - J for I S jc < 2 ;ind /Tjt3 * 0 cluwhcn. Dclffrmnc |j'( ?nd p1 |
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s[antiaid deviation. <h) If the iiwjin of a bjnnmiaJ diKtritiLiiian i\ J und ihe |
6* (d) Show ifim [he mean deviation from [he mean t\(a nunnal
vuruuuK is . find the probahEiiy of obtaining m Jem*
J UKCCW*.
7+ {j) A firm manufacture* two items A and it purchase,' c*\<ini which ore then raachioed. bored and pK>tahcd Castings lot ucms A and B cort R%b 3 hikI Rs. 4 rach and Jiie ld *l Rs. 6 und R* nesi>.\:livd> Running emit of ihew m3chia irtRt, 20, Kv Hand R*. 17.50 per htmr rt5*fKciiveTyr FtmMilate the pnubkro so that the product mil oiuiOhzb Ihe profit The capscihti of the michmca an
item A Item B
Machining 15 per hrT 40 p-r hr.
Bnrinf JS per hrT 35 per hr.
Pnliihin* 35 pci fir> 25 per
(bj Using Graphic*! meitod, solve the following jtfutrtem t Minimi#: Z = 20* + 10y subject to i + Jjr < 40 3j + jr a 30 Ax + ly 60 jrT rv 0.
S. {ii Use Simplex method to solve ihe following proNem : Man fnizc Z=i| + j2 + 3jj suh to 3j| + 2ij + JTj 3
2i, + Xj + 2ij 2 j,r J3. ij 0.
n {t>) StiJve ihe following LPP by Dual simptek method:
M i nim&ze Z = 2x, + 2ji; + Axj sub io 2jt, + 3j2 + Jjfj 2
/ 3*1 + J4 + txj 3
' jt| + 4jcj+ 5
JTt* -Ij* Jfj S 0.
A39760ftXlV1ll5 3
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| Earning: Approval pending. |
