Rajiv Gandhi Proudyogiki Vishwavidyalaya 2010 B.E __m3(301n) - Question Paper
Tt*(;>l Nii v>' Ouestums : 10 | | Iwul No. uf I'lgt-s : 4
Moll No.
K tHiiul ScimsUr) KWMIN VHON, l>ifn il
(New Scheme)
(Common lor all Hrum'he*)
I NGIM I UINC. MAIIU MAI ICS III
/ twit* Ihrte Hours
Shiximum Mi irks : 100
Mmimum /Um Marks : 55
\k : l u vurNtum pa pet in divided inlo live Units. 1 ach I mt carrifN an internal choicc Attempt one question from cacti Unit All queMionv carry equal maiks.
I nit I _
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i V) Show that the function u e~ Mn (j:2 - y2) is hJiimmic. l ind the conjugate function V ami express .. * iv as an analytic function of z. ib) \ ind the bilinear transformation which maps the point* > - (I IJ onto w i, 0, .
Op
1 (a) L*e Cauchy integral formula to evaluate
f MltJI Z + .
where C is (he circle U i * 3.
(b) Use residue calculus 10 evaluate the imegiul I
f:
S 4 sin ft 9 T O
i a I
Unit II
3- U) (i) Prove with the usual notation* that
(E1'2 + E~ (l + A)W2 + A
* (a) Apply Lagrange's formula to find f(\5), if:
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M Express y - 3r* + r2 + i + 1 in factorial (unction* and hence whow tlui A*> 18. (b) L'*ing Newton's divided difference formula, find f (10) from ihe following data : | ||||||||||||
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Or | ||||||||||||||
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(b) Find the real root of the equation xA - x - 10 * 0 correct to three places of decimal by using Newton-Raph*ons method.
Unit III
5. (a) rind the cube root of 15 correct lo four significant figures by iterative method.
) * I M*<Nt
VM Solve iHr following cgummm >n tl* aibcmm f I mmi|> tTiiinguliiftftitUm (1 i >) method 2a - 3i * I0r - .1
i i 4i : r n 5.i + t\ * - *7
* Apply Uunc Kuu mhmIukI fl otinh order) to f*W
approximate value of v when x 0-2. given lht
(y
d\
\ * v and v - I when - 0
(M Mum the equation
v-h in(jt? + r H))
over the Hjujr< with Mtlo a 0 ~ y, x * 3 * y wuh u (i. v) -* 0 on the bmmdur> imd mesh length I I nH-|\
It) I ving Sitnplo mcitvnl mKt ihe I HP M.i\<nn/c ' c - 3.t | 2 vj
Subject t >} .I} S * ........ (I)
, *:<? ........(2)
and vj. t? * 0
lh) Jwrfw the minima! alignment problem :
Mc*
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Jo b |
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*i U) Solve ihc folKwing I. P P. guphicalK Mawimitc .
ft T 0
Ml
Subject 10 the constraints
* + > s I 3* + 3y *9
andjr.y i 0.
of the foflovtntf
Supply 30 40 53
(b) Find the optimal solution transportation problem :
Pi i P3 04
S( 23
27 17
28 35
S2 12
Demand by 22
25
UnitV
9. (a) Obtain the steady state equations for the queuing model (M|M|!):((FCFS).
(b) The mean life time of sample of H)0 fluojescent tight bulb* yodtictu by is uompuied to be 1570
hours with a ttandard deviation of 120 hour* The company claim*, that the average life of the bulb* produced by it is 1600 hours. Using the level of wgmficance of 0 05, is the claim acceptable 7 Or
10. (a) We have three samples A. B. C from normal populations with equal variances. Analyte the population means are equal at 5% level:
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(b) Write short notes on the following <) Hiciorial deWgn (0) 'UfliK'hl low function 12.71* |
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Attachment: |
| Earning: Approval pending. |
