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<div><br /></div><div>method f variation of parameters, Stoke’s theorem, vector and probability. Cayley - Hamilton theorem, polynomial theorem, differential equation, equational problem.</div><div><br /></div><div>, , , </div><div><br /></div>
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-oll No....
iotal No. of Questions: 10I
(Please filt this Paper ID in OMR Sheet) B.PharmacY(Sem.'2"o) ADVAN(:ED MATHEMATICS^ (PHM.
Timc : 03l{ours Instruction to Candidates:
dt (i)' d x (^) $+ fiV*ry = sinx
clv (ii) (^) Y-T+ x= u ax
. d v ( i i i ) ( l + ) ' ) A + s r n x = x
(iv) ?+^ tl= r,^. dy^ ,:r^ x dx'^ r'++(lax^ -rx)2)'=sinx * e'. Detine an^ exactdifferentialequation. If tirerootsof theauxiliaryequationcoffesponclingto thegivendifferential
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b)
c) d)
J-91s6 :'**-^ PTO.
d ' t ' ^ d t ' , A + r - ' e) Calculateparticularintegralof }j-3 dx+6v= 0'
0 In rollinga dicc.whatis the^ probabilityof obtaininga sumnot^ exceeding 1 0. g) For eventsA and ll in SamplespaceS P(AUB)_..... h) Defile Vleanandvariance.What^ propertiesof a probabilitydistribution do they charucterize? i) Why areintervalestimatesin mostcasesmoreusefulthanpointestimates. j) (^) Defineieastsquareprinciple. k) DefineBaye'stheorem.
o) EvaluareL L(r.+3f I
(4x5=20)
Q2) Solve (,r73+-v)d:;*7(x21'21a+yo)dy= Q
Q3l Solvc-{y(t*r'')#=l
t - t ' S e1) Evaluarer. (l (^). ixr.l- t
QS) Amanuf'acturcrknowsthat the^ condensorshe makescontainson the average onepercenrclefectives..He packsthemin boxesof 100.What is theprobability that a bcx pickedat rarrdomwill contaiu3 or morefaulty^ condensors.
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