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-oll No....
iotal No. of Questions: 10I
PaperID [PHL22]
(Please filt this Paper ID in OMR Sheet) B.PharmacY(Sem.'2"o) ADVAN(:ED MATHEMATICS^ (PHM.
Timc : 03l{ours Instruction to Candidates:
- Section- A is CornPulsorY.
- Attempt any^ F'our questionsfrom Section- B.
- Attemptany'fhrec qtrestionsfrom Section- C'
8t)
Scction- A
( 1 5 x 2 = 3 0 )
Defineorcleranddegreeof a differentialequation.
Which6f thefollou'in-tdifferentialequationis linear?
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
equation^.^ aoa4+a,ft+oryd ' ) ,^ d y^ = 0 areof thetypea t iP. Thenwriteitsn^ r^ t t ,^^ r - - , - ^
qeneralsolution.
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b)
c) d)
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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.
- Writc probabilitydistributionf'unctionof Poissondistribution.^ ',.- m) Dcfinc^ shiftingproperiyof Laplacctransform'
n) IrLL(r)l=l(s),rhenwrite4+P
,_,['^ I
o) EvaluareL L(r.+3f I
Section- B
(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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