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Test Paper - Advanced Maths - Punjab Technical University - Bachelor of Pharmacy - 2nd Semester, Study notes of Pharmacy

<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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2010/2011

Uploaded on 09/24/2011

muhammad
muhammad 🇮🇳

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bg1
-oll No....
iotal No.
of Questions
: 10I
Paper
ID [PHL22]
(Please
filt this Paper ID in OMR Sheet)
B.PharmacY
(Sem.'2"o)
ADVAN(:ED MATHEMATICS (PHM .
Timc
: 03l{ours
Instruction
to Candidates:
1) Section
- A is CornPulsorY.
2) Attempt
any
F'our
questions
from Section
- B.
3) Attempt
any'fhrec qtrestions
from
Section
- C'
8t)
Scction
- A
(15x2=30)
Define
orcler
and
degree
of a differential
equation.
Which
6f
the
follou'in-t
differential
equation
is
linear?
dt
(i) $+
fiV*ry =
sinx
'dx
clv
(ii) Y-T+
x= u
ax
.dv
(iii) (l+)')A+srnx=x
tl=
r, . dy ,:r x
(iv)
?+ r'++(l -r
x)2
)'=
sin
x
* e'.
dx' ax
Detine
an exact
differential
equation.
If tire
roots
of
the
auxiliary
equation
coffesponcling
to
the
given
differential
. d'), dy n r tt, ^ r--,-^
equation
aoa4+a,ft+ory =
0 are of
the
type
a t iP. Then
write
its
qeneral
solution.
,".r\
b)
c)
d)
J-91s6 :'**- PTO.
pf3

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Download Test Paper - Advanced Maths - Punjab Technical University - Bachelor of Pharmacy - 2nd Semester and more Study notes Pharmacy in PDF only on Docsity!

-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:

  1. Section- A is CornPulsorY.
  2. Attempt any^ F'our questionsfrom Section- B.
  3. 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.

,".r
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.

  1. 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.

J-gi ltt