64 m kj izns'k jktf"kZ V.Mu eqDr fo'ofo|ky;] bykgkckn

37
95
m kj izns’k jktf"kZ V.Mu eqDr fo’ofo|ky;] bykgkckn
fo’k; % xf.kr
Subject : Mathematics
dkslZ “kh’kZd % Mathematical Modelhing
Course Title : Mathematical Modelhing
vf/kU;kl (Assignment) 2012-2013
Lukrd dyk dk;ZØe
Under Graduate Art Programme
Section - A
[k.M & d
fo’k; dksM% ;w0th0,e0,e0
Subject Code : UGMM
dkslZ dksM % ;w0th0,e0,e0-14
Course Code : UGMM-14
vf/kdre vad % 30
Maximum Marks:30
vf/kdre vad % 18
Max. Marks: 18
uksV % nhkZ mRrjh; iz”uA vius iz”uksa ds mRrj 800 ls 1000 “kCnksa esa fy[ksaA lHkh
iz”u vfuok;Z gSA
Note : Long Answer Questions. Answer should be given in 800 to 1000 words.
Answer all questions.
1(a) What do you mean by a methematical model 3
xf.krh; fun’kZ ls vki D;k le>rs gS\
(b) Why is it necessary to formulate the mathematical model 3
xf.krh; fun’kZ ds lw=.k dh D;k vko”;drk gS\
2(a) If the population of a country is doubled in 50 years, in how many years will
it be trepled, given that rate of increase is proportaional to the number of
inhobitants. 3
fdlh ns”k dh tula[;k 50 o"kksZ esa nqxquh gks tkrh gS] rks fdrus o"kksZ esa ;g
rhu xquh gks tk;xh] tgk¡ tula[;k o`f)nj jgus okyksa dh la[;k ds vuqikfrd
gSA
(b) A body is heated to 110 o C and placed in air at 10 o C. After one hour, its
temperature is 60 o C, How much time will be required for it to get the
temperature of 30 o C. 3
3(a)
(b)
fdlh oLrq dks 110 o C rd xeZdj 10 o C rkieku ds ok;q ds ek/;e esa j[kk
x;kA ,d kaVs ckn bldk 60 o C rkieku gks x;kA fdrus le; ckn bldk
rkieku 30 o C gks tk;sxkA
A particle of mass m is projected vertically under gravity, the resistance of
the air being mk times the velocity. show that greatest height attained by the
2
V
particle is [ l - log(1 + l)]
where V is the termial velocity of the
g
particle and lV
its initial velocity. 3
;fn m Hkkj dk dksbZ d.k] tgka ok;q dk izfrjks/k osx dk mk xq.kk gS]
xq:Rokd"kZ.k ls m/okZ/kj fn”kk esa NksM+k tkrk gS rks n”kkZb, fd d.k }kjk izkIr
2
V
dh xbZ egRre ÅWpkbZ [ l - log(1 + l)]
gS] tgka V d.k dk lhekUr osx
g
rFkk l V mldk izkjfEHkd osx gSA
A particls falls down in the air whose resistance varies as the squears of the
velocity. show that velocity of the particle at any time t is V tanh( gt / V )
where V is its terminal velocity. 3
ok;q esa dksbZ d.k uhps dh vksj fxj jgk gS ;fn ok;q dk izfrjks/k osx ds oxZ ds
vuqlkj ifjofrZr gks jgk gS] rks n”kkZb, fd fdlh le; t esa d.k dk osx
V tanh( gt / V ) gS] tgka V d.k dk lhekUr osx gSA
Section - B
[k.M & [k
vf/kdre vad % 12
Max. Marks: 12
uksV % ykq mRrjh; iz”uA vius iz”uksa ds mRrj 200 ls 300 “kCnksa esa fy[ksaA lHkh
iz”u vfuok;Z gSA
Note : Short Answer Questions. Answer should be given in 200 to 300 words.
Answer
all questions.
4 What do you mean by blood flow and oxygen transfer Define viscosity and
relate it to blood flow and oxygen transfer. 3
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ifjHkkf"kr djrs gq, blls rFkk vkDlhtu LFkkukUrj.k vkSj jDr izokg ls
vUrlZEcU/k LFkkfir dhft,A