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64 m kj izns'k jktf"kZ V.Mu eqDr fo'ofo|ky;] bykgkckn
64 m kj izns'k jktf"kZ V.Mu eqDr fo'ofo|ky;] bykgkckn 64 m kj izns'k jktf"kZ V.Mu eqDr fo'ofo|ky;] bykgkckn
36 94 m kj izns’k jktf"kZ V.Mu eqDr fo’ofo|ky;] bykgkckn fo’k; % xf.kr Subject : Mathematics dkslZ “kh’kZd % Discrete Mathematics Course Title : Discrete Mathematics 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,e0-13 Course Code : UGMM-13 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) Construct truth table of followings 3 mudh lR;rk dk pkVZ cuk;saA (i) ( P Ù q ) Ú ( q Ù R) Ú (P Ù ~ q ) Ú (P~ Ù q ) (ii) (~P Ù (~ q Ù R)) Ú ( q Ù R) Ú (P Ù R) (b) Show that (~P Ù Q) Û (~P Ù ~Q) is a tautology 3 fn[kk;sa fd (~P Ù Q) Û (~P Ù ~Q) ,d VkWVksyksth gSA 2(a) Define the terms: (i) min term and max term (ii) disjuction (iii) Biconditional ifjHkkf"kr djsaA (i) U;wure ,oa vf/kdre in (ii) ckbZ&dUMhluy 3 n n-1 n-1 (b) Show that Cr = Cr- 1+ Cr 3 fn[kk;s 3(a) Define and example of the following terms (i) Generating function 3 (ii) Diagraph (iii) Planar and non-planar graph. mnkgj.k ds lkFk ifjHkkf"kr djsaA (i) tsusjsfVax Qyu (ii) MkbZxzkQj (iii) /kzqoh; ,oa v/kzqoh; xzkQ (b) Define Hamistonian graph and give an example. 3 gSfeyVksfu;u xzkQ dk mnkgj.k ds lkFk ifjHkkf"kr djsaA 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 In how many ways n letters can be kept in m envelopes. 3 n i=] m fyQkQksa esa fdrus rjhdksa ls j[kk tk ldrk gSA 5 Define Boolean algebra by addition and multiplication. 3 ;ksx ,oa xq.ku ds lkis{k cqfy;u vYtscjk dks ifjHkkf’kr djsaA 6 Prove that the vertex connectivity of any graph G can never exceed the edge connectivity of G. 3 fdlh xzkQ G ds HkjVsDl dHkh Hkh mlds fdukjksa ls vf/kd ugha gks ldrk gSA fl) djsaA 7 Write one of the requence formula and solve it. 3 ,d jsDjsUl lw= dks fy[ksa rFkk gy djsaA
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 jDr izokg vkSj vkDlhtu LFkkukUrj.k ls vki D;k le>rs gS\ “;kurk ifjHkkf"kr djrs gq, blls rFkk vkDlhtu LFkkukUrj.k vkSj jDr izokg ls vUrlZEcU/k LFkkfir dhft,A
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36<br />
94<br />
m <strong>kj</strong> izns’k jktf"<strong>kZ</strong> V.<strong>Mu</strong> <strong>eqDr</strong> fo’ofo|ky;] <strong>bykgkckn</strong><br />
fo’k; % xf.kr<br />
Subject : Mathematics<br />
dkslZ “kh’<strong>kZ</strong>d % Discrete Mathematics<br />
Course Title : Discrete Mathematics<br />
vf/kU;kl (Assignment) 2012-2013<br />
Lukrd dyk dk;ZØe<br />
Under Graduate Art Programme<br />
Section - A<br />
[k.M & d<br />
fo’k; dksM% ;w0th0,e0,e0<br />
Subject Code : UGMM<br />
dkslZ dksM % ;w0th0,e0,e0-13<br />
Course Code : UGMM-13<br />
vf/kdre vad % 30<br />
Maximum Marks:30<br />
vf/kdre vad % 18<br />
Max. Marks: 18<br />
uksV % nh<strong>kZ</strong> mRrjh; iz”uA vius iz”uksa ds mRrj 800 ls 1000 “kCnksa esa fy[ksaA lHkh<br />
iz”u vfuok;Z gSA<br />
Note : Long Answer Questions. Answer should be given in 800 to 1000 words.<br />
Answer all questions.<br />
1(a) Construct truth table of followings 3<br />
mudh lR;rk dk pkVZ cuk;saA<br />
(i) ( P Ù q ) Ú ( q Ù R)<br />
Ú (P Ù ~ q ) Ú (P~ Ù q )<br />
(ii) (~P Ù (~ q Ù R)) Ú ( q Ù R) Ú (P Ù R)<br />
(b) Show that (~P Ù Q) Û (~P Ù ~Q) is a tautology 3<br />
fn[kk;sa fd (~P Ù Q) Û (~P Ù ~Q) ,d VkWVksyksth gSA<br />
2(a) Define the terms: (i) min term and max term (ii) disjuction (iii) Biconditional<br />
ifjHkkf"kr djsaA (i) U;wure ,oa vf/kdre in (ii) ckbZ&dUMhluy 3<br />
n n-1 n-1<br />
(b) Show that Cr<br />
= Cr-<br />
1+<br />
Cr<br />
3<br />
fn[kk;s<br />
3(a) Define and example of the following terms (i) Generating function 3<br />
(ii) Diagraph (iii) Planar and non-planar graph.<br />
mnkgj.k ds lkFk ifjHkkf"kr djsaA<br />
(i) tsusjsfVax Qyu (ii) MkbZxzkQj (iii) /kzqoh; ,oa v/kzqoh; xzkQ<br />
(b) Define Hamistonian graph and give an example. 3<br />
gSfeyVksfu;u xzkQ dk mnkgj.k ds lkFk ifjHkkf"kr djsaA<br />
Section - B<br />
[k.M & [k<br />
vf/kdre vad % 12<br />
Max. Marks: 12<br />
uksV % ykq mRrjh; iz”uA vius iz”uksa ds mRrj 200 ls 300 “kCnksa esa fy[ksaA lHkh<br />
iz”u vfuok;Z gSA<br />
Note : Short Answer Questions. Answer should be given in 200 to 300 words.<br />
Answer<br />
all questions.<br />
4 In how many ways n letters can be kept in m envelopes. 3<br />
n i=] m fyQkQksa esa fdrus rjhdksa ls j[kk tk ldrk gSA<br />
5 Define Boolean algebra by addition and multiplication. 3<br />
;ksx ,oa xq.ku ds lkis{k cqfy;u vYtscjk dks ifjHkkf’kr djsaA<br />
6 Prove that the vertex connectivity of any graph G can never exceed the edge<br />
connectivity of G. 3<br />
fdlh xzkQ G ds H<strong>kj</strong>VsDl dHkh Hkh mlds fdu<strong>kj</strong>ksa ls vf/kd ugha gks ldrk gSA<br />
fl) djsaA<br />
7 Write one of the requence formula and solve it. 3<br />
,d jsDjsUl lw= dks fy[ksa rFkk gy djsaA
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