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1 (ISO/IEC Certiied) Importt Istructios to emiers: ) Te swers sould be emied b ke words d ot s word-to-word s gie i te model swer sceme. ) Te model swer d te swer writte b cdidte m r but te emier m tr to ssess te uderstdig leel o te cdidte. ) Te lguge errors suc s grmmticl, spellig errors sould ot be gie more Importce.(Not pplicble or subject Eglis d Commuictio Skills) ) Wile ssessig igures, emier m gie credit or pricipl compoets idicted i te igure. Te igures drw b cdidte d model swer m r. Te emier m gie credit or equilet igure drw. 5) Credits m be gie step wise or umericl problems. I some cses, te ssumed costt swers d model swer. I cse o some questios credit m be gie b judgmet o prt o emier o 7) For progrmmig lguge ppers, credit m be gie to oter progrm bsed o equilet cocept. Attempt TEN o te ollowig: Fid d i i i 6 i i 6 6 i Epress i i ib orm i i i i i i i i i i i
2 MAHARASHTRA STATE BOARD OF TECHNICAL EDUCATION (ISO/IEC Certiied) b) c) As d) As e) As i i I 5 d, id t t d t t t t 5, I log, proe tt m m. log m log log m m log m log log m. m Elute:
3 (ISO/IEC Certiied) t t t t t t t t Elute: Elute: e e e Fid, i log t d log t d sec OR t d t d t d sec sec d d t d t d cot sec cot sec d d
4 (ISO/IEC Certiied) OR log t d t sec cos d si cos cosec sec d Fid,i d si, cos si, cos d cos d d d si d si d d cos d d si cos si d cot Dieretite cos si Let cos si d cos cos Sow tt tere eist root o te equtio 8 betwee d. Let 8 5 8
5 (ISO/IEC Certiied) root lies betwee d Sole te ollowig equtios b usig Guss-Seidl metod ol irst itertio z 9; z ; z 9 z z z Iitil pproimtios : z.9,.9, z.67 Attempt FOUR o te ollowig: Simpli usig De-Moier's teorem 6 cos i si cos 5 i si 5 cos8 i si8 6 cos i si cos 5 i si 5 cos8 i si8 6 cos isi cos isi = 8 cos i si cos cos cos i si i si isi Fid cube root o uit. w w Put w z z i, r z
6 (ISO/IEC Certiied) t Geerl polr orm is, z r cos isi w cos isi w cos isi w cos isi ;,, we w cos isi we w cos isi i we w cos isi i I i si A ib proe tt cos B si B i si A ib i siacos ib cos Asi ib si A cos B i cos Asi B si A cos B, cos Asi B si Acos B cos Asi B cos B si B cos B si B si A cos A Proe tt cos isi cos isi.cos.cos cos isi cos isi cos icos si cos icos si cos cos isi cos isi
7 (ISO/IEC Certiied) cos cos isi cos isi.cos. cos.cos.cos 5 5 I d t sow tt t 5 5 d t t 5 t t b I log, sow tt b b b b log log b b log. b b b log log b b b b b b b b
8 (ISO/IEC Certiied) b b log b b b b b b log b b b b b OR b log log b log. b log log log b b b b b b b b b b b b b b b b Attempt FOUR o te ollowig: I log sow tt log log log log log log. log I, te sow tt
9 (ISO/IEC Certiied), = OR LHS = = = RHS = = + Elute sec Elute: t sec t
10 (ISO/IEC Certiied) t t t t t t t t t 6 Elute 6 log log log log 5 Elute 5 5 log log Put 5 s 5, log 5 log log 5
11 (ISO/IEC Certiied) log 5 log 5 log log e log e Attempt FOUR o te ollowig: Usig irst pricipl id te deritie o si d si si d cos si d cos si d si cos. d cos d cos d
12 (ISO/IEC Certiied) Fid i (cos si ) d si cos d (cos si ), si cos d d si cos si cos d cos si cos si d d d d si d cos d t cos si Fid i si d si cos si si si cos cos si si si d OR si cos si si cos cos si si si cos si si
13 (ISO/IEC Certiied) d I e log, proe tt d log e loge log log d d log d log log OR d log d log log log d log d log log log log d log d log log log d log d log log I si, id. d si log log log.log si log..cos log si. d si log cot log si d log si log cot log si d I, id t te poit,.
14 (ISO/IEC Certiied) d d d d d d, d, Attempt FOUR o te ollowig: Elute = = e = e e
15 (ISO/IEC Certiied) cos cos Elute cos cos cos cos put, s, cos cos cos cos. si si si si si si. si si Usig Bisectio metod id te pproimte root o Tree itertios ol. Let root lies i, b <
16 (ISO/IEC Certiied) te root lies i (.5,) b OR te root lies i (.75,) b Let root lies i, b b Usig Regul-Flsi metod, Fid pproimte root o Let 9 9 Tree itertios ol 9 te root lies i,.7 root lies i.9, b b () ( 9).9 b 9
17 (ISO/IEC Certiied). te root lies i.9, OR.9.. Let 9 9 te root lies i,.9 Itertios b b b b b I II III Sole b Newto-Rpso metod Tree iterios ol Let. 8 ' ' Iitil root ' ' =.57.7
18 (ISO/IEC Certiied) '.695 OR Let, 8 ' ' Iitil root ' ',, Fid pproimte lue o b usig Newto-Rpso metod Tree itertios ol Let 6 5 5
19 (ISO/IEC Certiied) ' Iitil root =5 ' OR Let ' ' = ' ' Iitil root = 5 i Attempt FOUR o te ollowig: Dieretite cos wit respect to sec Let u cos d sec Put si si
20 (ISO/IEC Certiied) u u u u cos si si cos si cos cos si cos cos u u du d du d si sec sec si sec cos sec cos sec sec si d d du du d d d d du d OR Let u cos d sec
21 (ISO/IEC Certiied) Put cos cos u u u u cos cos cos cos cos si cos si cos cos u u du d du d cos sec sec cos sec si sec sec si cosec sec s ec d d du d cos du d d d
22 (ISO/IEC Certiied) du d I Acos log d Bsi log, proe tt d d Acos log Bsi log si log cos log A B d Asi log Bcos log d cos log A B si log d d d d Acos log Bsi log d d d d d d d d Sole b Guss-eitio metod z, z, z z z z z 6 z 5 z 8 5 5z 7 5z 8 8 z d 9 6z z 7 5z
23 (ISO/IEC Certiied) Note: I te boe solutio, irst is eited d te z is eited to id te lue o irst. I i cse te problem is soled b eitio o oter ukow i. e., eiter or z, pproprite mrks to be gie s per boe sceme o mrkig. Sole b Jcobi's metod z, z, z 5 Tree itertios ol z z z 5 Strtig wit z z...5 z z Sole b usig Guss-Seidel metod 6 z 5, 8 z 55, 5 z 65 Two itertios ol 5 z 6 55 z 8 z 65 5 Strtig wit z
24 (ISO/IEC Certiied) z z Sole b Guss-Seidl metod: 7 z, 5 z 8, 6z Two itertios ol 8 z 5 z 7 z 6 Strtig wit z z z Importt Note I te solutio o te questio pper, wereer possible ll te possible ltertie metods o solutio re gie or te ske o coeiece. Still studet m ollow metod oter t te gie erei. I suc cse, irst see weter te metod lls witi te scope o te curriculum, d te ol gie pproprite mrks i ccordce wit te sceme o mrkig.
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