Multiple Choice Questions

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1 B S. M. CHINCHOLE Multpl Co Qustons L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag

2 B S. M. CHINCHOLE L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag

3 B S. M. CHINCHOLE L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag

4 B S. M. CHINCHOLE L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag 4

5 B S. M. CHINCHOLE L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag 5

6 B S. M. CHINCHOLE L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag 6

7 B S. M. CHINCHOLE L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag 7

8 B S. M. CHINCHOLE 4. T ollowng n data ponts, (, ), (, ),...,( n, n) ar gvn. For ondutng quadrat spln ntrpolaton t -data nds to b quall spad n asndng or dsndng ordr ntgrs postv 5. In ub spln ntrpolaton, t rst drvatvs o t splns ar ontnuous at t ntror data ponts t sond drvatvs o t splns ar ontnuous at t ntror data ponts t rst and t sond drvatvs o t splns ar ontnuous at t ntror data ponts t trd drvatvs o t splns ar ontnuous at t ntror data ponts L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag 8

9 B S. M. CHINCHOLE 6. T ollowng nomplt vs. data s gvn ???????? T data s t b quadrat spln ntrpolants gvn b a, 4 9, 4 b d, , 6 7 wr a, b,, and d, ar onstants. T valu o s most narl T ollowng nomplt vs. data s gvn ???????? T data s t b quadrat spln ntrpolants gvn b a, 4 9, 4 b d, 4 6 g, 6 7 wr a, b,, d,,, and g ar onstants. T valu o d/ at =.6 s most narl L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag 9

10 NET/SET PREPARATION MCQ ON NUMERICAL ANALYSIS B S. M. CHINCHOLE 8. T ollowng nomplt vs. data s gvn ???????? T data s t b quadrat spln ntrpolants gvn b a,, 4 9, 4 b d, , 6 7 wr a, b,, d ar onstants. Wat s t valu o.5? A robot nds to ollow a pat tat passs troug s ponts as sown n t gur. To nd t sortst pat tat s also smoot ou would rommnd w o t ollowng? Pass a t ordr polnomal troug t data. Pass lnar splns troug t data Pass quadrat splns troug t data Rgrss t data to a sond ordr polnomal Pat o a Robot L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag 0

11 B S. M. CHINCHOLE 0. T two-sgmnt trapzodal rul o ntgraton s at or ntgratng at most ordr polnomals. rst sond trd ourt. T valu o 0. b usng t on-sgmnt trapzodal rul s most narl T valu o 0. b usng t tr-sgmnt trapzodal rul s most narl T vlot o a bod s gvn b v( t) t, t 5 5t, 5 t 4 wr t s gvn n sonds, and v s gvn n m/s. Us t two-sgmnt Trapzodal Rul to nd t dstan ovrd b t bod rom t= to t=9 sonds m 09.7 m 60.9 m m 4. T sadd ara sows a plot o land avalabl or sal. T numbrs ar gvn n mtrs masurd rom t orgn. Your bst stmat o t ara o t land n squar mtrs s most narl L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag

12 B S. M. CHINCHOLE T ollowng data o t vlot o a bod as a unton o tm s gvn as ollows. Tm (s) Vlot (m/s) T dstan n mtrs ovrd b t bod rom t= s to t=8 s alulatd usng usng Trapzodal Rul wt unqual sgmnts most narl s T gst ordr o polnomal ntgrand or w Smpson s / rul o ntgraton s at s rst sond trd ourt 7. T valu o 0. b usng two-sgmnt Smpson's / rul s most narl L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag

13 B S. M. CHINCHOLE T valu o 0. b usng our-sgmnt Smpson's / rul s most narl T vlot o a bod s gvn b v( t) t, t 5 5t, 5 t 4 wr t s gvn n sonds, and v s gvn n m/s. Usng two-sgmnt Smpson's / rul, t dstan ovrd n mtrs b t bod rom t= to t=9 sonds most narl s ( ) 40. T valu o b usng two-sgmnt Smpson s / rul s stmatd as T stmat o t sam ntgral usng our-sgmnt Smpson s / rul most narl s / [(7)-()+(5)] 70.9/ + 8/ [(7)-()+(5)] / [(7)+(5)] 70.9/ + 8/ [(7)+(5)] 4. T ollowng data o t vlot o a bod s gvn as a unton o tm. Tm (s) Vlot (m/s) L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag

14 B S. M. CHINCHOLE T bst stmat o t dstan n mtrs ovrd b t bod rom t=4 to t=5 usng ombnd Smpson s / rd rul and t trapzodal rul would b I I n s t valu o ntgral usng n-sgmnt Trapzodal rul, a bttr stmat o t ntgral an b ound usng Rardson s trapolaton as b a I I n n I I n n I 5 I n n I n I n I n I I n n 4.T stmat o an ntgral o 9 s gvn as usng -sgmnt Trapzodal rul. Gvn (7)=0.7, ()=45.5, and (4)=8., t valu o t ntgral usng -sgmnt Trapzodal rul would most narl b b a 44. T valu o an ntgral gvn usng,, and 4 sgmnts Trapzodal rul s gvn as 5.460,.7708, and.756, rsptvl. T bst stmat o t ntgral ou an nd usng Rombrg ntgraton s most narl.55.8 L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag 4

15 B S. M. CHINCHOLE Wtout usng t ormula or on-sgmnt Trapzodal rul or stmatng t tru rror, an b ound drtl as wll as atl b usng t ormula a b E t E t b a 5 5 " a b, or 46. For, t tru rror, n on-sgmnt Trapzodal rul s gvn b E t b a b a " a b,. 7. E t 0. T valu o or t ntgral.5 s most narl Gvn t vlot vs. tm data or a bod t(s) m/ s T bst stmat or dstan ovrd btwn s and 0s b usng Rombrg rul basd on Trapzodal rul rsults would b.456 m m 7.5 m 8.50 m L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag 5

16 B S. M. CHINCHOLE ( ) s atl (.5 7.5).5 (.5 7.5) 5 (5 5) 5 (.5 7.5) ( ) 49. For a dnt ntgral o an trd ordr polnomal, t two-pont Gauss quadratur rul wll gv t sam rsults as t -sgmnt trapzodal rul -sgmnt trapzodal rul -sgmnt trapzodal rul Smpson's / rul 50. T valu o b usng t two-pont Gauss quadratur rul s most narl A sntst uss t on-pont Gauss quadratur rul basd on gttng at rsults o ntgraton or untons ()= and. T on-pont Gauss quadratur rul appromaton or b a. 0. ( a) ( b) b a ( ) s a b ( b a) b a b a ( b a) ( a) b a b a b a 5. A sntst dvlops an appromat ormula or ntgraton as b a ) ( ), ( L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag 6

17 B S. M. CHINCHOLE wr a b. T valus o and ar ound b assumng tat t ormula s at or t untons o t orm a 0 + a polnomal. Tn t rsultng ormula would tror b at or ntgratng ( ) ( ) 5 ( ) 5 5. You ar askd to stmat t watr low rat n a pp o radus m at a rmot ara loaton wt a ars nvronmnt. You alrad know tat vlot vars along t radal loaton, but ou do not know ow t vars. T low rat Q s gvn b To sav mon, ou ar allowd to put onl two vlot probs (ts probs snd t data to t ntral o n Nw York, NY va satllt) n t pp. Radal loaton, r s masurd rom t ntr o t pp, tat s r=0 s t ntr o t pp and r=m s t pp radus. T radal loatons ou would suggst or t two vlot probs or t most aurat alulaton o t low rat ar 0,, 0, 0.4,.58 d 54. To solv t ordnar drntal quaton 5 sn, 0 5, b Eulr s mtod, ou nd to rwrt t quaton as 55. Gvn d 5 and usng a stp sz o =0., t valu o (0.9) usng Eulr s mtod s most narl ( ) Q d d 0 rvdr sn 5 d d, 0 5 sn 5, os sn, 0 5 sn,, L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag 7

18 B S. M. CHINCHOLE Gvn d 0., 0. 5 and usng a stp sz o =0., t bst stmat o d/(0.9) usng Eulr s mtod s most narl s T vlot (m/s) o a bod s gvn as a unton o tm (sonds) b v(t)=00 ln(+t) -t, t 0 Usng Eulr s mtod wt a stp sz o 5 sonds, t dstan n mtrs travld b t bod rom t= to t= sonds s most narl Eulr s mtod an b drvd b usng t rst two trms o t Talor srs o wrtng t valu o, tat s t valu o at, n trms o and all t drvatvs o at. I, t plt prsson or t rst tr trms o t Talor srs ar osn or t ordnar drntal quaton d 5, 0 7 would b A omd vtm s ound at 6:00PM n an o buldng tat s mantand at 7 F. Wn t vtm was ound, s bod tmpratur was at 85 F. Tr ours latr at 9:00PM, s bod tmpratur was rordd at 78 F. Assum t tmpratur o t bod at t tm o dat s t normal uman bod tmpratur o 98.6 F. L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag 8

19 B S. M. CHINCHOLE T govrnng quaton or t tmpratur θ o t bod s d k( a ) wr = tmpratur o t bod, F θ a = ambnt tmpratur, F t = tm, ours k = onstant basd on trmal proprts o t bod and ar. T stmatd tm o dat most narl s : PM : PM 4:4 PM 5: PM 60. To solv t ordnar drntal quaton b t Rung-Kutta nd ordr mtod, ou nd to rwrt t quaton as d sn, 0 5 d sn, 0 5 d d os sn, 0 5, 0 5 d sn, Gvn d 5 sn, 0. 5 and usng a stp sz o =0., t valu o (0.9) usng t Rung-Kutta nd ordr Hun's mtod s most narl Gvn d 5 0., 0. 5, L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag 9

20 B S. M. CHINCHOLE and usng a stp sz o =0., t bst stmat o d/(0.9) usng t Rung-Kutta nd ordr mdpont-mtod most narl s T vlot (m/s) o a bod s gvn as a unton o tm (sonds) b Usng t Rung-Kutta nd ordr Ralston mtod wt a stp sz o 5 sonds, t dstan n mtrs travld b t bod rom t= to t= sonds s stmatd most narl s t 00 ln t t, t T Rung-Kutta nd ordr mtod an b drvd b usng t rst tr trms o t Talor srs o wrtng t valu o + (tat s t valu o at + ) n trms o (tat s t valu o at ) and all t drvatvs o at. I = +-, t plt prsson or + t rst tr trms o t Talor srs ar osn or solvng t ordnar drntal quaton d 5, 0 7 would b A spral ball s takn out o a urna at 00K and s allowd to ool n ar. Gvn t ollowng, radus o ball = m sp at o ball = 40 J/(kg-K) dnst o ball = 7800 kg/m^ onvton ont = 50 J/s-m^-K T ordnar drntal quaton s gvn or t tmpratur, o t ball d L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag 0

21 B S. M. CHINCHOLE onl radaton s aountd or. T ordnar drntal quaton onvton s aountd or n adon to radaton s d d d d d 66. To solv t ordnar drntal quaton sn, 0 5, b Rung-Kutta 4 t ordr mtod, ou nd to rwrt t quaton as d d d d sn, 0 5 sn, 0 5 os sn, 0 5, Gvn d 5 sn, 0. 5 and usng a stp sz o 0., t valu o 0.9 usng Rung-Kutta 4 t ordr mtod s most narl Gvn d, 0. 5, and usng a stp sz o 0., t bst stmat o Rung-Kutta 4t ordr mtod s most narl d L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag

22 B S. M. CHINCHOLE L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag T vlot (m/s) o a parautst s gvn as a unton o tm (sonds) b Usng Rung-Kutta 4 t ordr mtod wt a stp sz o 5 sonds, t dstan travld b t bod rom to sonds s stmatd most narl as 4.4 m m m m 70. Rung-Kutta mtod an b drvd rom usng rst tr trms o Talor srs o wrtng t valu o, tat s t valu o at, n trms o and all t drvatvs o at. I, t plt prsson or t rst v trms o t Talor srs ar osn or t ordnar drntal quaton, would b 0 ),.8tan( t t t t t , 5 d

23 B S. M. CHINCHOLE 7. A ot sold lndr s mmrsd n an ool ol bat as part o a qunng pross. Ts pross maks t tmpratur o t lndr,, and t bat,, ang wt tm. I t ntal tmpratur o t bar and t ol bat s gvn as 600 C and 7 C, rsptvl, and b Ol Clndr Lngt o lndr = 0 m Radus o lndr = m Dnst o lndr = 700 kg/m^ Sp at o lndr = 895 J/kg-K Convton at transr ont = 00 W/(m^-K) Sp at o ol = 90 J/(kg-K) Mass o ol = kg T oupld ordnar drntal quatons govrnng t at transr ar gvn b d 6.4 b db b d 6.4 b db b d b db 6.4 b d b db 6.4 b T ollowng quatons ar usd to answr qustons#,, and 4 k k k 6 k, k 4 L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag

24 B S. M. CHINCHOLE k, k k, k k4, k 7. T drntal quaton s lnar nonlnar lnar wt d onstants undtrmnabl to b lnar or nonlnar 7. A drntal quaton s onsdrd to b ordnar t as on dpndnt varabl mor tan on dpndnt varabl on ndpndnt varabl mor tan on ndpndnt varabl 74. Gvn d sn, 0 () most narl s , d 75. T orm o t at soluton to, 0 5 s.5 A B A.5 B A.5 B A.5 B 76. T ollowng nonlnar drntal quaton an b solvd atl b sparaton o varabls. d 6 0 8, T valu o θ(00) most narl s L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag 4

25 B S. M. CHINCHOLE A spral sold ball takn out o a urna at 00K s allowd to ool n ar. Gvn t ollowng radus o ball= m dnst o t ball=7800 kg/m^ sp at o t ball=40 J/kg-K mmttan=0.85 Stan-Boltzman onstant=5.67e-8 J/s-m^-K^4 ambnt tmpratur=00k onvton ont to ar=50 J/s-m^-K. T drntal quaton govrnng t tmpratur, o t ball as a unton o tm, t s gvn b d d d d L. V. H. ARTS, SCIENCE AND COMMERCE COLLEGE, PANCHAVATI, NSAHIK - Pag 5