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IGNOU UNIVERSITY MCA - III (SEM 5) JUN 2009 : Numerical and Statistical Computing

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MCA (Revised) Term-End E xamination rl (o |une, 2009 f-. @ O MCSE-OO4 N UMERICAL A ND S TATISTICAL : COMPUTING Maximum M arks : 1 00 Time : 3 h ours Note : n 7 Q uestion umber i s c ompulsory. A ttempt a ny t hree fro* the rest. Useof calculatoris allowed. ( u) D ifferentiate b etween a bsolute,r elative and percentageerror with an example. (b) O btain t he p ositive r oot o f t he e quation x2-'1.-0 b y R egulaF alsi m ethod. (.) 1. Apply Gauss- Elimination method to solve the following sets of equation x+4y-z: -S x+y-62: -"12 3x-y-z- MCSE-004 -4. P.T.O. ( d) F ind N ewtons interpolating F orward polynomial d ifference for the following data : 0.1 0.2 0.4 0.5 f ( x ) I.40 1 . 5 6 1.76 2.00 2.28 x (e) 0.3 Calculate the value of integral : 6 a lax J.-,.,av 0^'^ (i) (ii) (0 Simpson's 1f ru\e. Simpson's 3/g rule. I n p artially d estroyed l aboratory r ecord o f an a nalysis o f c orrelation d ata, t he following r esults o nly a re l egible. Varianceo f x -9. Regressione quation : \rVhata re ( i) 8 x - 1 0y+ 6 6 : A M ean^::::':::::' (i1) C orrelation c oefficient between x and y. (iii) MCSE-004 Standard deviation of y. 2. ( ") S olve t he f ollowing s ystem o f e quation b y Jacobi'sm ethod. x+V-z:0 - x*3rt-2 x-22-3 (b) U se F alseP osition m ethod t o f ind r eal r oot of 1 3- 4 x - 9 :0. C orrect t o 3 -decimal places . (c) 3. E xplain t he p itfalls o f G auss Elimination method. ( u) E valuatet he m issing t erm i n t he f ollowing : 1 0 0 1 0 1 LA2 103 n4 x. tog (x ) 2.00 2.0043 7 2.0L28 2.0L70 (b) ur. ) Evalutet he i ntegralJ @'+x+2)dx u sing 0 Trapezoidalr ule, w ith h :L.0. MCSE-OO4 ( ") A m issile i s l aunched f rom a g round s tation. The a cceleration d uring i ts f irst 8 0 s econds of f light, a s r ecorded, i s g iven i n t he following t able : 60 50 20 40 10 30 0 a ( m/sz) 30 31,.63 33.34 35.47 37.75 40.33 43.25 f ( s) r(s): 70 80 a(ml s 2) 4 6.69 5 0.67 Compute t he v elocity o f m issile w hen f : 8 0s,u sing s impson'" 1 /3r d r ule. du 4. (u) Given ; : v-t ,* With i nitial c ondition y :1- a t t :0. Find y a pproximatelya t x - 0 .1i n f ive s teps, using E uler's M ethod. (b) Solve t he f ollowing d ifferential e quation fur ;- L0 t *y, w ith i nitial c ondition y (0):1., using F ourth o rder R unge-Kutta m ethod from f : 0 t o f - 0.4 t aking h -0.1. (.) Explain t he e ffect o f r ound o ff e rror i n scientific c alculations. MCSE-004 t P.T.O. 5. ( u) If a b ank r eceiveso n a n a verage t r:6 b ad chequesper dap what is the probability that it will receive 4 bad cheques on any given duy. (b) What is the utility of residual plot ? I,l/hat are its disadvantages ? (c) A farmer buys a quantity of cabbageseeds from a c ompany t hat c laims t hat approximately 9 0% o f t he s eeds w ill germinate if planted properly. If four seeds are p lanted, w hat i s t he p robability t hat exactly two will germinate. -oOo- MCSE-004

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Additional Info : Mca - III (sem 5) June 2009 Question Paper - Numerical and Statistical Computing (Revised Course)
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