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IGNOU UNIVERSITY MCA - III (SEM 5) DEC 2008 : Numerical and Statistical Computing

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MCA (Revised) Term-End Examination December,2008 MCSE - 0 04: N UMERICAL A ND S TATISTICAL COMPUTING sl: Time : 3 hours @ (.o Note : (f Maximum Marks : 100 A QuestionNumber 7 is compulsory. ttanpt any thrge is Questionsror.nthe rest. Useof Calculator allorned. f (u) I f 0 .333 i s t he a pproximate v alue o f L /3, find absolute,relative and percentageelTors. (b) Find the value of z (the number of term required) in the expansion of ex, such that their s um y ields t he v alue c orrect t o 8 decimal p lacesa t r :1,. (.) Find the root of the equationxe{: cosr using the R egula-Falsi m ethod c orrect t o f our decimal places. (d) Find the polynomial function/(x) given that / ( o ) : 2 ' f ( 1 ) : 3 ' f ( 2 ) : L 2 a n d" f ( 3 ) : 3 s . Hence f ind / (5) u sing interpolation formula L agrange's ta. (e) 11 dx b Y u sing E valuate J , , *, (t) TraPezoidal rule (ii) SimPsort'sL/3 raLe (0 T he p robability t hat a n e vening c ollege student will graduate is 0'4' Determine the probability that out of 5 students (i) none (it) one and (iii) atleast one will be graduate' (g) T he f ollowing d ata a bout t he s ales a nd advertisement expenditure of a firm is given below: Sales (in crores of Rg) Means expenditure (in c rores o f R s) 40 itandard deviations Advertisement 10 b 1.5 = Coefficient of Correlation (r) 0'9 (0 Estimate the likely salesfora proposed advertisement expenditure of Rs' 10' crores. (ii) IAtrhatshould be the advertisements expenditure, if the firm ProPoses a sales target of 60 ctores of ruPees ? 2. (a) By u sing t he B isection m ethod, f ind a n approximate of theequationirr r= I root , r that l ies b etween x :L (measured i n r adians). a nd r = 1 ..5 C arry o ut computation upto 5th stage. (b) E stimate t he n umber o f s tudents, w ho obtained l ess t han 4 5 m arks f rom t he following u sing N ewton's F orward Difference : Marks 0-40 No. o f S tudents 31 (c) 40-50 42 50-50 51 60 - 70 35 70-80 31 Municipal Corporation installed ?000 bulbs in the streets. If thesebulbs have an average life of 1,000burning hours, with a standard deviation o f 2 00 h ours, w hat n umber o f bulbs might be excepted to fail in first 700 burning hours ? Given Z Probability 3. (a) 1.00 0.159 t_25 0.106 Solve the equation : xl+x2*x3:6 3rt * 3 x2-l4x3:20 2xr* x r* 3 rr:13 using Gauss Elimination method. 1.50 0.067 (b) Evaluate the integraU: using f !I.a, "1, +r' the Gauss-Legendre 1-point, 2-point and 3-point Quadrature rules. Compare with the e xact s olution I :Tan-l(+)+I (c) 4 It is known from the past experience that in a certain plant there are on an average 4 accidents per month. Find the probabilify that in a given year there will be less than 4 accidents. (a) Apply LU decomposition metho4 to solve the following equations : Axr* x 2* x g=3 xr*4xr*2xu:g Zxr+x r+Sxr:4 (b) UsrngRunge-Kutta ethodof fourth order m - k t u 2 - x2 solve 1 i:* w ith y (0) = L a t x = 0 .2 dx y '+xc. and r = 0.4. (c) A randomvariable'X is defined as the sum of faces when a pair of dice is thrown. Find the expected value of.'K. (u) Find a real root of the equation 3r: cos.r* 1r using Newton-Raphson method. &) Solve the following differential equation by Euley's method dv v -x :1 ;;: i i*'slven Y( o) Find'y' a pproximately f or r :0.L steps. (c) Write a short notes on : (i) Chi-Square Distribution. (ii) Least Squares Estimation. -oOo- i n f ive

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Additional Info : Mca - III (sem 5) December 2008 Question Paper - Numerical and Statistical Computing (Revised Course)
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