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CSMAT41USN 1 M S

M.S. R4MAIAH INSTITUTE OF TECHNOLOGY(AUTONOMOUS INSTITUTE, AFFILIATED TO VTU)

BANGALORE - 560 054SUPPLEMENTARY SEMESTER EXAM NATIONS - 2010

Course & Branch : B.E (Computer Science and E ngineering ) Semester : IVSubec Engineering Mathematics - IV Max. Marks : 100Subject Code : CSMAT41 Duration : 3 hrs

Instructions to the Candidates:1. Answer One Full Question From Each Unit.

UNIT-I1. a) Solve the following system of linear equations using the method of Gaussian (06)

elimination.xi + 2x2 + 3x3 + 2x4 = -1- X1- 2x2- 2x3+X4=22x1+4x2+8x3+12x44

1 1 =1b) Find the condition number of the matrix A = 40 1 Decide whether a0 41(07)

system of linear equations defined by such a matrix of coefficients is well-behaved.

c) Find a real root of the equation cosx=3x-lcorrect to three decimal places (07)using i) Iteration method ii) Aitken's V2 method.

2. a) Solve the following system of equations using LU decomposition. (06)2x1+x2+3x3=-14x1 +x2+7x3 =5- 6x1- 2x2 -12.x3 = -2

b) Solve the following system of equations using pivoting and scaling, working (07)to five significant figures.0.002 x1 + 4x2 - 2x30.001x1+2.0001x2+x3 = 20.001x1+3x2+3x3 =-1Explain briefly the rugula - falsi method to find a real root of f (x) = 0 . Also (07)find a real root of the equation x3 -2x-5 = 0 by regula - falsi method correctto three decimal places.

UNIT-II3. a) From the following tabe, estimate the number of students who obtained (06)

marks between 40 and 45.M arksks 30 - 4 0 4 0-500 40-50 60-700-700- 4 0 50-60 70-800-80

42 5150-60

42N1f studentsts 311 51 3 5 3f students 35 31 Page 1 of 4

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No mobttepho fey , CSMAT41b) Find f'(10)from the following data using Newton's divided difference (07)

formula.x 3 5 11 27 34.fi(x) -13 23 899 17315 35606

c ) Estimate the following from the curve 3y = x3 defined(0,0)-. (1,)3) using Simpson's 1/3 rd rule taking 8 subintervals

i) Area under the curve

from

ii) Volume of the solid obtained by rotating the curve about x-axis

(07)

4. a) Apply Bessel 's formua toobtain y25 given (06)y20 = 2854, y24 = 3162, y28 = 3544, y32 = 3992

b) Using the Lagrange's interpolation formula find the interpolation polynomial (07)from the following data and hence find f(2).

x 0 1 3 4y -12 0 6 12

c )6

Evaluate f 1 dx by0 1+x2i) Trapezoidal rule ii) Simpson's 1/3^d rule iii) Simpson's 3/8th ruleiv) Waddle's rule and compare the results with its actual value.

(07)

UNIT-III5. a) The transverse displacement 'u' of a point at a distance 'x' from one end and (06)22^ witht any time 't' of a vibrating string satisfies the equation a-u = 4-wtha axboundary conditions ii 0 at x = 0, t > 0 and u = 0 atx = 4, t > 0 and intial

conditions u = x(4-x) and a- = 0, 0< x

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