Rajasthan Technical University 2010 B.Tech Mechanical Engineering Numerical Methods and Applied Statistics - Question Paper
RTU Numerical Methods and Applied Statistics
Rajasthan tech. University
B.tech six sem (Main/back)
Year June 2010
b) Use power method to find the largest eigenvalue and corresponding
eigen vector of the matrix A>
OR
i 2 0 2 I 0 0 0-1
a) Obtain the missing terms in the following table: x : 1 2 3 4 5 6 78 /(x): I 8 9 64 9 216 343 512 and find/(7.S)
b) Using Newton's divided difference formula, find/(8) and/(15) from the following table
x : 4 5 7 10 II 13
f(x): 48 100 294 900 1210 2028 Unit-Ill
3. a) Find first and second derivative at x 1.1 from the following table
x : 1 1.2 1.4 1.6 1.8 2.0
/(*): 0 0.1280 0.5440 1.2960 2.4320 4.00
b) Evaluate f (** * **) * by Gauss Quadrature formula.
OR
a) Given >) and >-(l) = I. ><l.l) * 1.233. >(1.2) - 1.548,
1.3) 1.979 evaluate 1.4) by Adams* Bashforth method.
b) Apply Runge-Kutia meihod to find the approximate value ofy for x * 0.2 in stepofO.l if given thatI whenx - 0.
Unit-IV
4. a) The first three moments ofa distribution about the value 2 of a variable are
1,16 and -40. Show that the mean is 3. the variance 15 and A s~*6' Also find the first three moments about x * 0.
6E3054 (2)
b) Use power method to find the largest eigenvalue and corresponding
eigen vector of the matrix A>
OR
i 2 0 2 I 0 0 0-1
a) Obtain the missing terms in the following table: x : 1 2 3 4 5 6 78 /(x): I 8 9 64 9 216 343 512 and find/(7.S)
b) Using Newton's divided difference formula, find/(8) and/(15) from the following table
x : 4 5 7 10 II 13
f(x): 48 100 294 900 1210 2028 Unit-Ill
3. a) Find first and second derivative at x 1.1 from the following table
x : 1 1.2 1.4 1.6 1.8 2.0
/(*): 0 0.1280 0.5440 1.2960 2.4320 4.00
b) Evaluate f (** * **) * by Gauss Quadrature formula.
OR
a) Given >) and >-(l) = I. ><l.l) * 1.233. >(1.2) - 1.548,
1.3) 1.979 evaluate 1.4) by Adams* Bashforth method.
b) Apply Runge-Kutia meihod to find the approximate value ofy for x * 0.2 in stepofO.l if given thatI whenx - 0.
Unit-IV
4. a) The first three moments ofa distribution about the value 2 of a variable are
1,16 and -40. Show that the mean is 3. the variance 15 and A s~*6' Also find the first three moments about x * 0.
6E3054 (2)
OR
a) Fit a Poisson distribution to the following data and show whether ihc fit in satisfactory or not:
x.: 0 I 2 3 4 5 6 7
I
o: 364 376 218 89 33 13 2 I
I
b) Ten competitors in a beauty conlcst got marks by three judges in the following orders:
First Judge :165I0 3 249 7 8
Second Judge: 6498 I 23 10 5 7
Third Judge : 3 5 8 4 7 10 2 I 6 9
Use rank correlation coefficient to discuss which pair of judge have (he nearest approach to common tastes in beauty.
OR
a) Fit a Poisson distribution to the following data and show whether ihc fit in satisfactory or not:
x.: 0 I 2 3 4 5 6 7
I
o: 364 376 218 89 33 13 2 I
I
b) Ten competitors in a beauty conlcst got marks by three judges in the following orders:
First Judge :165I0 3 249 7 8
Second Judge: 6498 I 23 10 5 7
Third Judge : 3 5 8 4 7 10 2 I 6 9
Use rank correlation coefficient to discuss which pair of judge have (he nearest approach to common tastes in beauty.
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