COMPUTER BASED NUMERICAL TECHNIQUE (CBNST)

COMPUTER BASED NUMERICAL TECHNIQUE (CBNST)
SEM-III,2010-11
B.TECH EXAMINATION
UTTARAKHAND TECHNICAL UNIVERSITY
(UTU)

Time: 2 hours

Total Marks: 75

Attempt any three parts of the following:

1. If X = 2.536, find the absolute error and relative error when
   (i) X is rounded and
   (ii) X is truncated to two decimal digits.
2. Find a real root of cos x = 3x - 1, correct to three decimal places by iteration method.
3. Using Regula-Falsi method, compute the smallest positive root of the equation x e^x - 2 = 0, correct upto four decimal places.
4. Find the root of the equation x³ - x -1 = 0 by using Muller's methods.

Attempt any two parts of the following:

1. (i) With usual notations, prove that
   
   (ii) Prove that,
   
2. Use Gauss forward formula to find y for x =30 given that.
   
3. Using Stirling's formula to find Y₂₈, given that Y₂₀= 49225
   Y ₂₅= 48316, Y₃₀ = 47236, Y₃₅ = 45926, Y₄₀= 44306.

Attempt any two parts of the following:

1. Find f'(1.1) and f"(1.1) from the following table:
   
2. Evaluate
   by Simpson's 1/3 rule using 11 ordinates.
3. Evaluate
   by using Weddle's rule taking twelve intervals.

Attempt any two parts of the following:

1. Use the method of least-square, fit a curve of the form y = a x^b to the following data:
   
2. A drilling machine bores holes with a mean diameter of 0.5230 cm and a standard deviation of 0.0032 cm. Calculate the 2-sigma and 3-sigma upper and lower control limits for means of sample of 4.
3. Obtain a regression plane by using multiple linear regression to fit the data given below:
   

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