Download AKTU B-Tech 2nd Sem 2016-17 Computer Based Numerical And Statistical Techniques Question Paper

THEORY EXAMINATION (SEM–II) 2016-17

COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES

Time: 3 Hours

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Max. Marks : 70

Note : Be precise in your answer. In case of numerical problem assume data wherever not provided.

SECTION-A

1. Attempt all questions :

1. a) Explain Pitfalls of floating-point Representation in detail.

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2. b) Prove that = 82 +81+ 82 2 4 7 x2 = 14
3. c) Suppose 1.414 is used as an approximation to√2. Find the absolute and relative errors.
4. d) Write down Gauss's forward interpolation formula.
5. e) Prove that x4 = [3T(x) + 4T2(x) + T4(x)] 8
6. f) What do you mean by Histograms?

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7. g) Explain Null hypothesis.

SECTION-B

2. Attempt any five of the following : 7 x5 = 35

1. a) Find a real root of the equation 3x + sinx - ex = 0 by the method of Regula falsi position correct to four decimal places.
2. b) Find the missing term in the following table:

   X	2	2.1	2.2	2.3	2.4	2.5	2.6
   y	0.135		0.111	0.082	0.074

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3. c) find y25 by Bessel's interpolation formula.
4. d) Given dy = y - x,y(0) = ) and y(0.2) correct to four decimal places using Runge- Kutta method.
5. e) By the method of least squares, find the curve y = ax + bx² that best fits the following data :

   X	1	2	3	4	5
   y	1.8	5.1	8.9	14.1	19.8

6. f) Apply Gauss-Seidel iteration method to solve the following equation (three iteration only)
   20x + y – 2z = 17
   

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   3x + 20y - z = -18
   2x - 3y + 20z = 25
7. g) Find the cubic Lagrange's interpolating polynomial from the following data :

   X	0	1	2	5
   f(x)	2	3	12	147

8. h) For 10 observations on price(x) and supply(y), the following data were obtained (in appropriate units) : FirstRanker.com

SECTION-C

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Attempt any two of the following : 10.5 x2 = 21

1. 3. Find y(2) if y(x) is the solution of = (x + y) where y(0) = 2, y(0.5) = 2.636, y(1) = dx 2 3.595,y(1.5) = 4.968 using Milne's method.
2. 4. dy Given that = log10(x + y)with the initial condition that y = 1 when x = 0, find y for x = 0.2 dx and x = 0.5 using Euler's modified formula.
3. 5. Derive the Newton-divided difference formula, calculate the value of f(6) from the following data

   X	1	2	7	8
   f(x)	1	5	5	4

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