This download link is referred from the post: AKTU B-Tech Last 10 Years 2010-2020 Previous Question Papers || Dr. A.P.J. Abdul Kalam Technical University
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 :
- a) Explain Pitfalls of floating-point Representation in detail.
- b) Prove that = 82 +81+ 82 2 4 7 x2 = 14
- c) Suppose 1.414 is used as an approximation to√2. Find the absolute and relative errors.
- d) Write down Gauss's forward interpolation formula.
- e) Prove that x4 = [3T(x) + 4T2(x) + T4(x)] 8
- f) What do you mean by Histograms?
- g) Explain Null hypothesis.
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SECTION-B
2. Attempt any five of the following : 7 x5 = 35
- a) Find a real root of the equation 3x + sinx - ex = 0 by the method of Regula falsi position correct to four decimal places.
- 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 - c) find y25 by Bessel's interpolation formula.
- d) Given dy = y - x,y(0) = ) and y(0.2) correct to four decimal places using Runge- Kutta method.
- 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 - f) Apply Gauss-Seidel iteration method to solve the following equation (three iteration only)
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3x + 20y - z = -18
2x - 3y + 20z = 25 - g) Find the cubic Lagrange's interpolating polynomial from the following data :
X 0 1 2 5 f(x) 2 3 12 147 - h) For 10 observations on price(x) and supply(y), the following data were obtained (in appropriate units) : FirstRanker.com
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SECTION-C
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Attempt any two of the following : 10.5 x2 = 21
- 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.
- 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.
- 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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This download link is referred from the post: AKTU B-Tech Last 10 Years 2010-2020 Previous Question Papers || Dr. A.P.J. Abdul Kalam Technical University