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BCA III (Third) Semester Examination 2014-15 Course Code: BCA301 Paper ID: 0833201 Computer Based Numerical Analysis and Statistical Techniques Time: 3 Hours Max. Marks: 70 Note: Attempt six questions in all. Q. No. 1 is compulsory. 1. a) b) c) d) e) Answer any five of the following (limit your answer to 50 words). (4x5=20) State the scope and use of Computer Based Numerical analysis And Statistical Techniques. Solve the following system of equations using Gauss – Seidel method: 10x + y + z = 12, 2x + 10y + z = 13, 2x + 2y + 10z = 14. What do you understand by rate of convergence of a method to find out the root of an equation? What is Interpolation? Differentiate between Newton’s forward and backward interpolation formulae. E By using Newton – Divided Difference formula, calculate f(3) from the following data: x 0 1 2 4 5 6 f f) g) h) 1 14 15 5 6 19 1 Evaluate the integral ∫ 0 x2 / (1 + x3) dx using Simpson’s 1 /3rd rule. Discuss the Central difference formulae for interpolation. What do you know about central Tendency? 2. Apply Gauss – Jordan method to solve the equations : x + y + z = 9, 2x – 3y + 4z = 13, 3x + 4y +5z = 40. (10) 3. Find a root of the equation x3 – 4x – 9 = 0, using the Bisection method correct to three decimal places. (10) 4. Find a root of the equation cos x = xex, using the Regula – Falsi method correct to four decimal places. (10) 5. By using Lagrange’s method of interpolation, Find the polynomial P(n) of degree two such that: P(1) = 1, P(3) = 27, P(4) = 64. (10) 6. Apply Iteration method to find the negative root of the equation x3 – 2x + 5 = 0, correct to four decimal places. (10) 7. Evaluate ∫60 dx / (1 + x2) using Trapezoidal Rule. 8. Write down the principle of least squares method for curve fitting. (10) (10)