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- Numerical Methods - NM
- 2018
- PYQ
**Biju Patnaik University of Technology Rourkela Odisha - BPUT**- Electronics and Instrumentation Engineering
- B.Tech
**1249 Views**- 22 Offline Downloads
- Uploaded 1 year ago

Registration No : Total Number of Pages : 02 B.Tech. FESM6301 6th Semester Back Examination 2017-18 NUMERICAL METHODS BRANCH : AEIE, ECE, EIE, ETC, IEE Time : 3 Hours Max Marks : 70 Q.CODE : C200 Answer Question No.1 which is compulsory and any five from the rest. The figures in the right hand margin indicate marks. Q1 Answer the following questions : a) b) c) d) e) f) g) (2 x 10) Find the error and absolute error when X = 2.5364 is Rounded to two decimal digits. What is the Rate of convergence of the Newton-Raphson method? What is the number of real root present in the equation interval − , . Find the smallest positive root of the equation (0,1) by Bisection method after two iteration. State Intermediate value theorem. Evaluate ∫ Let = 0 in the − 5 + 2 = 0 in the interval using Trapezoidal rule taking step size h = 0.25. , (0) = 1 then find = − cos (0.1) using Euler’s method with step size h = 0.1 h) i) j) Q2 Q3 Write the condition for the failure of LU – Decomposition method. Find forward difference table for the following data y(0) = 1; y(1) = 0; y(2) = 1; y(3) = 10 Find the Linear interpolating polynomial using Lagrange interpolation for the data (2) = 4, (2.5) = 5.5 a) Find smallest positive root of the equation − 5 + 1 = 0 in the interval (0,1) after four iterations by Newton-Raphson method . (5) b) Find a root of the equation − 5 + 1 = 0 correct to three decimal places in the interval (0,1) after four iterations by Secant method . (5) a) Find the inverse of the matrix A = 2 1 3 2 using LU decomposition method 2 2 (5) Find two iteration of Gauss-Seidel method to solve the following system of equations 27x + 6y – z = 85; x + y + 54z = 110; 6x + 15y + 2z = 72. (5) with b) = = =1. 3 2 1

Q4 a) Evaluate y = x y= b) Q5 a) b) 0.00 0.10 0.20 0.30 0.40 1.00 1.2214 1.4918 1.8221 2.255 (5) Find f(1.38) for the following data x 1.1 1.2 1.3 1.4 f(x) 7.831 8.728 9.627 10.744 (5) Using Newton’s divided difference formula find f(8) from the following table x 4 5 7 10 11 13 f(x) 48 100 294 900 1210 2028 For the function , prove that the third divided difference with argument a, b, c and d is equal to Q6 (5) for x = 0.05 using the following table . a) Evaluate ∫ 0.5 b) Determine a, b and c such that the formula ∫ (ℎ) is exact for polynomial of degree upto 2. using Simpson’s rule and Romberg’s method for h = 1 and Q7 Using the Runge-Kutta fourth order method find problem = − + , ( )= . Q8 Write short answer on any TWO : (5) + (5) ( . ) for the initial value (10) ( ) = ℎ{ (0) + (5 x 2) a) Let = + , (0) = 1 then find step size h = 0.1 b) Evaluate ∫ c) Find a real root of the equation − 5 + 2 = 0 correct to three decimal places in the interval (0,1) after four iterations by False position method. Prove that rate of convergence for the Secant method is 1.618. d) (5) (0.2) using modified Euler’s method with dividing the range into 4 equal parts by Trapezoidal rule.

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