8. Find the positive root of the equation 3x - cos x - 1 using Regula Falsi method and correct upto 4 decimal places. a) 0.6701 b) 0.5071 c) 0.6071 d) 0.5701 9. Find the positive root of the equation x³ + 2x² + 10x - 20 using Regula Falsi method and correct upto 4 d) 1.6488 b) 1.3866 c) 1.4688 equation 3x + sin x - e* using b) 0.4306 c) 0.3604 decimal places. a) 1.3688 10. Find the positive root of the decimal places a) 0.4604 11. Rate of convergence of the Newton-Raphson method is generally a) Linear b) Quadratic c) Super-linear d) Cubic ESTD: 2001 RNS INSTITUTE OF TECHNOLOGY, BENGALURU - 98 DEPARTMENT OF MATHEMATICS Regula Falsi method and correct upto 4 d) 0.4304 12. The Newton-Raphson method of finding roots of nonlinear equations falls under the category of which of the following methods? a) bracketing b) open c) random d) graphical 13. The Newton Raphson method is also called as a) Tangent method b) Secant method c) Chord method 14. The Iterative formula for Newton Raphson method is given by f(xn) c) x₂ = xo- f1(xn) f(xn) f'(xn) 15. In Newton Raphson method f'(x) for a given point is given by the formula a) y/x' b) y'/x c) y/x d) y' /x' 16. In Newton Raphson method if the curve f(x) is constant then a) f'(x) = 0 b) f(x) = 0 c) f'(x) = 0 d) f'(x) = c 17. For decreasing the number of iterations in Newton Raphson method: a) The value of f'(x) must be increased b) The value of f"(x) must be decreased c) The value of f'(x) must be decreased d) The value of f"(x) must be increased. 18. The equation f(x) is given as x³ - x² + 4x -4 = 0. Considering the initial approximation at x=2 then the value of next approximation correct upto 2 decimal places is given as a) 0.67 b) 1.33 c) 1.00 d) 1.50 19. The equation f(x) is given as x²-4-0. taking the initial approximation at x=6 then the value of next approximation correct to 2 decimal places is given as a) 3.33 b) 1.33 c) 2.33 d) 4.33 20. The equation f(x) is given as x³+4x+1=0. Considering the initial approximation at x=1 then the value of x₁ is given as a) 1.67 b) 1.87 c) 1.86 d) 1.85 21. At which point the iterations in the Newton Raphson method are stopped? a) When the consecutive iterative values of x are not equal a) Xn+1 = Xo - f(xn) b) Xn+1 = Xn=' f1(xn) d) Diameter method d) Xn+1 = Xn+ b) When the consecutive iterative values of x differ by 2 decimal places c) When the consecutive iterative values of x differ by 3 decimal places d) When the consecutive iterative values of x are equal 22. The Newton Raphson method fails if a) f'(x) = 0 b) f"(x) = 0 c) f(x) = 0 23. The points where the Newton Raphson method fails are called? a) floating b) continuous c) non-stationary formula can be used 24. Newton- Gregory Forward interpolation a) only for equally spaced intervals b) only for unequally spaced intervals c) for both equally and unequally spaced intervals d) for unequally intervals d) f(x) = 0 d) stationary f(xn) f'(xn)