Numerical Methods MCQs Question and Answer in Engineering Maths

The accuracy of Simpson's rule quadrature for a step size h is

The table below gives values of a function F(x) obtained for values of x at intervals of 0.25.

x	0	0.25	0.5	0.75	1.0
F(x)	1	0.9412	0.8	0.64	0.50

The value of the integral of the function between the limits 0 to 1 using Simpson's rule is

A numerical solution of the equation f(x) = x + √x - 3 = 0 can be obtained using Newton-Raphson method. If the starting value is x = 2 for the iteration, the value of X that is to be used in the next step is

To solve the equation 2sin x = x, by Newton Raphson method, the initial guess value is chosen to be x = 2. Consider x in radius only. The value of x (in radius) obtained after one iteration will be closed to

A 2^nd degree polynomial, f(x) has values of 1, 4 and 15 at x = 0, 1 and 2, respectively. The integral $$\int\limits_0^2 {{\text{f}}\left( {\text{x}} \right){\text{dx}}} $$   is to be estimated by applying the trapezoidal rule to this data. What is the error (defined as "true value - approximate value") in the estimate?

Starting from x₀ = 1, one step of Newton-Raphson method in solving the equation x³ + 3x - 7 = 0 gives the next value (x₁) as

The equation x³ - x² + 4x - 4 = 0 is to be solved using the Newton-Raphson method. If x = 2 is taken as the initial approximation of the solution, then the next approximation using this method will be

The iteration step in order to solve for the cube roots of a given number N using the Newton-Raphson's method is

Equation e^x - 1 = 0 is required to be solved using Newton's method with an initial guess x₀ = -1. Then, after one step of Newton's method, estimate x₁ of the solution will be given by

Match List-I with List-II and select the correct answer:

List-I	List-II
a. Newton-Raphson method	1. Solving nonlinear equations
b. Runge-Kutta method equations	2. Solving simultaneous linear equations
c. Simpson's Rule equations	3. Solving ordinary differential
d. Gauss elimination	4. Numerical integration
	5. Interpolation
	6. Calculation of Eigenvalues