List of top Mechanical Engineering Questions on Numerical Methods

Which of the following is not the property of a distribution function \( F(x) \) of a random variable \( X \)?

If the particular integral of \( y'' - 4y' = x^2 e^{2x} \) is in the form \( y_p = e^{2x} y(x) \), then \( y(x) \) is

\( \mathcal{L}\{ \sin(t-3)u(t-3) \} = \)

The Laurent's series for the function \( f(z) = 1 + \frac{3}{z+2} - \frac{8}{z+3} \) in the region \( |z| \lt 2 \) is

Given \( x_0 \neq 0 \), if the iteration formula \( x_{n+1} = \frac{1}{2}\left( -\frac{7}{x_n} + x_n \right) \), \( n \geq 0 \) is used to find the root of \( f(x) = 0 \), then \( f(x) = \)

If a random variable \( X \), defined such that \( E(X-1)^2 = 10 \) and \( E(X-2)^2 = 6 \) then mean \( (\mu) \) and variance \( (\sigma^2) \) are

Let the matrix \( A = \begin{bmatrix} 1 & 4 \\ 2 & -1 \end{bmatrix} \).
Statement-I: \( A^2 = 9I \)
Statement-II: The eigen values of \( A \) are \( -3 \) and \( 3 \)

Statement-I: The function \( u = x^2 + y^2 \), \( v = \tan^{-1}\left(\frac{y}{x}\right) \) are functionally independent.
Statement-II: The Jacobian \( \frac{\partial(u,v)}{\partial(x,y)} \) is non-zero.

If \( f \) and \( g \) are the solutions of Laplace equation then \( \nabla \cdot \{(f \nabla g) - (g \nabla f)\} = \)

If \( \lambda_1, \lambda_2 \) and \( \lambda_3 \) are the eigen values of a square matrix \( A \), then the eigen values of \( A^{-1} + 2I + A \) are

Using Runge-Kutta method of fourth order, an approximate value of \(y\) at \(x=0.2\), given that \(\frac{dy}{dx}=\frac{y^2-x^2}{y^2+x^2}\) and \(y(0)=1\), is:

Using the method of Regula Falsi, a root of the equation \( x^3 + x^2 - 3x - 3 = 0 \) lying between 1 and 2 is

The value of the integral
\[ \int_{0.2}^{1.4} (\sin x - \log_e x + e^x) \, dx \]
using Simpson's three-eighth rule, by taking interval size \( h = 0.2 \), is: