List of top Engineering Mathematics Questions

Two consecutive estimates of the root of a function $f(x)$ obtained using the Newton-Raphson method are $x_i = 8.5$ and $x_{i+1 = 13.5$, and the value of the function at $x_i$ is 15. The numerical value of the first derivative of the function evaluated at $x_i$ is ............ (in integer).}

The value of $\lim_{x \to 0 \frac{6(x - \sin x)}{x^3}$ is ......... (in integer).}

For a two-dimensional field described by $T(x,y) = \tfrac{1{3}xy(x+y)$, the magnitude of its gradient at the point (1,1) is .............. (rounded off to two decimal places).}

Which one of the following matrices is orthogonal?

For two continuous functions M(x,y) and N(x,y), the relation M dx + N dy = 0 describes an exact differential equation if

The hydrostatic stress for the stress tensor provided below is .............. MPa (in integer). \[ \begin{bmatrix} 150 & 0 & 0
0 & -100 & 100
0 & 100 & 250 \end{bmatrix} \, \text{MPa} \]

Which of the following functions is/are expandable using Maclaurin series?

Which one of the following matrices has eigenvalues 1 and 6?

Which one of the following options is correct for the given data in the table? \[ \begin{array}{|c|c|c|c|c|} \hline \text{Iteration (i)} & 0 & 1 & 2 & 3
\hline \text{Input (I)} & 20 & -4 & 10 & 15
\hline \text{Output (X)} & 20 & 16 & 26 & 41
\hline \text{Output (Y)} & 20 & -80 & -800 & -12000
\hline \end{array} \]

If $P e^{x = Q e^{-x}$ for all real values of $x$, which one of the following statements is true?}

Solve the differential equation:
\[ \frac{d^2y}{dx^2} - 4y = 0 \]

Evaluate the integral:
\[ \int_0^1 x e^x \, dx \]

Determine the rank of the matrix:
\[ \begin{pmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \end{pmatrix} \]

Find the inverse of the matrix:
\[ \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix} \]

Evaluate the limit:
\[ \lim_{x \to 0} \frac{\sin x - x}{x^3} \]

Solve the differential equation:
\[ \frac{dy}{dx} + y = e^x \]

Find the residue of the function \[ f(z) = \frac{1}{z^2 + 1} \] at the pole $z = i$.

If a die is rolled twice, what is the probability that the sum of the numbers is 7?

Evaluate the integral: \[ \int_0^\pi \sin^2(x) \, dx \]

Find the eigenvalues of the matrix: \[ A = \begin{pmatrix} 4 & 1 \\ 2 & 3 \end{pmatrix} \]