List of top Engineering Mathematics Questions asked in GATE Metallurgical Engineering

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?}

The sum of eigenvalues of the matrix \( \begin{bmatrix} 4 & 3 & 2 \\ 0 & -1 & 2 \\ 0 & 0 & -3 \end{bmatrix} \) is ................... (in integer).

Order (O) and degree (D) of the differential equation \( \left(\frac{dy}{dx}\right)^3 = \sqrt{\frac{d^2y}{dx^2} + 10} \) are

The maximum value of function \(f(x) = 4x^3 - 24x^2 + 36\) in the domain [-1, 5] is ................... (round off to nearest integer).

A fluid flow field is given by the velocity vector \( \vec{V} = e^{xyz}(x\hat{i} + z\hat{k}) \). The curl of velocity at (1, 2, 3) is

Given, \( \vec{\phi} = xy\hat{i} + yz\hat{j} + xz\hat{k} \). S is a surface bounded by the planes x = 0, y = 0, z = 0, x = 3, y = 2, and z = 1. If \( \hat{n} \) is the unit vector normal to S, then \( \iint_S \vec{\phi} . \hat{n} dS \) is

The probability of setting an easy exam paper by three setters are \( \frac{1}{2}, \frac{1}{3}, \) and \( \frac{1}{4} \). If all three are setting one paper each, then the probability that at least one of the papers will be easy is ................... (round off to 2 decimal places).

The value of \( \lim_{x\to 1} \frac{7x^7-20x^5+13x}{3x^3+x-4} \) is