List of top Engineering Mathematics Questions asked in GATE MN

The directional derivative of a function \( f(x, y, z) = 4x^2 + 8y^2 + 9z^2 \) at the point \( P(3, 4, 5) \) in the direction vector \( \vec{b} = 2\hat{i} - 3\hat{j} + 4\hat{k} \) is _______ (rounded off to 1 decimal place).
The area bounded by the curves \( y = \sqrt{x} \) and \( y = 8x^2 \) is:
The characteristic polynomial of a third order matrix \( A \) is given by \[ f(x) = x^3 - 6x^2 + 11x - 6. \] If one of the eigenvalues of \( A \) is 1, then the sum of the other two eigenvalues is:

The percent Fe content of a random sample consisting of five observations is shown:

If the mean grade of the stockpile is estimated using the above data, the standard error of the mean grade, in %, is _______ (rounded off to 3 decimal places).
 

The rank of \(3 \times 3\) matrix \(A\) is 2. The determinant of the matrix is
If \( y = x^x \), then \( \frac{dy}{dx} \) is:
The value of \( \lim_{x \to 0} \left( \frac{\tan 11x}{\tan 5x} \right) \) is: