List of top Engineering Mathematics Questions asked in GATE Agricultural Engineering

If \( u = x^4 + y^4 + 3x^2 y^2 \), the value of \( \left( x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} \right)^{-1} \) is:
The value of \( \lim_{x \to 0} \frac{x \cos x - \sin x}{x^2 \sin x} \) is:
The median of the following set of numbers: 154, 130, 144, 137, 156, 146, 138, 149, 160, 138 is:

The equation \[ y'' + p(x)y' + q(x)y = r(x) \] is a _________ ordinary differential equation.

If the matrix \[ \begin{pmatrix} x & -3 \\ 2 & x - 5 \end{pmatrix} \] is singular, sum of the values of \( x \) is:
The value of \( y \) at \( x = 0.3 \) and \( y(x = 0) = 0 \) for the differential equation \[ \frac{dy}{dx} = 3y + 2e^x \] is _________. (Rounded off to 3 decimal places)
The series \[ \sum_{n=0}^{r} q^n = 1 + q + q^2 + \cdots + q^r \] has the sum:
The Laplace transform of \( \frac{s}{s^2 + a^2} \) is: