List of top Engineering Mathematics Questions asked in GATE Aerospace Engineering

The largest eigenvalue of the given matrix is: \[ \begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{bmatrix} \]

The real function \( y = \sin^2(|x|) \) is

Consider the differential equation \(\frac{d^2y}{dx^2} - 2 \frac{dy}{dx} + y = 0\). The boundary conditions are \(y = 0\) and \(\frac{dy}{dx} = 1\) at \(x = 0\). Then the value of \(y\) at \(x = \frac{1}{2}\) is

Consider the partial differential equation \(\frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} = 0\) where \(x, y\) are real. If \(f(x, y) = a(x)b(y)\), where \(a(x)\) and \(b(y)\) are real functions, which one of the following statements can be true?

The height of a right circular cone of maximum volume that can be enclosed within a hollow sphere of radius \(R\) is

The arc length of the parametric curve: \( x=\cos\theta,\; y=\sin\theta,\; z=\theta \) from \( \theta=0 \) to \( \theta=2\pi \) is equal to _________ (round off to one decimal place).

If $\hat{a}, \hat{b}, \hat{c}$ are three mutually perpendicular unit vectors, then $\hat{a} \cdot (\hat{b} \times \hat{c})$ can take the value(s):

Let \(\hat{i}, \hat{j}, \hat{k}\) be the unit vectors in the x, y, and z directions, respectively. If the vector \(\hat{i} + \hat{j}\) is rotated about positive \(\hat{k}\) by \(135^\circ\), one gets

The equation of the straight line representing the tangent to the curve \(y = x^2\) at the point (1, 1) is