List of top Engineering Mathematics Questions asked in GATE Chemical Engineering

Consider the matrix:

\[ A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix} \]

The eigenvalues of the matrix are 0.27 and ____ (rounded off to 2 decimal places).

Consider the differential equation \(\frac{dy}{dx} + \frac{y}{x} = 0\). Choose the CORRECT option(s) for the solution \(y\).
Consider a Cartesian coordinate system with orthogonal unit basis vectors \( \hat{i}, \hat{j} \) defined over a domain: \( x, y \in [0,1] \). Choose the condition for which the divergence of the vector field \( \mathbf{v} = ax\hat{i} - by\hat{j} \) is zero.
Given the random variable \( X \) which takes the values 0, 1, 2, 7, 11, and 12 with the following probabilities: \[ P(X = 0) = 0.4, \quad P(X = 1) = 0.3, \quad P(X = 2) = 0.1, \quad P(X = 7) = 0.1, \quad P(X = 11) = ? \]
Find the maximum value of the function \( f(x) = -x^3 + 2x^2 \) in the interval \( [-1, 1.5] \).
Given that \( \lambda \) is an eigenvalue of matrix \( A \) with the corresponding eigenvector \( x \), and \( x \) is also an eigenvector of \( B = A - 2I \), find the relationship between \( \lambda \) and the eigenvalue of \( B \).
Find the sum of the series: \[ 1 + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \cdots \]