List of top Mathematics Questions asked in GATE Mathematics

Let \( A \in M_2({C}) \) be given by \[ A = \begin{bmatrix} 0 & 2
2 & 0 \end{bmatrix}. \] Let \( T: M_2({C}) \to M_2({C}) \) be the linear transformation given by \( T(B) = AB \). The characteristic polynomial of \( T \) is:

Let \( X \) be a topological space and \( A \subseteq X \). Given a subset \( S \) of \( X \), let \( {int}(S), \partial S, \) and \( \overline{S} \) denote the interior, boundary, and closure, respectively, of the set \( S \). Which one of the following is NOT necessarily true?

Let \( C \) be the ellipse \( \{ z \in \mathbb{C} : |z - 2| + |z + 2| = 8 \} \) traversed counter-clockwise. The value of the contour integral \[ \int_C \frac{z^2 \, dz}{z^2 - 2z + 2} \] is equal to:

Consider the following condition on a function \( f : {C} \to {C} \): \[ |f(z)| = 1 \quad {for all } z \in {C} { such that } \operatorname{Im}(z) = 0. \] Which one of the following is correct?