If a continuous function $$f(x)$$ does not have a root in the interval $$\left[ {a,b} \right],\,\,$$ then which one of the following statements is TRUE?

If the sum of the diagonal elements of a $$2 \times 2$$ matrix is $$-6$$, then the maximum possible value of determinant of the matrix is ____________.

The maximum value of $$'a'$$ such that the matrix $$\left[ {\matrix{ { - 3} & 0 & { - 2} \cr 1 & { - 1} & 0 \cr 0 & a & { - 2} \cr } } \right]$$ has three linearly independent real eigenvectors is

Given Set $$\,\,\,A = \left\{ {2,3,4,5} \right\}\,\,\,$$ and Set $$\,\,\,B = \left\{ {11,12,13,14,15} \right\},\,\,\,$$ two numbers are randomly selected, one from each set. What is the probability that the sum of the two numbers equal $$16?$$