Let $$ \oplus $$ and $$ \odot $$ denote the Exclusive OR and Exclusive NOR operations, respectively.

Which one of the following is NOT CORRECT?

Consider the sequential circuit shown in the figure, where both flip-flops used are positive edge-triggered $$D$$ flip-flops.

The number of states in the state transition diagram of this circuit that have a transition back to the same state on some value of “in” is _____.

The value of $$\int_0^{\pi /4} {x\cos \left( {{x^2}} \right)dx} $$ correct to three decimal places (assuming that $$\pi = 3.14$$ ) is ________.

Consider a matrix $$A = u{v^T}$$ where $$u = \left( {\matrix{ 1 \cr 2 \cr } } \right),v = \left( {\matrix{ 1 \cr 1 \cr } } \right).$$ Note that $${v^T}$$ denotes the transpose of $$v.$$ The largest eigenvalue of $$A$$ is _____.