Which one of the following options is correct given three positive integers $$x, y$$ and $$z$$, and a predicate
$$P\left( x \right) = \neg \left( {x = 1} \right) \wedge \forall y\left( {\exists z\left( {x = y * z} \right) \Rightarrow \left( {y = x} \right) \vee \left( {y = 1} \right)} \right)$$

Consider the matrix as given below. $$$\left[ {\matrix{ 1 & 2 & 3 \cr 0 & 4 & 7 \cr 0 & 0 & 3 \cr } } \right]$$$

Which of the following options provides the Correct values of the Eigen values of the matrix?

$$K4$$ and $$Q3$$ are graphs with the following structures.

Which one of the following statements is TRUE in relation to these graphs?

Given $$i = \sqrt { - 1} ,$$ what will be the evaluation of the definite integral $$\int\limits_0^{\pi /2} {{{\cos x +i \sin x} \over {\cos x - i\,\sin x}}dx?} $$