The equation of a circle which passes through the points $(2,3)$ and $(4,5)$ and whose center lies on the straight line $y - 4x + 3 = 0$ is

The value of $\lim_{x \to 3} \dfrac{[x] - 3}{x - 3}$, where $[\cdot]$ denotes the greatest integer function, is.....

If the truth value of the compound statement $[(p \vee q) \wedge (q \rightarrow r) \wedge (\sim r)] \rightarrow (p \wedge q)$ is False then the truth values of $p \rightarrow q$ and $q \rightarrow p$ are respectively......

The statement pattern $(p \vee q) \rightarrow \sim r$ is logically equivalent to