The value of $\lim_{n\to\infty} \dfrac{(n+2)! + (n+1)!}{(n+2)! - (n+1)!}$ 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...

Which of the following statements is logically equivalent to $\sim(p \leftrightarrow q)$ ?

If $A = \begin{bmatrix} \sec\theta & -\tan\theta \\ -\tan\theta & \sec\theta \end{bmatrix}$, $\theta \in \left(0, \dfrac{\pi}{2}\right)$ such that $A + adj\,A = 4I$, then $\theta =$