The statement pattern $[p \wedge(q \vee r)] \vee[\sim r \wedge \sim q \wedge p]$ is equivalent to

If $8 \mathrm{f}(x)+6 \mathrm{f}\left(\frac{1}{x}\right)=x+5$ and $y=x^2 \mathrm{f}(x)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=-1$ is

The number of ways in which 5 boys and 3 girls can be seated on a round table, if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other, is

The value of $\cot \left(\operatorname{cosec}^{-1} \frac{5}{3}+\tan ^{-1} \frac{2}{3}\right)$ is