If $x=a \sin 2 t(1+\cos 2 t), y=b \cos 2 t(1-\cos 2 t)$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

The contrapositive of the statement $\sim p \vee(q \wedge \sim r)$ is

If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-\mathrm{k}}{2}=\frac{\mathrm{z}}{1}$ intersect, then the value of k is

If $y=\sqrt{x+\sqrt{y+\sqrt{x+\sqrt{y+\ldots \ldots \ldots \ldots \ldots \ldots . \infty}}}}$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}=$