If the curve $y=a x^2-6 x+b$ passes through $(0,4)$ and has its tangent parallel to the X-axis at $x=\frac{3}{2}$, then the values of $a$ and $b$ respectively are

The negation of $(p \wedge \sim q) \rightarrow(p \vee \sim q)$ is

If $\mathrm{a}\left(4+x^2\right)=x$ and $y-x^3=\mathrm{a}^2$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=1$ is $\qquad$

The equivalent statement of "If three vertices of a triangle are represented by cube roots of unity, then the triangle is an equilateral triangle" is