If $\mathrm{f}(x)=x^3+b x^2+c x+d$ and $0< b^2< c$, then in $(-\infty, \infty)$

If $\mathrm{f}\left(\frac{x-4}{x-2}\right)=2 x+1, x \in \mathbb{R}-\{1,-2\}$, then $\int \mathrm{f}(x) \mathrm{d} x$ is equal to

If $\sin (\theta-\alpha), \sin \theta$ and $\sin (\theta+\alpha)$ are in H.P., then the value of $\cos ^2 \theta$ is

The equation of the plane passing through the point $(1,1,1)$ and perpendicular to the planes $2 x-y-2 z=5$ and $3 x-6 y+2 z=7$ is