A plane passes through $(1,-2,1)$ and is perpendicular to two planes $2 x-2 y+z=0$ and $x-y+2 z=4$. The distance of the plane from the point $(1,2,2)$ is:

If $f(x)=\min \left\{1, x^2, x^3\right\}$, then

A tangent drawn to the curve $y=f(x)$ at $\mathrm{P}(x, y)$ cuts the X -axis and Y -axis at A and B respectively such that $\mathrm{BP}: \mathrm{AP}=3: 1$, given that $f(1)=1$, then

If a hyperbola passes through the focus of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ and its transverse and conjugate axes coincide with the major and minor axes of the ellipse, and the product of eccentricities is 1 , then