Which classification system was proposed by $Woese$?

The following band-energy diagram represents:

The $x-$intercept of the tangent to a curve is equal to the ordinate of the point of contact. The equation of the curve passing through the point $(1, 1)$ is

Which one of the following is a correct set?

The position of a particle moving in the $xy-$ plane at any time $t$ is given by $x = (3t^2 - 6t) \, m$ and $y = (t^2 - 2t) \, m$. Select the correct statement about the moving particle from the following:

$A$ point object is placed at a distance of $30 \, cm$ from a convex mirror of focal length $30 \, cm$. The image will form at