Active transport of ions by the cell requires

The perpendicular distance from the point $(1, \pi)$ to the line joining $(1, 0^{\circ})$ and $(1, \frac{\pi}{2})$ (in polar coordinates) is:

The gas used in the hydrogenation of vegetable oils in the presence of nickel as catalyst is

Give the correct order of initials $T$ or $F$ for the following statements. Use $T$ if the statement is true and $F$ if it is false.
$(I)$ Sulphide ions react with $Na_2[Fe(CN)_5(NO)]$ to form a purple-coloured compound $Na_4[Fe(CN)_5(NOS)]$. In the reaction,the oxidation state of iron changes.
$(II)$ $Pt(IV)$ compounds are relatively more stable than $Ni(IV)$ compounds.
$(III)$ The welding of magnesium can be done in an atmosphere of Helium.
$(IV)$ $LiAlH_4$ on hydrolysis will give $H_2$.

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:

Mass $M$ is divided into two parts $xM$ and $(1-x)M$. For a given separation,the value of $x$ for which the gravitational attraction between the two pieces becomes maximum is