Which of the following acids has the lowest $pK_a$ value?

The cubic equation whose roots are thrice to each of the roots of $x^3+2 x^2-4 x+1=0$ is

The product of the perpendicular distances from the origin to the pair of straight lines $12x^2+25xy+12y^2+10x+11y+2=0$ is

$A$ metal $M$ and its compound can give the following observable changes in a sequence of reactions: $M$ $\xrightarrow{\text{dil. } HNO_3} M(NO_3)_2$ $\xrightarrow{NaOH} \text{White ppt.}$ $\xrightarrow{\text{Excess } NaOH} \text{Colourless solution}$ $\xrightarrow{H_2S} \text{White ppt.}$. Identify the metal $M$.

If for some reason our goblet cells are non-functional,this will adversely affect:

If $x=p+q$,$y=p \omega+q \omega^2$,and $z=p \omega^2+q \omega$,where $\omega$ is a complex cube root of unity,then $xyz$ is equal to: