At what $pH$ will an indicator with $K_b = 1 \times 10^{-11}$ show a color change in a $1 \times 10^{-4} \ M$ solution?

The rapid change of $pH$ near the stoichiometric point of an acid-base titration is the basis of indicator detection. The $pH$ of the solution is related to the ratio of the concentrations of the conjugate acid $(HIn)$ and base $(In^{-})$ forms of the indicator by the expression:

Which of the following statements is incorrect regarding the use of indicators in acid-base titration?

The different colours of litmus in acidic, neutral and basic solutions are, respectively.

Which indicator is used for the titration of a weak acid (oxalic acid) and a strong base (caustic soda)?

The pink colour of phenolphthalein in an alkaline medium is due to -