$A$ $0.1 \ N$ solution of $Na_2CO_3$ is titrated with $0.1 \ N$ $HCl$ solution. The best indicator to be used is

In an acid-base titration,the rapid change in $pH$ near the equivalence point depends on the indicator used. 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 which equation?

Given below are two statements.
Statement $I:$ In the titration between a strong acid and a weak base,methyl orange is a suitable indicator.
Statement $II:$ For the titration of acetic acid with $NaOH$,phenolphthalein is not a suitable indicator.
In the light of the above statements,choose the most appropriate answer from the options given below:

The $pH$ range of methyl red indicator is .......?

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?

If we use phenolphthalein as an indicator in a titration of $Na_2CO_3$ with $HCl$,the usual result is: