(i)
When HCN reacts with a compound, the attacking species is a nucleophile, CN⁻. Therefore, as the negative charge on the compound increases, its reactivity with HCN decreases. In the given compounds, the +I effect increases as shown below. It can be observed that steric hindrance also increases in the same.

Hence, the given compounds can be arranged according to their increasing reactivities toward HCN as:

Di-tert-butyl ketone < Methyl tert-butyl ketone < Acetone < Acetaldehyde

(ii) After losing a proton, carboxylic acids gain a negative charge as shown:

$\mathrm{R}-\mathrm{COOH}\to \mathrm{R}-{\mathrm{COO}}^{-}+{\mathrm{H}}^{+}$

Now, any group that will help stabilize the negative charge will increase the stability of the carboxylate ion and as a result, will increase the strength of the acid.

Thus, groups having the +I effect will decrease the strength of the acids, and groups having a −I effect will increase the strength of the acids. In the given compounds, the −CH₃ group has a +I effect, and Br− atom has a −I effect. Thus, acids containing Br− are stronger.

Now, the +I effect of the isopropyl group is more than that of the n-propyl group. Hence, (CH₃)₂CHCOOH is a weaker acid than CH₃CH₂CH₂COOH.

Also, the −I effect of an electronegative element gets weaker as distance increases. Hence, CH₃CH(Br)CH₂COOH is a weaker acid than CH₃CH₂CH(Br)COOH.

Hence, the strengths of the given acids increase as:

(CH₃)₂CHCOOH < CH₃CH₂CH₂COOH < CH₃CH(Br)CH₂COOH < CH₃CH₂CH(Br)COOH

(iii)

As we have seen in the previous case, electron-donating groups decrease the strengths of acids, while electron-withdrawing groups increase the strengths of acids.

As the methoxy group is an electron-donating group, 4-methoxybenzoic acid is a weaker acid than benzoic acid.

The Nitro group is an electron-withdrawing group and will increase the strengths of acids. As 3,4-dinitrobenzoic acid contains two nitro groups, it is a slightly stronger acid than 4-nitrobenzoic acid. Hence, the strengths of the given acids increase as:

4-Methoxybenzoic acid < Benzoic acid < 4-Nitrobenzoic acid < 3,4-Dinitrobenzoic acid