Which of the following statements is correct?

In a reaction of aniline,a coloured product $C$ was obtained as shown below:
$A$ $\xrightarrow{NaNO_2/HCl} B$ $\xrightarrow{N,N-dimethylaniline, \text{cold}} C$
The structure of $C$ would be:

Consider the following reaction sequence:
$p$-Nitrotoluene $\xrightarrow{P} Q$ $\xrightarrow{R} S$ $\xrightarrow{H_2O} T$
$S \xrightarrow{U} \text{Benzoic acid}$
Identify the correct statements from the following:
$(A) P = H_2/Pd, \text{ethanol}; R = NaNO_2/HCl; U = 1. H_3PO_2, 2. KMnO_4-KOH, \text{heat}$
$(B) P = Sn/HCl; R = HNO_2; S = p-\text{toluenediazonium chloride}$
$(C) S = p-\text{toluenediazonium chloride}; T = p-\text{cresol}; U = 1. CH_3CH_2OH, 2. KMnO_4-KOH, \text{heat}$
$(D) Q = p-\text{nitrobenzoic acid}; R = H_2/Pd, \text{ethanol}; T = p-\text{cresol}$
Which of the following combinations is correct?

The relative rate of reaction of the following amines with methyl iodide is:

Given below are two statements:
Statement-$I$ : Oxidation of $p$-nitrotoluene with acidic $KMnO_4$ gives an acid that is stronger than benzoic acid.
Statement-$II$ : Reduction of $p$-nitrotoluene with $Sn/HCl$ followed by neutralization gives an amine that is more basic than aniline.
In light of the above statements, choose the most appropriate answer from the options given below.

You have been given four bottles marked $A, B, C$ and $D$ each containing one of the organic compounds given below:

$I: C_6H_5CH_2NH_2$	$II: C_6H_5CH_2COOH$
$III: C_6H_5CH_2CH_3$	$IV: C_6H_5CH_2CH(NH_2)COOH$

The following observations were made:
$(i)$ The compound in bottle $A$ did not dissolve in either $1 \ N \ NaOH$ or $1 \ N \ HCl$.
$(ii)$ The compound in bottle $B$ dissolved in $1 \ N \ NaOH$ but not in $1 \ N \ HCl$.
$(iii)$ The compound in bottle $C$ dissolved in both $1 \ N \ NaOH$ and $1 \ N \ HCl$.
$(iv)$ The compound in bottle $D$ did not dissolve in $1 \ N \ NaOH$ but dissolved in $1 \ N \ HCl$.
$(a)$ Indicate the compounds in: bottle $A = \dots$,bottle $B = \dots$,bottle $C = \dots$ and bottle $D = \dots$.
$(b)$ The compound with the highest solubility in distilled water is .......