The correct increasing order of basic strength of amine is:

(A)	$C_6{H}_5{\mathrm{NH}}_2<{\mathrm{NH}}_3<C_6{H}_5{\mathrm{CH}}_2{\mathrm{NH}}_2<C_2{H}_5{\mathrm{NH}}_2<(C_2{H}_5{)}_2\mathrm{NH}$
(B)	${\mathrm{NH}}_3<C_6{H}_5{\mathrm{NH}}_2<C_6{H}_5{\mathrm{CH}}_2{\mathrm{NH}}_2<C_2{H}_5{\mathrm{NH}}_2<(C_2{H}_5{)}_2\mathrm{NH}$
(C)	$C_6{H}_5{\mathrm{CH}}_2{\mathrm{NH}}_2<C_6{H}_5{\mathrm{NH}}_2<{\mathrm{NH}}_3<C_2{H}_5{\mathrm{NH}}_2<(C_2{H}_5{)}_2\mathrm{NH}$
(D)	$C_2{H}_5{\mathrm{NH}}_2<(C_2{H}_5{)}_2\mathrm{NH}<C_6{H}_5{\mathrm{NH}}_2<{\mathrm{NH}}_3$

$\text{Choose the correct answer from the options given below:}$

The correct option is (A) only, which corresponds to the following correct increasing order of basic strength:
$$C_6{H}_5{\mathrm{NH}}_2<{\mathrm{NH}}_3<C_6{H}_5{\mathrm{CH}}_2{\mathrm{NH}}_2<C_2{H}_5{\mathrm{NH}}_2<(C_2{H}_5{)}_2\mathrm{NH}$$

To understand why this order is correct, we can analyze the basic strength of each chemical species based on the availability of the lone pair of electrons on the nitrogen atom to accept a proton (H⁺). Factors that increase electron density on the nitrogen atom increase basicity, whereas factors that decrease electron density decrease basicity.

1. Aniline ($C_6{H}_5{\mathrm{NH}}_2$):
In aniline, the lone pair of electrons on the nitrogen atom is conjugated with the π-electron system of the benzene ring. This resonance delocalization makes the lone pair significantly less available for protonation. Therefore, aniline is the weakest base in the given series.

2. Ammonia (${\mathrm{NH}}_3$):
In ammonia, there is no resonance or electron-withdrawing/donating group. The lone pair on nitrogen is fully localized, making it more basic than aniline where the lone pair is delocalized into the aromatic ring.

3. Benzylamine ($C_6{H}_5{\mathrm{CH}}_2{\mathrm{NH}}_2$):
In benzylamine, the nitrogen atom is attached to an sp³-hybridized carbon atom ($-{\mathrm{CH}}_2-$), which isolates the nitrogen's lone pair from direct conjugation with the benzene ring. Hence, no resonance delocalization occurs. However, the benzyl group ($-{\mathrm{CH}}_2{C}_6{H}_5$) exerts a mild electron-withdrawing inductive effect (-I effect) due to the sp²-hybridized carbons of the phenyl ring compared to simple alkyl groups. Consequently, it is stronger than ammonia but weaker than simple aliphatic alkylamines.

4. Ethylamine ($C_2{H}_5{\mathrm{NH}}_2$) and Diethylamine ($(C_2{H}_5{)}_2\mathrm{NH}$):
Alkyl groups release electrons via the inductive effect (+I effect), which increases the electron density on the nitrogen atom and stabilizes the conjugate acid. Thus, aliphatic amines are stronger bases than benzylamine, ammonia, and aniline.
Comparing ethylamine (a primary amine) and diethylamine (a secondary amine) in aqueous medium:
Secondary amines are stronger bases than primary amines because of the cumulative +I effect of two ethyl groups, which dominates over steric hindrance and solvation effects for ethyl-substituted amines. Therefore, diethylamine is the most basic species in this sequence.

Combining all the analyses, we obtain the increasing order of basic strength:
$$C_6{H}_5{\mathrm{NH}}_2<{\mathrm{NH}}_3<C_6{H}_5{\mathrm{CH}}_2{\mathrm{NH}}_2<C_2{H}_5{\mathrm{NH}}_2<(C_2{H}_5{)}_2\mathrm{NH}$$ This perfectly matches statement (A).