The increasing order of stability is for the following complexes will be:

A. \([Cu(NH_3)_4]^{2+}\)

B. \([Cu(CN)_4]^{2-}\)

C. \([Cu(en)^{2+}]\)

D. \([Cu(H_2O)_4]^{2+}\)

Choose the correct answer from the options given below:

\(D < A <  C < B\)

The correct answer is option 1. \(D < A <  C < B\).

\([Cu(H_2O)_4]^{2+}\) (Complex D): Water \((H_2O)\) is a moderately strong ligand. While it's not as strong as cyanide or ethylenediamine, it still forms relatively stable complexes. Thus, this complex is expected to be more stable than the complex with ammonia but less stable than the complexes with stronger ligands like ethylenediamine and cyanide.

\([Cu(NH_3)_4]^{2+}\) (Complex A): Ammonia \((NH_3)\) is a weaker ligand compared to water, cyanide, and ethylenediamine. Therefore, the complex formed with ammonia is expected to be the least stable among the given options.

\([Cu(en)^{2+}]\) (Complex C): Ethylenediamine (en) is a strong ligand, forming stable complexes with metal ions. This complex is expected to be more stable than both \([Cu(H_2O)_4]^{2+}\) and \([Cu(NH_3)_4]^{2+}\) but less stable than \([Cu(CN)_4]^{2-}\).

4. \([Cu(CN)_4]^{2-}\) (Complex B): Cyanide \((CN^-)\) is a very strong ligand, known for forming highly stable complexes with metal ions. Therefore, the complex formed with cyanide is expected to be the most stable among the given options.

Considering these factors, the correct stability order is indeed: Option 1: \(D < A < C < B\)

This arrangement aligns with the expected stability trends based on the strength of the ligands involved in each complex.