The entities which do not dissociate into simple ions are:

(A)    \([Fe(CN)_6]^{4-}\)

(B)    \(KCl.MgCl_2. 6H_2O\)

(C)    \(K_4[Fe(CN)_6]\)

(D)   \(KAl(SO_4)_2. 12H_2O\)

(E)    \(FeSO_4.(NH_4)_2SO_4.6H_2O\)

Choose the correct answer from the options given below:

(A) and (C) only

The entities that do not dissociate into simple ions are those that remain as intact compounds without breaking into individual ions when dissolved in water. Let's analyze each option:
(A) \([Fe(CN)_6]^{4-}\): This is a complex ion and does not dissociate into simple ions when dissolved in water.
(B) \(KCl.MgCl_2. 6H_2O\): This appears to be a combination of salts and water molecules, but when dissolved in water, it will dissociate into K⁺, Cl⁻, Mg²⁺ ions, and water molecules.
(C) \(K_4[Fe(CN)_6]\): This is a complex salt, but when dissolved in water, it will dissociate into K⁺, Fe³⁺, and [Fe(CN)₆]⁴⁻ ions.
(D) \(KAl(SO_4)_2. 12H_2O\): This compound contains water of crystallization, but when dissolved in water, it will dissociate into K⁺, Al³⁺, SO₄²⁻ ions, and water molecules.
(E) \(FeSO_4.(NH_4)_2SO_4.6H_2O\): This compound also contains water of crystallization, but when dissolved in water, it will dissociate into Fe²⁺, NH₄⁺, SO₄²⁻ ions, and water molecules.
So, the entities that do not dissociate into simple ions are (A) \([Fe(CN)_6]^{4-}\) and (C) \(K_4[Fe(CN)_6]\). The correct answer is option (1) - (A) and (C) only.