Statement 1: An increase in entropy leads to decrease of randomness.
Statement 2: The lower energy states of ordered crystals have a high entropy.
A.Statement 1 and statement 2 are correct and statement 2 is the correct explanation of statement 1
B.Both the statement 1 and statement 2 are correct and statement 2 is not the correct explanation of statement 1
C.Statement 1 is correct but statement 2 is incorrect
D.Statement 1 is incorrect but statement 2 is correct
E.Both the statement 1 and statement 2 are incorrect

Hint: Entropy is associated with the order or disorder in a thermodynamic system. Entropy and randomness are interconnected terms. In an ordered crystal the atoms are tightly packed in a lattice and they only move very less.

Complete step by step answer:
The question above mainly focuses on a very important thermodynamic variable termed ‘entropy’. Entropy is denoted as $ S $ , which serves to establish the criteria of the spontaneity of processes. Entropy is an extensive variable defined in terms of differences, by the relationship:
  $ \Rightarrow dS = \dfrac{{d{q_{rev}}}}{T} $
Where, $ dS $ is the entropy change that occurs when a system undergoes an infinitesimally small change of state at $ TK $ and $ d{q_{rev}} $ is the infinitesimally small quantity of the heat absorbed reversibly by it during the process. As we know, the above equation represents the mathematical formulation of the second law of thermodynamics.
Although it is difficult to assign an absolute definition to the term ‘entropy’, in terms of its physical significance, we may describe it as follows:
“Entropy is a property which is a measure of disorder or randomness in a system; the greater the disorder, the greater the entropy.”
From this definition, it is clear that statement 1 is incorrect, as an increase in entropy leads to an increase in randomness.
For a given substance, its entropy is related to its physical state and increases in the order of increasing disorder:
Solid $ < $ liquid $ < $ gas
So in the case of an ordered crystal which is in solid-state, we know that the atoms are tightly packed in a crystal lattice and they are unable to move freely. So, in a state of low energy, the movement is further decreased and the disorder is much lower and hence the randomness is also reduced.
From this, it is clear for us that statement 2 is also incorrect, as the lower energy states of ordered crystals have a lower entropy.
As you can see, from the above explanations we can conclude that both the statements are incorrect.

So, the correct answer is Option E .

Note:
Clausius invented the idea of entropy as a precise means of describing the second law of thermodynamics to provide an objective indicator for the direction of the spontaneous transition. Entropy is an extensive characteristic such that its value depends on the quantity of a substance in the system. Note that it is also a state function, which means it is independent of the path followed in a process.