(i) Listen to me, Ravi!

The sentence “Listen to me, Ravi! “Is an exclamatory sentence.

∴ It is not a statement.

(ii) Every set is a finite set.

This sentence is always false, because there are sets which are not finite.

∴ It is a statement.

(iii) Two non-empty sets have always a non-empty intersection.

This sentence is always false, because there are non-empty sets whose intersection is empty.

∴ It is a statement.

(iv) The cat ***** is black.

There are some cats which are black, and not black, So, the given sentence may or may not be true.

∴ It is not a statement.

(v) Are all circles round?

The given sentence is an interrogative sentence.

∴ It is not a statement.

(vi) All triangles have three sides.

The given sentence is a true declarative sentence.

∴ It is a true statement.

(vii) Every rhombus is a square.

This sentence is always false, because Rhombuses are not a square.

∴ It is a statement.

(viii) x² + 5|x| + 6 = 0 has no real roots.

Firstly, let us solve the given expression.

If x > 0,

x² + 5|x| + 6 = 0

x² + 5x + 6 = 0

x = -3 or x = -2

Since x > 0, the equation has no roots.

If x < 0,

x² + 5|x| + 6=0

x² – 5x + 6=0

Since x < 0, the equation has no real roots.

∴ It is a statement.

(ix) This sentences is a statement.

The statement is not indicating the correct value, hence we can say that value contradicts the sense of the sentence.

∴ It is not a statement.

(x) Is the earth round?

The given sentence is an interrogative sentence.

∴ It is not a statement.