(i) Paris is in France, is a statement.

Paris is located in France, so the sentence is true.

So, the statement is true.

(ii) Each prime number has exactly two factors, is a statement.

This is a mathematically proven fact.

So, the statement is true.

(iii) The equation x² + 5|x| + 6 = 0 has no real roots.

Find the roots of x² + 5|x| + 6 = 0:

Case 1: x ≥ 0

x² + 5x + 6 = (x + 2)(x + 3) = 0 ⇒ x = −2, −3 but we already assumed x ≥ 0, which is a contradiction.

Case 2: x < 0

x² − 5x + 6 = (x − 2)(x − 3) = 0 ⇒ x = (2,3) but we already assumed x < 0, which is a contradiction.

So, equation x² + 5|x| + 6 = 0 has no real roots.

Therefore, the given sentence is true, and it is a statement.

(iv) (2 + √3) is a complex number, is a statement.

Complex numbers are in the form ‘a+ib’.

(2 + √3) cannot be expressed in ‘a+ib’ form,.

2 + √3 is not a complex number.

The given sentence is a statement, and it is false.

(v) Is 6 a positive integer?

This is an interrogative sentence, so it is not a statement.

(vi) The product of -3 and -2 is -6, is a statement.

Product of -3 and -2 = -3 x -2 = 6 ≠ -6

This statement is false.

(vii) The angles opposite the equal sides of an isosceles triangle are equal, is a statement.

It is a mathematically proven result.

So the given sentence is true.

(viii) Oh! it is too hot.

This is an exclamatory sentence, so it is not a statement.

(ix) Monika is a beautiful girl, is not a statement.

The given sentence is an opinion, can be true for some cases, false for some other case.

(x) Every quadratic equation has at least one real root, is a statement.

Because not every quadratic equation will have a real root.

So the given sentence is false.