Let X be a matrix of order 3 x 3, Y be a matrix of order 2 x 3 and Z be a matrix of order 3 × 2. Which of the following statements are correct?

I. (ZY)X is defined and is a square matrix of order 3.

II. Y(XZ) is defined and is a square matrix of order 2.

III. X(YZ) is not defined.

Select the answer using the code given below.

Consider the following statements:

I. The set of all irrational numbers between $\sqrt{12}$ and $\sqrt{15}$ is an infinite set.

II. The set of all odd integers less than 1000 is a finite set.

Which of the statements given above is/are correct?

How many 4-digit numbers are there having all digits as odd? 

If ω ≠ 1 is a cube root of unity, then what is (1 + ω - ω²)¹⁰⁰ + (1 - ω + ω²)¹⁰⁰ equal to?