If A = $\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & \cos \theta & \sin \theta \\ 0 & \sin \theta & −\cos \theta\end{array}\right)$, then which of the following are correct?

1. A + adj A is a null matrix

2. A−1 + adj A is a null matrix

3. A − A−1 is a null matrix

Select the correct answer using the code given below :

If X is a matrix of order 3 × 3, Y is a matrix of order 2 × 3 and Z is a matrix of order 3 × 2, then which of the following are correct?

1. (ZY)X is a square matrix having 9 entries.

2. Y(XZ) is a square matrix having 4 entries.

3. X(YZ) is not defined.

Select the correct answer using the code given below :

For how many quadratic equations, the sum of roots is equal to the product of roots?

Consider the following statements :

1. The set of all irrational numbers between $\sqrt{2}$ and $\sqrt{5}$ is an infinite set.

2. The set of all odd integers less than 100 is a finite set.

Which of the statements given above is/are correct?