If ABC is a triangle, then what is the value of the determinant

$$ \left|\begin{array}{ccc} \cos C & \sin B & 0 \\ \tan A & 0 & \sin B \\ 0 & \tan (B+C) & \cos C \end{array}\right| ? $$

What is the number of different matrices, each having 4 entries that can be formed using 1, 2, 3, 4 (repetition is allowed)?

Let $A = \{x \in \mathbb{R} : -1 <x <1\}$. Which of the following is/are bijective functions from A to itself?

1. $f(x) = x|x|$

2. $g(x) = \cos(\pi x)$

Select the correct answer using the code given below:

Let $R$ be a relation on the open interval $(-1, 1)$ and is given by $R = \{(x, y) : |x + y| < 2\}$. Then which one of the following is correct?