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. \( g(x) = \cos(\pi x) \)
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If a, b, c are the sides of triangle ABC, then what is
\( \begin{vmatrix} a^{2} & b\sin A & c\sin A \\ b\sin A & 1 & \cos A \\ c\sin A & \cos A & 1 \end{vmatrix} \)
equal to?
If a, b, c are in AP; b, c, d are in GP; c, d, e are in HP, then which of the following is/are correct?
1. a, c and e are in GP
2. \( \frac{1}{a}, \frac{1}{c}, \frac{1}{e} \) are in GP
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If \( A = \begin{bmatrix} \sin 2\theta & 2\sin^{2}\theta - 1 & 0 \\ \cos 2\theta & 2\sin\theta\cos\theta & 0 \\ 0 & 0 & 1 \end{bmatrix} \), then which of the following statements is/are correct?
1. \( A^{-1} = adj A \)
2. A is skew-symmetric matrix
3. \( A^{-1} = A^{T} \)
Select the correct answer using the code given below.
