For the next two (2) items that follow:
Consider the function \( f(x) = \frac{a^{[x]+x} - 1}{[x] + x} \), where [.] denotes the greatest integer function.
For the next two (2) items that follow:
Let \( z_{1} \), \( z_{2} \) and \( z_{3} \) be non-zero complex numbers satisfying \( z^{2} = i\bar{z} \), where \( i = \sqrt{-1} \).
Consider the following statements:
1. \( z_{1}z_{2}z_{3} \) is purely imaginary.
2. \( z_{1}z_{2} + z_{2}z_{3} + z_{3}z_{1} \) is purely real.
Which of the above statements is/are correct?
For the next two (2) items that follow:
Given that \( \log_{x} y \), \( \log_{z} x \), \( \log_{y} z \) are in GP, xyz = 64 and \( x^{3} \), \( y^{3} \), \( z^{3} \) are in AP.
Which one of the following is correct?
x, y and z are
