If  log102,  log10(2x - 1), log10(2x + 3) are in AP, then what is x equal to?

Let S = {2, 3, 4, 5, 6, 7, 9}. How many different 3-digit numbers (with all digits different) from S can be made which are less than 500?

If p = (1111 ... up to n digits), then what is the value of 9p² + p?

The quadratic equation 3x² - (k² + 5k)x + 3k² - 5k = 0 has real roots of equal magnitude and opposite sign. Which one of the following is correct?