Consider the following statements:
1. If \( (a + b) \) is directly proportional to \( (a - b) \), then \( (a^{2} + b^{2}) \) is directly proportional to ab.
2. If a is directly proportional to b, then \( (a^{2} - b^{2}) \) is directly proportional to ab.
Which of the statements given above is/are correct?
The combined age of a man and his wife is 6 times the combined age of their children. Two years ago their combined age was 10 times the combined age of their children; and six years later their combined age will be 3 times the combined age of their children. How many children do they have if each child is at least 2 years old?
Which one of the following is a value of \( \theta \), if \( \theta \) satisfies the equation \( \tan 2\theta \tan 4\theta - 1 = 0 \); \( 0 < \theta < \frac{\pi}{2} \)?
