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If (a, a²) falls inside the angle made by the lines y = x/2, x > 0 and y = 3x, x > 0, then a belong to

1. (0, 1/2)
2. (3, ∞)
3. (1/2, 3)
4. (−3, −1/2)

Correct answer: (1/2, 3)

Solution

The point (a, a²) must lie between the lines y = x/2 and y = 3x for positive x values. For a to satisfy this condition, its corresponding y-value a² must be greater than x/2 and less than 3x, which leads to the conclusion that a must be in the interval (1/2, 3).

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