In the adjoining diagram, AB = x cm, BC = y cm and x - y = 7 cm. Area of △ ABC = 30 cm². The length of AC is :

1. 10 cm

2. 12 cm

3. 13 cm

4. 15 cm

If p, q, and r are in continued proportion, then :

1. p : q = p : r

2. q : r = p² : q²

3. p : q² = r : p²

4. p : r = p² : q²

If the polynomial 2x³ + 3x² - 2x - 3 is completely divisible by (2x + a), and the quotient is equal to (x² - 1), then one of the values of a is :

1. -3

2. -1

3. 1

4. 3

A polynomial in x is x³ + 5x² - kx - 24. Which of the following is a factor of the given polynomial so that the value of k is 2?

1. (x + 2)

2. (x - 3)

3. (x + 4)

4. (x - 4)