1. If \(b ∝ a^3\) and \(a\) increases in the ratio \(2:3\), then determine the ratio in which \(b\) increases.

2. If \(b ∝ a^2\) and \(a\) increases in the ratio \(2:3\), then determine the ratio in which \(b\) increases.

3. If \(b\propto a^3\) and \(a\) increases in the ratio \(2:3\), determine the ratio in which \(b\) will increase.

4. If \(b ∝ a^3\) and the increase in \(a\) is in the ratio \(2 : 3\), then determine the ratio of increase in \(b\).

5. If \(y \propto x^3\) and \(x\) increases in the ratio \(2:3\), then determine the ratio in which \(y\) increases.

6. PQRS is a cyclic quadrilateral in which side QR is extended up to point T. If the measures of angles ∠SRQ and ∠SRT are in the ratio 4:5, then find the measures of ∠SPQ and ∠SRQ.

7. If \(A = \frac{4}{3}B\) and \(B = \frac{5}{4}C\), then find the ratio \(A : B : C\).

(a) 20 : 15 : 16 (b) 15 : 20: 16 (c) 16: 15 : 20 (d) 15 : 16 : 20

8. If two individuals invest \(a\) currency units and \(b\) currency units in a business for \(x\) and \(y\) months respectively, then their profit ratio is -

(a) \(ay:bx\) (b) \(ab:xy\) (c) \(ax:by\) (d) none of the above

9. If the quadratic equation \(ax^2 + 7x + b = 0\) has roots \(\cfrac{2}{3}\) and \(-3\), then find the values of \(a\) and \(b\).

10. If the quadratic equation \(ax^2 + 7x + b = 0\) has two roots \(\frac{2}{3}\) and \(-3\), then let us find the values of \(a\) and \(b\).

11. If \(a : b = 3 : 2\) and \(b : c = 3 : 2\), then find the value of the ratio \((a + b) : (b + c)\).

12. If the roots of the equation \(x^2 + ax + b = 0\) are \(-2\) and \(3\), then find the values of \(a\) and \(b\).

(a) 1,6 (b) -1,-6 (c) -1,6 (d) 1,-6