What number must be added to each of the numbers 7, 11 and 19 so that the resulting numbers may be in continued proportion?

1. −4

2. −3

3. 3

4. 4

Two numbers are in the ratio of 3 : 5. If 9 is subtracted from each, they are in the ratio of 12 : 23. The larger number is :

1. 40

2. 45

3. 55

4. 60

Six numbers a, b, c, d, e, f are such that ab = 1, bc = $\dfrac{1}{2}$, cd = 6, de = 2 and ef = $\dfrac{1}{2}$. What is the value of (ad : be : cf)?

1. 4 : 3 : 27

2. 6 : 1 : 9

3. 8 : 9 : 9

4. 72 : 1 : 9

If a = $\dfrac{4xy}{x+y}$, then $\Big(\dfrac{a+2x}{a-2x} + \dfrac{a+2y}{a-2y}\Big)$ equals :

1. 1

2. 2

3. $\dfrac{1}{2}$

4. none of these