Question : The third proportional of $a$ and $\frac{b^4}{4a}$ is:

Option 1: $\frac{b^8}{16 a^2}$

Option 2: $\frac{b^8}{8 a^2}$

Option 3: $\frac{b^8}{8 a^3}$

Option 4: $\frac{b^8}{16 a^3}$

Question : A, B, and C made certain investments and the ratio of their time periods is 3 : 2 : 7 respectively. The ratio of the profits of A, B, and C is 4 : 3 : 14 respectively. What is the ratio of the investments of A, B, and C?

Option 1: 1 : 3 : 4

Option 2: 7 : 9 : 11

Option 3: 8 : 9 : 12

Option 4: 2 : 3 : 11

Question : The lengths of the two adjacent sides of a rectangle inscribed in a circle are 5 cm and 12 cm, respectively. Then, the radius of the circle will be:

Option 1: 6 cm

Option 2: 6.5 cm

Option 3: 8 cm

Option 4: 8.5 cm

Question : A person marks an article 36% above the cost price and offers a 30% discount on the marked price. What is the loss or gain percentage?

Option 1: Loss 6.5%

Option 2: Loss 4.8%

Option 3: Gain 8.5%

Option 4: Gain 7.2%

Question : A and B can do a piece of work in 5 days and 10 days, respectively. They began the work together but A left after some days and B finished the remaining work in 8 days. After how many days did A leave?

Option 1: $3\frac{1}{8}$

Option 2: $5\frac{1}{8}$

Option 3: $6\frac{1}{8}$

Option 4: $\frac{2}{3}$