The question given below is followed by three statements. Study the question and the statements. Identify which option is necessary to answer the question.

A right-angled triangle is inscribed in a given circle. What is the area of the given circle$($ in $\left.{\mathrm{cm}}^2\right)$ ?

I. The base and the height of the triangle (in $\mathrm{cm}$ ) are both the roots of the equation .

II. The sum of the base and the height of the triangle is $23 \mathrm{cm}$.

III. The height of the right-angled triangle is greater than the base of the same.

The question given below is followed by three statements. Study the question and the statements. Identify which option is necessary to answer the question.

What is the ratio of the marked price of two identical items, A and B, which had been purchased at the same price?

I. Item A was sold at a profit of $20\%$, while item B was sold at a loss of $10\%$.

II. Item A was sold at a discount of $16\frac{2}{3}\%$. The percentage by which item B's cost price had been marked up is the same as the profit $\%$earned on selling item A.

III. The overall profit earned on selling items A and B was ₹ $576$.

The question given below is followed by three statements. Study the question and the statements. Identify which option is necessary to answer the question.

Three workers A, B and C complete a given piece of work within different time spans, while working individually. What is the ratio of efficiency of C to that of B?

I. A takes $100\%$ more time than C to complete the given piece of work.

II. B completes the given piece of work in $8$ days.

III. B takes $2$ days less than A to complete the given piece of work.

The question given below is followed by three statements. Study the question and the statements. Identify which option is necessary to answer the question.

What is a three-digit number having each digit different from the other?

I. Each of the digits of the given number is a multiple of $3$

II. The digit in the unit's place is $50 \%$ less than that in the hundred's place.

III. Sum of digits is $18$.