Question

A class has $21$ students. The class teacher has been asked to make n groups of r students each and go to the zoo taking one group at a time. The size of the group i.e. the value of r for which the teacher goes to the zoo, the maximum number of times is (no group can go to the zoo twice)

• A. $9or10$
• B. $10or11$
• C. $11or12$
• D. $12or13$

Answer 1

The correct option is B

$10or11$

Explanation for the correct option:

Calculate the maximum number of times :

Given, that there are $21$ students

Since the teacher has to make $n$ groups of $r$ students, so the number of groups formed $={}^{21}C_r$

The number of times the teacher goes to the zoo is maximum when the number of groups formed is maximum.

The size of the group i.e. the value of $r$ for which the teacher goes to the zoo, the maximum number of times is (no group can go to the zoo twice)

$$\begin{gathered} r=\frac{21-1}{2}or\frac{21+1}{2} \\ \Rightarrow r=\frac{20}{2}or\frac{22}{2} \\ \Rightarrow r=10or11 \end{gathered}$$

Hence ,the correct option is (B).