Question

Numbers from 1 to 5000 are written on 5000 separate slips (one number on one slip). These slips are kept in a bag and mixed well. If one slip is chosen from the bag without looking into it, then the probability that the number on the slip is a perfect square as well as a perfect cube is

• A. $\frac{1}{500}$
• B. $\frac{1}{1000}$
• C. $\frac{1}{1250}$
• D. $\frac{3}{5000}$

Answer 1

The correct option is C $\frac{1}{1250}$

Total number of slips in the bag$=5000$

no of ways of choosing a slip which is a perfect square and a perfect cube is the number of values of $n^6$ such that

$nϵN$ and $n^6<5000$

i.e., for only $n=1,2,3$ and $4$ $n^6<5000$ is possible

so, no of ways of choosing a slip which is perfect square and perfect cube is $4$

probability of choosing $=\frac{4}{5000}=\frac{1}{1250}$