Question

A card is drawn at random from a pack of 900 cards numbered 101 to 1000. The probability of getting a number which is a perfect square as well as a perfect cube is

• A. $\frac{1}{900}$
  
• B. $\frac{1}{450}$
  
• C. $\frac{1}{300}$
  
• D. $\frac{1}{225}$
  

Answer 1

The correct option is A $\frac{1}{900}$


Total number of cards = 900
From the numbers, 101 to 1000, only 729 is the number which is a perfect square as well as a perfect cube as, ${27}^2=9^3=729$.
$\therefore \text{Number of favourable outcomes}=1$
$\therefore \text{Required Probability}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
$=\frac{1}{900}$
Hence, the correct answer is option (a).