Probability
Exactly one perfect square among divisors
MMTS_Full_Test_18
Grade 12
Question:
Neha lists all positive divisors of $(2010)^2$. She randomly selects 2 distinct divisors. Probability that exactly one is a perfect square is
(A) $\dfrac{32}{81}$
(B) $\dfrac{26}{81}$
(C) $\dfrac{16}{81}$
(D) $\dfrac{34}{81}$
Step-by-Step Solution
Key Concept: $(2010)^2=2^2\cdot3^2\cdot5^2\cdot67^2$. Total divisors $=(2+1)^4=81$. Perfect square divisors$=(1+1)^4=16$. Non-square$=65$.
$P=\dfrac{26}{81}$.
Correct Answer: (B) $\dfrac{26}{81}$