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How many odd perfect squares are divisors of the product 1!2! ....9! ?

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How many odd perfect squares are divisors of the product 1!2! ....9! ?

(A)  22 

(B)  42 

(C)  30

(D)  None of these

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Correct option  (C) 30

Exponent of 3 in 2!.3!5! ....9! = 1 + 1 + 1 + 1 + 1+ 1 + 3 = 9

Exponent of 5 in 2!.3!.5!....9! = 1 + 1 + 1 + 1 + 1 = 5

Exponent of 7 in 2!.3!.5! .....9! = 1 + 1 + 1 = 3

⇒ Number of odd perfect squares = 5 x 3 x 2 = 30

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