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Statement-1: The number of divisors of 1...

Statement-1: The number of divisors of 10! Is 280.
Statement-2: 10!=`2^(p)*3^(q)*5^(r)*7^(s)`, where p,q,r,s`in`N.

A

Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for statement-1

B

Statement-1 is true, statement-2 is true, statement-2 is not a correct explanation for statement-1

C

Statement-1 is true, statement-2 is false

D

Statement-1 is false, statement-2 is true

Text Solution

Verified by Experts

The correct Answer is:
D
`because 10!=2(8)*3^(4)*5^(2)*7^(1)`
`therefore`Total number of divisors
`=(8+1)(4+1)(2+1)(1+1)=270`
hence, statement-1 is false and statement-2 is true.
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