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Statement-1: The smallest positive integ...

Statement-1: The smallest positive integer n such that n! can be expressed as a product of n-3 consecutive integers, is 6.
Statement-2: Product of three consecutive integers is divisible by 6.

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:
B
Statement-1 is true
`therefore6!=720=8xx9xx10` i.e., product off 6-3=3 consecutive integers and statement-2 is also true, but statement-2 is not a correct explanation for statement-1.
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Knowledge Check

  • The product of r consecutive integers is divisible by

    A
    `r!`
    B
    `(r-1)!`
    C
    `(r+1)!`
    D
    none of these

  • The sum of the cubes of three consecutive integers is divisible by

    A
    36
    B
    18
    C
    12
    D
    9

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