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Suppose a(2),a(3),a(4),a(5),a(6),a(7) ar...

Suppose `a_(2),a_(3),a_(4),a_(5),a_(6),a_(7)` are integers such that
`5/7=(a_(2))/(2!)+(a_(3))/(3!)+(a_(4))/(4!)+(a_(5))/(5!)+(a_(6))/(6!)+(a_(7))/(7!),`
where `0lea_(j)ltj"for "j=2,3,4,5,6,7.` The sum `a_(2)+a_(3)+a_(4)+a_(5)+a_(6)+a_(7)` is-

A

8

B

9

C

10

D

11

Text Solution

Verified by Experts

The correct Answer is:
B
`5xx6!=2520a_(2)+840a_(3)+210a_(4)+42a_(5)+7a_(6)+a_(7)`
`:. 3600=2520a_(2)+840a_(3)+210a_(4)+42a_(5)+7a_(6)+a_(7)`
Now`a_(j)inI{"from "2" to "7}`
soabove equation is true if
`a_(2)=a_(3)=a_(4)=1`
`a_(5)=0`
`a_(6)=4,a_(7)=2`
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