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Statement-1: If f:{a(1),a(2),a(3),a(4),a...

Statement-1: If `f:{a_(1),a_(2),a_(3),a_(4),a_(5)}to{a_(1),a_(2),a_(3),a_(4),a_(5)}`, f is onto and `f(x)nex` for each
`xin {a_(1),a_(2),a_(3),a_(4),a_(5)}`, is equal to 44.
Statement-2: The number of derangement for n objects is
`n! sum_(r=0)^(n)((-1)^(r))/(r!)`.

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:
a
`becauseD_(n)=n!underset(r=0)overset(n)(sum)((-1)^(r))/(r!)=n!(1-(1)/(1!)+(1)/(2!)-(1)/(3!)+ . . .+((-1)^(n))/(n!))`
`thereforeD_(5)=5!(1-(1)/(1!)+(1)/(2!)-(1)/(3!)+(1)/(4!)-(1)/(5!))`
`=120((1)/(2)-(1)/(6)+(1)/(24)-(1)/(120))`
`=6-20+5-1`
`=65-21`
=44
Hence, statement-1 is true, statement-2 is true and statement-2 is a correct explanation for statement-1.
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