1.

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!).

Answer»

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

Solution :`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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