InterviewSolution
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InterviewSolution
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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-1B. Statement-1 is true, statement-2 is true, statement-2 is not a correct explanation for statement-1C. Statement-1 is true, statement-2 is falseD. Statement-1 is false, statement-2 is true |
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Answer» Correct Answer - 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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