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Mathematics

Functions

Easy

Question

The number of functions from {1,2,3,.....20} onto {1,2,3,......,20} such that f(k) is a multiple of 3 whenever K is a multiple of 4 is

$(15)! \times 6!$
$5^{6} \times 15$
$5! \times 6!$
$6^{5} \times (15)!$

The correct answer is: $left parenthesis 15 right parenthesis factorial cross times 6 factorial$

$text Multiples of end text 4 text are end text 4 comma 8 comma 12 comma 16 comma 20 semicolon text Multiples of end text 3 text are end text 3 comma 6 comma 9 comma 12 comma 15 comma 18 4 comma 8 comma 12 comma 16 comma 20 text mapped to end text 3 comma 6 comma 9 comma 12 comma 15 comma 18 text in end text 6 cross times 5 cross times 4 cross times 3 cross times 2 equals 6 factorial text ways. end text text Remaining end text 15 text numbers mapped in end text 15 factorial text ways. end text therefore text The number of onto (bijective) functions is end text 6 factorial cross times 15 factorial$

Related Questions to study

The number of linear functions which map from $text end text left square bracket negative 1 comma 1 right square bracket text onto end text left square bracket 0 comma 2 right square bracket text is end text$

The number of linear functions which map from $text end text left square bracket negative 1 comma 1 right square bracket text onto end text left square bracket 0 comma 2 right square bracket text is end text$

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Let A and B are two sets such that $A intersection B equals left curly bracket 1 comma 2 right curly bracket comma A union B equals left curly bracket 1 comma 2 comma 3 comma 4 comma 5 right curly bracket text . If end text n subscript 1 comma n subscript 2 text are end text$ maximum and minimum number of functions from A to B respectively, then n₁ - n₂ =

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If a set A contains 10 elements and a set B contains 20 elements then the number of functions from A into B is

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Consider the function $f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 2 x plus 3 comma x less or equal than 1 end cell row cell negative x squared plus 6 comma x greater than 1 end cell end table close$ . then draw the graph of the function $y equals vertical line f left parenthesis x right parenthesis vertical line$

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Two hours after 10 o’clock is _____.

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1 hour before 1 o’clock is ____.

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