If domain and range of f(x){ = ^{9 - x}}{C_{x - 1}} contains m and n elements respective

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1.Relation and Function

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If the domain and range of $f(x){ = ^{9 - x}}{C_{x - 1}}$ contains $m$ and $n$ elements respectively, then

A

$m = n$

B

$m = n + 1$

C

$m = n -1$

D

$m = n + 2$

Solution

Clearly $9-x \geq 0, x-1 \geq 0 $ and $ 9-x-(x-1) \geq 0$

$\Rightarrow 1 \leq \mathrm{x} \leq 5, \quad \mathrm{x} \in \mathrm{I}$

$\therefore m=5$

Range of $f({\rm{x}}) = \,\left\{ {^8{{\rm{C}}_0},{\,^7}{{\rm{C}}_1},{\,^6}{{\rm{C}}_2},{\,^5}{{\rm{C}}_3},{\,^4}{{\rm{C}}_4}} \right\}$

or $\{1,7,15,10\}$

$\therefore n=4$

Standard 12

Mathematics

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