The number of surjections from A -1-2-3- - n - n lgeql 2 onto B - a - b isA- None of these B- n P -2C- 2 n -1D- 2 n -2

The correct option is D 2^n 2Number of surjections from A onto B is ∑_r=1^n( 1)^n r^nC_r r^m, provided m ≥ n =∑_n^r=1( 1)^2 r^2C_r r^n=( 1) ^12C_1^n + ( 1)^02 ...

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Standard XII

Mathematics

Definition of Functions

The number of...

Question

The number of surjections from A = {1, 2, 3, …………….. ,n}, n $\geq$ 2 onto B = {a, b} is

^{n} P - 2

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2^{n} - 2

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2^{n} - 1

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N o n e o f t h e s e

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Solution

The correct option is B $2^{n} - 2$
Number of surjections from A onto B is
$\sum_{r = 1}^{n} (- 1)^{n - r}^{n} C_{r} r^{m}$ , provided m $\geq$ n
$= \sum_{n}^{r = 1} (- 1)^{2 - r}^{2} C_{r} r^{n} = (- 1)^{12} C_{1}^{n} + (- 1)^{02} C_{2} 2^{n}$
$= - 2 + 2^{n} = 2^{n} - 2$

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The number of surjections from A = {1, 2, 3, …………….. ,n}, n \(\geq\) 2 onto B = {a, b} is

The correct option is B 2n−2Number of surjections from A onto B is ∑nr=1(−1)n−rnCrrm, provided m ≥ n =∑r=1n(−1)2−r2Crrn=(−1)12Cn1+(−1)02C22n =−2+2n=2n−2

The correct option is B $2^{n} - 2$
Number of surjections from A onto B is
$\sum_{r = 1}^{n} (- 1)^{n - r}^{n} C_{r} r^{m}$ , provided m $\geq$ n
$= \sum_{n}^{r = 1} (- 1)^{2 - r}^{2} C_{r} r^{n} = (- 1)^{12} C_{1}^{n} + (- 1)^{02} C_{2} 2^{n}$
$= - 2 + 2^{n} = 2^{n} - 2$