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Let A={1,2,..., n} and B={a , b }. Then ...

Let `A={1,2,..., n}` and `B={a , b` }. Then number of surjections from `A` into `B` is nP2 (b) `2^n-2` (c) `2^n-1` (d) nC2

A

`^(n)P_(2)`

B

`2^(n)-2`

C

`2^(n)-1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
The total number of mappings from A to B is `2^(n)` of which two 2 mappings f(x)=a for all x satisfying `1 le x lt n` and g(x)=b for all x satisfying `1 le x le n` are not surjective. Thus, the number of surjective mappings is `2^(n)-2`
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OBJECTIVE RD SHARMA ENGLISH-FUNCTIONS-Chapter Test
  1. Let A={1,2,..., n} and B={a , b }. Then number of surjections from A i...

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  2. The number of bijective functions from set A to itself when A contains...

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  3. If f(x)=|sin x| then domain of f for the existence of inverse of

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  4. The function f:[-1//2,\ 1//2]->[-pi//2,pi//2\ ] defined by f(x)=s in^(...

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  5. Let f: R->R be a function defined by f(x)=(e^(|x|)-e^(-x))/(e^x+e^(-x)...

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  6. If f: (e,oo) rarr R & f(x)=log[log (logx)], then f is - (a)f is one-...

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  7. Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) , where m!=n...

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  8. Find the inverse of the function: f(x)=(e^(x)-e^(-x))/(e^(x)+e^(-x))+2

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  9. Find the inverse of the function :y=(1 0^x-1 0^(-x))/(1 0^x+1 0^(-x))+...

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  10. Let f(x+(1)/(x))=x^(2)+(1)/(x^(2)),(x ne 0) then f(x) equals

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  11. Let f : R rarr R, g : R rarr R be two functions given by f(x) = 2x - 3...

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  12. If g(x)=1+sqrtx and f(g(x))=3+2sqrtx+x then f(x) is equal to

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  13. If f(x)=(1-x)/(1+x), x ne 0, -1 and alpha=f(f(x))+f(f((1)/(x))), then

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  14. Let f:R to R be a function defined by f(x)=(x^(2)-8)/(x^(2)+2). Then f...

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  15. If f:(-oo,2]to (-oo,4] where f(x), then f ^(-1) (x) is given by :

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  16. Find the inverse of the function, (assuming onto). " " ...

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  17. f: R->R is defined by f(x)=(e^(x^2)-e^(-x^2))/(e^(x^2)+e^(-x^2)) is :

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  18. If f(x)=log((1+x)/(1-x))a n dt h e nf((2x)/(1+x^2)) is equal to {f(x)...

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  19. If f(x)=(2^x+2^(-x))/2 , then f(x+y)f(x-y) is equals to 1/2{f(2x)+f(2y...

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  20. The function f:R to R given by f(x)=x^(2)+x is

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  21. Let f:R to R and g:R to R be given by f(x)=3x^(2)+2 and g(x)=3x-1 for ...

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