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If ""^(n)P(r)=""^(n)P((r+1))and ""^(n)...

If ` ""^(n)P_(r)=""^(n)P_((r+1))`and `""^(n)C_(r) = ""^(n)C_(r-1),` then (n,r) =

A

`8,9`

B

`6,7`

C

`4,5`

D

`3,2`

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The correct Answer is:
D
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DIPTI PUBLICATION ( AP EAMET)-PERMUTATIONS & COMBINATIONS-EXERCISE 1B (COMBINATIONS )
  1. IF ""^(n) P(r)=720,""^(n)C(r)=120then (n,r)=

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  2. If ""^(n)P(r)=30240and ""^(n)C(r)=252 then the ordered pair (n,r)...

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  3. If ""^(n)P(r)=""^(n)P((r+1))and ""^(n)C(r) = ""^(n)C(r-1), then (n,...

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  4. If ""^(n)C(r)=""^(n)C(r-1) and ""^(n)P(r+1) = 9 .""^(n)P(r) then ...

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  5. ""^((n+1))C(3)-""^(n-1)C(3)=

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  6. ""^(2n)C(2)-2""^(n)C(2)=

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  7. If n and r are integers such that 1 le r le n then n. C (n-1...

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  8. IF n and r are positive inegers such that r le n then ""^(n) ...

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  9. If ""^(n)C(r) +""^(n) C(r+1)= ""^((n+1)) C(x) then x=

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  10. If ""^(15)C(4) +""^((n+5))C(5)=""^(16)C(5) then n=

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  11. ""^(n) C(r+1)+2""^(n)C(r) +""^(n)C(r-1)=

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  12. ""^(2n)C(n+1)+2. ""^(2n)C(n) + ""^(2n) C(n-1) =

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  13. ""^(n) C(r) + 4 . ""^(n) C(r-1) + 6 . ""^(n) C(r-2) + 4. ""^(n)C(r...

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  14. For 1 le r le n, the value of ""^(n)C(r) +""^(n-1) C(r) + ""^...

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  15. IF S= overset ( m) sum "" ^(n+r ) C(k), then

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  16. ""^(14) C(4) + overset(4) sum ( 18 - j ) C (3) =

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  17. ""^(47 ) C(4 )+ underset( j =1) overset( 5 ) sum ""^((52- j)) C(3)...

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  18. the value of ""^50C(4) + underset( r=1) overset( 6 ) sum ""^(56...

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  19. sum( r=0 )^ ( 10) ( 40 -r)C (5)=

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  20. The least value of n so that ""^(n) C(5) + ""^(n ) C(6) gt (...

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