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If "^(n-1)Cr : ^nCr : ^(n+1)Cr= 6:9: 13,...

If `"^(n-1)C_r : ^nC_r : ^(n+1)C_r= 6:9: 13`, find n and r.

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MODERN PUBLICATION-PERMUTATIONS AND COMBINATIONS-EXERCISE
  1. If "^(2n)C3 : ^nC2= 12: 1, find n .

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  2. If .^(n)C(r )r: ^(n)C(r+1)=1:2 and .^(n)C(r+1): ^(n)C(r+2)=2:3, find ...

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  3. If "^(n-1)Cr : ^nCr : ^(n+1)Cr= 6:9: 13, find n and r.

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  4. If m= "^nC2, prove that "^m C2 =3xx ^(n+1)C4.

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  5. Prove that "^nCr+2 ^(n)C(r-1)+ ^(n)C(r-2) = ^(n+2)Cr.

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  6. Prove that "^nPr= ^nCr ^rPr.

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  7. Prove that "^nCr ^rC5= ^nC5 ^(n-5)C(r-5).

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  8. Prove that the product of any k consecutive integers is divisible by k...

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  9. Show that ((n+1)(n+2)(n+3)...... (n+r))/(r!) is a whole number.

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  10. Prove that "^(n-1)C3+ ^(n-1)C4 > ^nC3 if n >7.

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  11. Verify that ""^nCr= frac (n)(r) "^(n-1)C(r-1) and hence prove that "^n...

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  12. Find n if ""^nC4 , ""^nC5 and ""^nC6 are in A.P.

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  13. In how many ways can 5 sportsmen be selected from a group of 10 ?

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  14. How many selections of 4 books can be made from 8 different-books ?

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  15. A committee of 2 boys is to be selected from 4 boys. In how many ways ...

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  16. In how many ways can a committee be selected from 15 persons if the co...

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  17. In how many ways can a committee be selected from 15 persons if the co...

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  18. Sudha wants to choose any 9 stamps from a set of 11 different stamps. ...

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  19. How many lines can be drawn through 6 points on a circle ?

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  20. How many triangles can be drawn through n points on a circle ?

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