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If .^(m)C(1)=.^(n)C(2) prove that m=(1)/...

If `.^(m)C_(1)=.^(n)C_(2)` prove that `m=(1)/(2)n(n-1)`.

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`.^(m)C_(1)=.^(n)C_(2)rArr m=(n(n-1))/(2)`.
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RS AGGARWAL-COMBINATIONS-Exercise 9D
  1. If .^(20)C(r)=.^(20)C(r-10) then find the value of .^(17)C(r).

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  2. If .^(20)C(r+1)=.^(20)C(r-1) then find the value of .^(10)C(r).

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  3. If .^(n)C(12)=.^(n)C(8) then find the value of .^(22)C(n).

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  4. If .^(35)C(n+7)=.^(35)C(4n-2) then find the value of n.

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  5. Find the values of (i) .^(200)C(198), (ii) .^(76)C(0), (iii) .^(15)...

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  6. If .^(m)C(1)=.^(n)C(2) prove that m=(1)/(2)n(n-1).

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  7. \ ^5C1+\ ^5C2+\ ^5C3+\ ^5C4+\ ^5C5 is equal to 30 b. 31 c. 32 d. 33

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  8. If .^(n+1)C(3)=2(.^(n)C(2)), find the value of n.

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  9. If .^(n)P(r)=720 and .^(n)C(r)=120 then find the value of r.

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  10. If.^((n^(2)-n))C(2)=.^((n^(2)-n))C(4) then find the value of n.

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  11. Write the total number of words formed by 2 vowels and 3 consonants ...

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  12. Write the number of diagonals of an n-sided polygon.

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  13. There persons enter a railway compartment. If there are 5 seats vacant...

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  14. There are 12 points in a plane, out of which 3 points are collinear. ...

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  15. In how many ways can a committee of 5 be made out of 6 men and 4 women...

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  16. There are 13 circket players, out of which 4 are bowlers. In how many ...

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  17. How many different committees of 5 can be formed from 6 men and 4 wome...

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  18. The number of parallelograms that can be formed from a set of four par...

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