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Find the value of n: (i) .^(n)C(10)=^...

Find the value of n:
(i) `.^(n)C_(10)=^(n)C_(16)` (ii) `.^(15)C_(n) =^(15)C_(n+3)`
(iii) `.^(10)C_(n) =^(10)C_(n+2)` (iv) `.^(25)C_(3n) =.^(25)C_(n+1)`
(v) `.^(n)C_(r) =.^(n)C_(r-2)`

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Verified by Experts

The correct Answer is:
(i) `n - 26` (ii) `n = 6` (iii) `n = 4` (iv) `n = 6` (v) `n = 2r - 2`
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NAGEEN PRAKASHAN ENGLISH-PERMUTATION AND COMBINATION -Exercise F
  1. Evaluate: .^(20)C(5)+^(20)C(4)+^(21)C(4)+^(22)C(4)

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  2. Prove that: (i) r.^(n)C(r) =(n-r+1).^(n)C(r-1) (ii) n.^(n-1)C(r-1)...

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  3. Find the value of n: (i) .^(n)C(10)=^(n)C(16) (ii) .^(15)C(n) =^(15...

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  4. If .^(n)C(10) = .^(n)C(15), then evaluate .^(27)C(n).

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  5. If .^(18)C(r) = .^(18)C(r+2), then evaluate .^(r)C(5).

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  6. If .^(n)C(5) = .^(n)C(7), then find .^(n)P(3)

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  7. If .^(16)C(r) = .^(16)C(r+6), then find .^(5)C(r).

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  8. Determine n if (i) ^2n C2:^n C2=12 :1 (ii) ^2n C3:^n C3=11 :1

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  9. Determine n if (i) .^(2n) C2: "^n C2=12 :1 (ii) .^(2n) C3: "^n C...

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  10. Determine n if (i) ^2n C2:^n C2=12 :1 (ii) ^2n C3:^n C3=11 :1

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  11. If .^(15)C(r): .^(15)C(r-1) = 1:5, then find r.

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  12. If .^(n-1)P3 :^(n+1)P3 = 5 : 12, find n.

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  13. If .^(n)P(r) = 720 and .^(n)C(r) = 120, then find r. .

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  14. If .^(n+1)C(r+1.): ^nCr: ^(n-1)C(r-1)=11:6:3 find the values of n and ...

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  15. If ""^(n)C(4),""^(n)C(5) and ""^(n)C(6) are in A.P. then the value of ...

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  16. If alpha=\ \ ^m C2,\ then find the value of \ ^(alpha)C2dot

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  17. In how many ways can a team of 11 players be selected from 14 players?

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  18. In how many ways 2 persons can be selected from 4 persons?

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  19. In how many ways can a person invites his 2 or more than 2 friends out...

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  20. In how many ways can 11 players be selected from 14 players if (i) a...

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