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If \ ^(20)Cr=\ ^(20)C(r+4),\ t h e n\ \ ...

If `\ ^(20)C_r=\ ^(20)C_(r+4),\ t h e n\ \ ^r C_3` is equal to a. 54 b. 56 c. 58 d. none of these

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Verified by Experts

As
`n_(C_x)=n_(C_y)`
So,
`r+r+4=20`
`2r+4=20`
`2r=16`
`r=8`
So,
...
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RD SHARMA-COMBINATIONS-Solved Examples And Exercises
  1. Write the total number of words formed by 2 vowels and 3 consonants ...

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  2. If \ ^20 Cr=\ ^20 C(r-10) ,\ t h e n\ \ ^18 Cr is equal to a. 4896 b. ...

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  3. If \ ^(20)Cr=\ ^(20)C(r+4),\ t h e n\ \ ^r C3 is equal to a. 54 b. 56 ...

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  4. If \ ^(15)C(3r)=\ \ ^(15)C(r+3)\ then\ r is equal to a. 5 b. 4 c. 3 d....

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  5. If \ ^(20)C(r+1)=\ \ ^(20)C(r-1),\ t h e n\ r is equal to a. 10 b. 11 ...

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  6. If C(n , 12)=C(n ,8),\ t h e n\ C(22 , n) is equal to a. 231 b. 210 c....

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  7. If \ ^ C1=\ \ ^n 2 then 2m=n m=(n-1) d. 2n=m(m-1)

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  8. If \ ^n C(12)=\ \ ^n C8 then n = a. 20 b. 12 c. 6 d. 30

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  9. If \ ^n Cr+\ ^n C(r-1)=\ \ ^(n+1)Cx ,\ t h e n x = r b. r-1 c. n d. r...

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  10. If \ ^(a^2-a)C2=\ \ ^(a^2-a)C4\ t h e n= 2 b. 3 c. 4 d. none of ...

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  11. \ ^5C1+\ ^5C2+\ ^5C3+\ ^5C4+\ ^5C5 is equal to 30 b. 31 c. 32 d. 33

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  12. Total number of words formed by 2 vowels and 3 consonants taken from 4...

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  13. There are 12 points in a lane. The number of the straight lines joinin...

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

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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 10 points in a plane and 4 of them are collinear. The number...

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  17. There are 13 players of cricket, out of which 4 are bowlers. In how ...

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  18. The number of ways in which a host lady can invite for a party of 8 ou...

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

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  20. The number of diagonals that can be drawn by joining the vertices of a...

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