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For n in N , Prove that (n+1)[n!n+(n-...

For ` n in N` , Prove that `(n+1)[n!n+(n-1)!(2n-1)+(n-2)!(n-1)]=(n+2)!`

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CHHAYA PUBLICATION-PERMUTATION AND COMBINATION -EXERCISE 7B ( Short Answer Type Questions )
  1. If (.^(n)C(r-1))/(a)=(.^(n)C(r))/(b)=(.^(n)C(r+1))/(c) n=(ab+2ac...

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  2. If the number of permutations of n different things taken r at time be...

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  3. For n in N , Prove that (n+1)[n!n+(n-1)!(2n-1)+(n-2)!(n-1)]=(n+2)!

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  4. Evaluate : .^(20)C(5)+sum(j=2)^(5).^(25-j)C(4)

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  5. If .^(n)C(1),^(n)C(2)and^(n)C(3) are in A.P ., find n .

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  6. Solve : ((2x+1)!)/((x+2)!)xx((x-1)!)/((2x-1)!)=(3)/(5),( x in N N)

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  7. Prove that if ngt7 then .^(n-1)C(3)+.^(n-1)C(4)gt^(n)C(3)

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  8. How many different triangles can be formed by joining the angular poi...

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  9. How many words each consisting of five different letters can be formed...

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  10. find the number of different words that can be formed from 12 consonan...

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  11. A person has got 15 acquaintances of whom 10 are relatives . In how ma...

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  12. In how many different ways can 9 men be selected from 15 men so as to ...

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  13. In how many ways can a committee of a 3 ladies and 4 gentlemen be appo...

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  14. m men and n women are to be seated in a row that no two women sit tog...

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  15. Eight prizes are to be distributed by a lottery . The first participa...

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  16. In an election there are 7 candidates and 4 members are to be elected...

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  17. In a plane there are 10 points out of which no three are collinear exc...

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  18. If 20 straight lines be drawn in a plane , no two of them being parall...

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  19. If 10 parallel lines in a plane are intersected by a family of anothe...

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  20. There are 15 points in a plane of which 4 points lie in one stright li...

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