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CHHAYA PUBLICATION-PERMUTATION AND COMBINATION -EXERCISE 7B ( Short Answer Type Questions )
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Play - Find n and r if .^(n)P(r)=.^(n)P(r+1)and^(n)C(r)=^(n)C(r-1).
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Play - Show that ,.^(n)C(r)=(n-r+1)/(r).^(n)C(r-1).
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Play - Show that .^(n)C(r)+.^(n-1)C(r-1)+.^(n-1)C(r-2)=.^(n+1)C(r).
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Play - .^(n)C(r)+2.^(n)C(r-1)+.^(n)C(r-2)=.^(n+2)C(r)(2lerlen).
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Play - Show that , (.^(n)C(r)+^(n)C(r-1))/(.^(n)C(r-1)+^(n)C(r-2))=(.^(n+1)p...
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Play - Prove that , .^(45)C(8)+sum(r=1)^(7).^(52-r)C(7)+sum(k=1)^(5).^(57-K)C...
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Play - Prove that , .^(15)C(8)+^(15)C(9)-.^(15)C(6)-^(15)C(7)=0
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Play - Prove that , .^(n)C(r)+3.^(n)C(r-1)+3.^(n)C(r-2)+^(n)C(r-3)=^(n+3)C(r)
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Play - Show that (.^(4n)C(2n))/(.^(2n)C(n))=(1.3.5......(4n-1))/({1.3.5........
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Play - If .^(n)C(r-1)=36,.^(n)C(r)=84and.^(n)C(r+1)=126 find n and r .
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Play - For n in N , Prove that (n+1)[n!n+(n-1)!(2n-1)+(n-2)!(n-1)]=(n+2)!
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Play - Evaluate : .^(20)C(5)+sum(j=2)^(5).^(25-j)C(4)
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Play - If .^(n)C(1),^(n)C(2)and^(n)C(3) are in A.P ., find n .
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Play - Solve : ((2x+1)!)/((x+2)!)xx((x-1)!)/((2x-1)!)=(3)/(5),( x in N N)
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Play - Prove that if ngt7 then .^(n-1)C(3)+.^(n-1)C(4)gt^(n)C(3)
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