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Let f(n)= sum(k=1)^(n) k^2 ^"(n )Ck)^ 2 ...

Let `f(n)= sum_(k=1)^(n) k^2 ^"(n )C_k)^ 2` then the value of f(5) equals

A

`""^(8)C_(4)`

B

`25xx""^(8)C_(4)`

C

`25 xx""^(8)C_(5)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
`f(n) = sum_(r=1)^(n) r^(2) C_(r)""^(2)`
`rArr f(0)= sum_(r=1)^(n) (r ""^(n)C_(r))^(2) = n^(2) sum_(r=1)^(n) (""^(n-1)C_(r-1))^(2)`
`rArr f(n) = n^(2)""^(2n -2)C_(n-1)`
`rArr (5) = 25xx""^(8)C_(4)`
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OBJECTIVE RD SHARMA ENGLISH-BINOMIAL THEOREM AND ITS APPLCIATIONS -Section I - Solved Mcqs
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