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If sum(r=0)^(n) (pr+2).""^(n)C(r)=(25)(6...

If `sum_(r=0)^(n) (pr+2).""^(n)C_(r)=(25)(64)` where `n, p in N`, then (a) p=3 (b) p=4 (c) n=7 (d) n=6

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The correct Answer is:
A, C
`S = underset(r=0)overset(n)sum(pr+2)..^(n)C_(r)`
`:. =underset(r=0)overset(n)sum(p(n-r)+2). .^(n)C_(r) ," " (:'.^(n)C_(r)=.^(n)C_(n-r))`
Adding these, we get
`2S = (pn+4) underset(r=0)overset(n)sum.^(n)C_(r)`
`rArr S = (pn+4) xx 2^(n-1)`
So, `n = 7` and `7p + 4 = 25` or `p = 3`.
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