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If r^[th] and (r+1)^[th] term in the ex...

If `r^[th]` and `(r+1)^[th]` term in the expansion of `(p+q)^n` are equal, then `[(n+1)q]/[r(p+q)]` is (a) `1/2` (b) `1/4` (c) 1 (d) 0

A

`(1)/(2)`

B

`(1)/(4)`

C

`1`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `T_(r )=^(n)C_(r-1)p^(n-r+1)*q^(r-1)`
`=T_(r+1)=^(n)C_(r)p^(n-r)*q^(r )` (given)
`impliesp^(n-r+1)*q^(r-1)=(n-r+1)/(r )p^(n-r)*q^(r )`
`implies(p)/((n-r+1))=(q)/(r )`
`implies((n+1)q)/((p+q)r)=1`
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