Question

If the sum of the coefficients in the expansion of `(q+r)^(20)(1+(p-2)x)^(20)` is equal to square of the sum of the coefficients in the expansion of `[2rqx-(r+q)*y]^(10)`, where `p`, `r`,`q` are positive constants, then
A. ` le P`
B. `(r+q)/(2) ge p`
C. `r`, `p` and `q` are in `G.P.`
D. `1//r`, `1//p` an `1//q` are in `H.P.`

Answer 1

Correct Answer - B
`(b)` Sum of coefficient of `(q+r)^(20)(1+(p-2)x)^(20)`
`=(q+r)^(20)(p-1)^(20)` [put `x=1`]
Square of the sum of coefficient of `(2rpx-(r+q)*y^(10)`
`=(2rq-(r+q))^(20)` [put `x=y=1`]
So `(q+r)^(20)(p-1)^(20)=(2rq-(q+r))^(20)`
`impliesp-1=(2rq)/(r+q)-1`
`impliesp=(2rq)/(r+q)`
`impliesp=H.M.` of `r` and `q`
` le A.M. ` of `r` and `q`
`=(r+q)//2`