If the` p^(th), q^(th)` and `r^(th)` terms of a G.P are a,b,c respectively then the value of `a^(q-r).b^(r-p).c^(p-q)=`

Options

A. 0
B. 1
C. 3
D. `-1`

Answer

B

Explanation

Let first term and common ratio of a GP are m and n respectively.
Then, `A=m(n^(p-1))` . . . (i)
`B=m(n^(q-1))` . . (ii)
and `c=m(n^(r-1))` . . . (iii)
Now, `A^(q-r)*B^(r-p),C^(p-q)`
`m^((q-r))*n^((q-r)(p-1))*m^((r-p))*n^((r-p)(q-1))*m^((p-q))*n^((p-q)(r-1))`
`m^(q-r+r-p+p-q)*n^(q" "p-rp+r+rq-r-pq+p+pr-p-qr+q)`
`=m^(0).n^(0)=1xx1=1`