A) 1
B) 2
C) 4
D) 0
Correct Answer: A
Solution :
(a): Let GP be \[a,ar,a{{r}^{2}}\] p = mth term \[\to a{{r}^{m-1}}\] q = nth term \[\to a{{r}^{n-1}}\] t = sth term \[\to a{{r}^{s-1}}\] \[\therefore \] \[{{p}^{n-s}}\,\,{{q}^{s-m}}\,\,{{r}^{m-n}}=\left( {{a}^{n-s}}.{{a}^{s-m}}.{{a}^{m-n}} \right)\] \[\times \left[ {{r}^{(m-1)(n-s)}}\times {{r}^{(n-1)(s-m)}}\times {{r}^{(s-1)(m-n)}} \right]\] \[={{a}^{(n-s+s-m+m-n)}}\times \left[ {{r}^{(m-1)(n-s)+(n-1)(s-m)+(s-1)(m-n)}} \right]\] \[={{a}^{0}}\times {{r}^{0}}=1\]You need to login to perform this action.
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