A) 0
B) 1
C) \[abc\]
D) \[pqr\]
Correct Answer: B
Solution :
Let \[a,\ b,\ c,\ d\] ?..(i) \[A{{R}^{q-1}}=b\] ?..(ii) and \[A{{R}^{r-1}}=c\] ?..(iii) So \[{{a}^{q-r}}{{b}^{r-p}}{{c}^{p-q}}\]\[={{\left\{ A{{R}^{p-1}} \right\}}^{q-r}}\left\{ A{{R}^{q-1}} \right\}{{\,}^{r-p}}{{\left\{ A{{R}^{r-1}} \right\}}^{p-q}}\] \[{{12}^{th}}\] \[={{A}^{0}}{{R}^{0}}=1\]. Note: Such type of questions \[i.e.\] containing terms of powers in cyclic order associated with negative sign, reduce to 1 mostly.
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