| Column-l | Column-II |
| (P) \[\left[ {{({{5}^{3}})}^{2}}\times {{5}^{5}} \right]\div {{5}^{9}}\] | (i) \[{{(-6)}^{3}}\] |
| (Q) \[{{(-6)}^{5}}\div {{(6)}^{2}}\] | (ii) 2 |
| (R) \[({{5}^{0}}+{{3}^{0}})\div ({{8}^{0}})\] | (iii) 1 |
| (S) \[{{(7/19)}^{0}}\] | (iv) 25 |
A) (P)\[\to \](i), (Q)\[\to \](ii), (R)\[\to \](iii), (S)\[\to \](iv)
B) (P)\[\to \](ii), (Q)\[\to \](iii), (r)\[\to \](iv), (S)\[\to \](i)
C) (P)\[\to \](iv), (Q)\[\to \](i). (R)\[\to \](ii), (S)\[\to \](iii)
D) (P)\[\to \](iv), (Q)\[\to \](ii), (R)\[\to \](i), (S)\[\to \](iii)
Correct Answer: C
Solution :
(P) \[\left[ {{\left( {{5}^{3}} \right)}^{2}}\times {{5}^{5}} \right]\div {{5}^{9}}=\left( {{5}^{6}}\times {{5}^{5}} \right)\div {{5}^{9}}\] \[=({{5}^{6+5}})\div {{5}^{9}}={{5}^{2}}=25\] (Q) \[{{(-6)}^{5}}\div {{(6)}^{2}}={{(-1)}^{5}}\times {{(6)}^{5}}\div {{(6)}^{2}}\] \[=(-1)\times ({{6}^{5-2}})={{(-1)}^{3}}\times {{6}^{3}}=-{{(-6)}^{3}}\] (R) \[({{5}^{0}}+{{3}^{0}})\div ({{8}^{0}})=(1+1)\div (1)=2\] (S) \[{{\left( \frac{7}{19} \right)}^{0}}=2\]
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