| Column-l | Column-II |
| (P) Rational form of \[0.\overline{32}\]is | (i) \[\frac{14}{55}\] |
| (Q) Rational form of \[0.\overline{254}\]is | (ii) \[\frac{11}{45}\] |
| (R) Rational form of \[0.\overline{12}\]is | (iii) \[\frac{32}{99}\] |
| (S) Rational form of \[0.\overline{24}\]is | (iv) \[\frac{11}{90}\] |
A) (P)\[\to \](iii);(Q)\[\to \](iv);(R)\[\to \](i);(S)\[\to \](ii)
B) (P)\[\to \](iv);(Q)\[\to \](i);(R)\[\to \](ii);(S)\[\to \](iii)
C) (P)\[\to \](iii);(Q)\[\to \](i);(R) \[\to \](iv);(S)\[\to \](ii)
D) (P)\[\to \](i);(Q)\[\to \](iii);(R)\[\to \](iv);(S)\[\to \](ii)
Correct Answer: C
Solution :
(P) Let \[x=0.\overline{32}\] \[\Rightarrow \] \[x=0.3232332.......\] ?..(1) \[\Rightarrow \] \[100x=32.3232.....\] ?..(2) Subtracting (1) from (2), we get \[99x=32\Rightarrow x=\frac{32}{99}\] (Q) Let \[x=0.2\overline{54}\] \[\Rightarrow \] \[x=0.25454.....\] ?..(1) \[\Rightarrow \] \[100x=25.45454.....\] ??(2) Subtracting (1) from (2), we get \[99x=25.2\,\Rightarrow x=\frac{252}{990}=\frac{14}{55}\] (R) Let \[x=0.1\overline{2}\] \[\Rightarrow \] \[x=0.1222....\] ?.(1) \[\Rightarrow \] \[10x=1.222.....\] ?.(2) Subtracting (1) from (2), we get \[\Rightarrow \] \[9x=2.2\,\,\Rightarrow x=\frac{22}{90}=\frac{11}{45}\]
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