| Column - I | Column - II | ||
| P. | 13/125 | 1. | Irrational |
| Q. | \[\sqrt{2}\] | 2. | Terminating decimal expansion |
| R. | 200/25 | 3. | Non-terminating repeating decimal expansion |
| S. | 61/455 | 4. | Rational number |
A) P-2, Q-4, R-1, S-3
B) P-2, Q-1, R-4, S-3
C) P-1, Q-2, R-3, S-4
D) P-1, Q-2, R-4, S-3
Correct Answer: B
Solution :
| (P) \[\frac{13}{125}=\frac{13}{{{5}^{3}}}\] |
| \[125\text{ }=\text{ }{{5}^{3}}\]is of the form \[{{2}^{n}}\times {{5}^{m}}\] |
| So, it is terminating decimal expansion. |
| (Q)\[\sqrt{2}\] is irrational |
| (R) \[\frac{200}{25}=8\], it can be represented as p/q |
| form, so it is a rational number. |
| (S) \[\frac{61}{455}=\frac{61}{5\times 7\times 13}\] |
| \[455={{5}^{1}}\times 13\times 7\] is not of the form \[{{2}^{n}}\times {{5}^{m}}\] |
| So, it is non-terminating repeating decimal expansion. |
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