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The simplified value of :

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20 101 -
100 101 - 2
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90 101 - None of these
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Correct Option: D
| Let, a = 1 + | |||||
| 10 + | |||||
| 10 | |||||
| = 1 + | |||||
| 10 | |||||
| = 1 + | |||||
| 10 | |||||
| = 1 + | |
| 101 |
| = | = | ||
| 101 | 101 |
Again,
| b = 1 − | |||||
| 10 + | |||||
| 10 | |||||
| = 1 − | |||||
| 10 | |||||
| = 1 − | |
| 101 |
| = | = | ||
| 101 | 101 |
∴ Expression
= (a2 − b2) ÷ ab
= {(a + b) (a – b)} ÷ ab
| = | ![]() | + | ![]() | ![]() | − | ![]() | ÷ | ![]() | × | ![]() | |||||||||
| 101 | 101 | 101 | 101 | 101 | 101 |
| = | × | × | |||
| 101 | 101 | 111 × 91 |

