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| 1. |
The number of rational numbers of the form p/q , where p, q ∈ {3, 4, 8, 9, 12} is(1) 25(2) 21(3) 19(4) 23 |
| Answer» <p></p><p class="MsoNormal" style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000"><strong>Correct option (3) 19</strong></span></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000"><strong>Explanation:</strong></span></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">There are 5 numbers of the form P/q with 3 in the numerator. Similarly for each of 4, 8, 9 and 12.</span></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">∴ total number of numbers of the form p q is 5 × 5 = 25. </span></span></p><p class="MsoNormal" style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">But the value 1 is repeated 5 times, 1/3 is repeated twice and 3/4 is repeated twice.</span></span></p><p style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">∴ the number of distinct rational numbers formed</span></span></p><p style="text-align: justify;"><span style="font-family:Arial,Helvetica,sans-serif"><span style="color:#000000">= 25 − 4 − 1 − 1 = 19.</span></span></p> | |