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If a and b are any two distinct numbers belonging tothe set {1,2,......100}, then the number of pairs (a, b) such that product ofa and b is divisible by 3 is5478 2.5278 3. 27393. 2639 5. 2837A. `5478`B. `5278`C. `2739`D. `2639` |
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Answer» Correct Answer - A If a and b are …………. `S = {1, 2, 3,…..100}` elements of `S` are of from `3n : 3,6,9,….00 rarr 33` number `3n+1:1,4,7,…..100 rarr 34` `3n+2:2,5,8….98 rarr 33` If ab is to be divisible by 3 either a or b is divisible by 3 or both a and b are to be divisible by 3. The number of ways a and b can be `=(.^(33)C_(2)+^(33)C_(1)xx^(34)C_(1)+^(33)C_(1))xx2` `= 2739xx2=5478` |
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