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If `a = underset(55 "times")underbrace(111.....1), b= 1+10+10^(2)+10^(3)+10^(4) and c=1+10^(5)+10^(10)+……+10^(50)` thenA. `b, (a)/(2), c` are in `A.P`B. `b, sqrt(a), c` are in `G.P`C. `a` is `a` prime numberD. `a` is `a` composite number |
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Answer» Correct Answer - B::D If `a = underset(55 "times")underbrace(111....1)` …………. `a = underset(55 "times")underbrace(111....1) = 1+10+10^(2)+……+10^(54)= (10^(55)-1)/(9)` `b=1+10+10^(2)+10^(2)+10^(3)+10^(4)= (10^(5)-1)/(9)` `c=1+10^(5)+10^(10)+……+10^(50)` `= ((10^(5))^(11)-1)/(10^(5)-1)=(10^(55)-1)/(10^(5)-1)=(((10^(55)-1)/9)/(10^(5)-1))/(9) =(a)/(b)` `a = bc :. b, sqrt(a) , c are in G.P` |
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