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If number of integral values of x satisfying the inequality `((x)/(100))^(7logx-log^(2)x-6)le10^(12)` are `alpha` thenA. `alpha` is divisible by 5B. `alpha` is divisible by 2C. sum of digits of `alpha` is a composite numberD. sum of digits of `alpha` is a prime number |
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Answer» Correct Answer - A::D taking log with base 10 both sides `(7logx-(logx)^(2)-6)(logx-2)ge12` `logx=t` `(t-2)(7t-t^(2)-6)ge12` `7t^(2)-14t-t^(3)+2t^(2)-6t+12ge12` `-t^(3)+9t^(2)-20tge0` `t(t^(2)-9t+20)le0` `t in (-infty,0]cup[4,5]` `x in (0,1)cup[10^(4),10^(5)]` `becausealpha=90002` |
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