If number of integral values of x satisfying the inequality `((x)/(100))^(7logx-log^(2)x-6)le10^(12)` are `alpha` then

Options

A. `alpha` is divisible by 5
B. `alpha` is divisible by 2
C. sum of digits of `alpha` is a composite number
D. sum of digits of `alpha` is a prime number

Answer

A, D

Explanation

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`