If `cot^(-1)((n^2-10 n+21. 6)/pi)>pi/6,`where `x y

1.	If `cot^(-1)((n^2-10 n+21. 6)/pi)>pi/6,`where `x y
Answer» Correct Answer - A::C We have `cot^(-1) ((n^(2) -10n + 21.6)/(pi)) gt (pi)/(6)` `rArr (n^(2) - 10n + 21.6)/(pi) lt cot.(pi)/(6)` (as cot x decreasing for `0 lt x lt pi`) or `n^(2) - 10n + 21.6 lt pisqrt3` or `n^(2) - 10n + 25 + 21.6 - 25 lt pi sqrt3` or `(n-5)^(2) lt pi sqrt3 + 3.4` or `-sqrt(sqrt3 po + 3.4) lt n - 5 lt sqrt(sqrt3 pi + 3.4)` or `5 -x sqrt(sqrt5 pi + 3.4) lt n - 5 lt sqrt(sqrt3 pi + 3.4)` ...(i) Since `sqrt3 pi = 5.5`, nearly , `sqrt(sqrt3 pi + 3.4) ~ sqrt(8.9) ~ 2.9` `rArr 2.1 lt n lt 7.9` `:. n = 3, 4, 5, 6, 7 " " {"as " n in N}`

Discussion

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