1.

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

Answer» `cot^-1((n^2-10n+21.6)/pi) gt pi/6`
`=>(n^2-10n+21.6)/pi gt cot (pi/6)`
`=>(n^2-10n+25 -25 + 21.6)/pi gt sqrt3`
`=>(n-5)^2 - 3.4 gt sqrt3pi`
`=>(n-5)^2 gt sqrt3pi+3.4`
`=>-sqrt(sqrt3pi+3.4) lt n-5 lt sqrt(sqrt3pi+3.4)`
`=>2.1 lt n lt 7.9`
So, integral values of `n` can be `3,4,5,6,7`.
So, options `a` and `c` are the correct options.


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