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The number of integer x satisfying sin^...

The number of integer `x` satisfying `sin^(-1)|x-2|+cos^(-1)(1-|3-x|)=pi/2` is (a)` 1` (b) ` 2` (c)` 3` (d)` 4`

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`sin^(-1)|x-2|+cos^(-1)(1-|3-x|)=pi/2`
`alpha=beta`
`|x-2|=1-|3-x|`
`|x-2|+|3-x|=1|(x-2)+(3-x)|`
`(x-2)(3-x)>=0`
`2<=x<=3`
Option B is correct.
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