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The number of integral values of x in th...

The number of integral values of x in the domain of `f(x) = sqrt(3-x)+sqrt(x-1)+log{x}` , where {} denotes the fractional part of x, is

A

`[1, pi )`

B

`( 0,2 pi) ~[1,pi) `

C

`(0 ,(pi)/( 2))~{1}`

D

`(0,1)`

Text Solution

Verified by Experts

The correct Answer is:
D
We must have `cos(sin x) ge 0 rArr (pi)/(2) ge sin x ge -(pi)/(2)`
which is true for all real x.
Secondly `log, {x} ge 0`
If `0 lt x lt 1`, then `0 lt {x} le 1 rArr 0 lt x lt 1`
If `x gt 1` then `{x} ge 1`, which is not possible. Thus domain is (0, 1)
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