The set of all real values of x satisfying `sin^(-1)sqrt(x)lt(pi)/(4)`, is

Options

A. `(0,(1)/(2))`
B. `[0,(1)/(2))`
C. `(0,(1)/(2)]`
D. `[0,(1)/(2)]`

Answer

B

Explanation

We have `sin^(-1)sqrt(x)lt (pi)/(4)`
`therefore 0 le x le 1` ….(1)
Also, `sqrt(x) lt (1)/(sqrt(2))rArr x lt (1)/(2)` …(2)
From (1) and (2), we get
`rArr x in [0,(1)/(2))`