A ladder makes an angle of 60° with the ground, when placed against a wall. If the foot of the ladder is 2m away from the wall, then the length of the ladder (in metres) is

Options

A. (1) 4/√2 m
B. (2) 4√3 m
C. (3) 2/√2 m
D. (4) 4 m

Answer

B

Explanation

`f(x)=x^(2),g(x)=sinx`
`(gof)(x)=sin x^(2)`
`go(gof)(x)=sin(sinx^(2))`
`(fogogof)(x)=(sin(sin x^(2)))^(2) " …(i)" `
Again, `(gof)(x)=sin x^(2)`
`(gogof)(x)=sin(sin x^(2)) " …(ii)" `
Given, `(fogogof) (x)=(gogof)(x)`
`rArr (sin(sin^(2)))^(2)=sin(sin x^(2))`
`rArr sin(sin x^(2)) {sin (sin x^(2))-1}=0`
`implies sin(sin x^(2) )=0 or sin(sin x^(2))=1`
`rArr sin x^(2)=0 or sin x^(2)=(pi)/(2)`
` therefore x^(2) = n pi `
`[ sin x^(2)=(pi)/(2) " is not possible as " -1 le sin theta le 1]`
` x =pm sqrt(n pi)`