Number of integral values of k for which the equation `4 cos^(-1)(-|x|)=k` has exactly two solutions, is: (a) 4 (b) 5 (c) 6 (d) 7

Options

A. 4
B. 5
C. 6
D. 7

Answer

C

Explanation

`4 cos^(-1)(-|x|)=k`
`implies cos^(-1)(-|x|)=(k)/(4) " (1)" `
The graph of `y= cos^(-1) (-|x|)` is as shown in the following figure

Clearly from the figure equation (1) has two solutions if line
`y=(k)/(4)` intersect the graph between `(pi)/(2) and pi `
` :. (pi)/(2) lt (k)/(4) le pi`
` :. 2pi lt k le 4pi`
Therefore, integral values of k are `7,8,9,10,11,12.`