Which of the following curves represents the function \(y = \ln\left( {\left| {{e^{\left[ {\left| {\sin \left( {\left| x \right|} \right)} \right|} \right]}}} \right|} \right)for\left| x \right| < 2\pi ?\) Here, x represents the abscissa and y represents the ordinate.

Which of the following curves represents the function \(y = \ln\left( {\left| {{e^{\left[ {\left| {\sin \left( {\left| x \right|} \right)} \right|} \right]}}} \right|} \right)for\left| x \right| < 2\pi ?\) Here, x represents the abscissa and y represents the ordinate. Correct Answer <img alt="General Aptitude 2016-2017 GATE ME with Solution images Q20c" src="//storage.googleapis.com/tb-img/production/17/05/General%20Aptitude%202016-2017%20GATE%20ME_with%20Solution_images_Q20c.PNG" style="height:266px; width:441px">

Here we check for the values of y by putting x as 0, π/2, π.

sin(0) = 0, sin(π/2) = 1, sin(π) = 0

So respective values of y will be,

We get, ln(e⁰) = y = 0 and ln(e¹) = y = 1 and so on.

f(0) = 0, f(π/2) = 1, f(π) = 0, f2π) = 0