question_answer

If the function f(x) = \[\left\{ \begin{align}   & a|\pi -x|+1,x\le 5 \\  & b|x-\pi |+3,x>5 \\ \end{align} \right.\]is continuous at \[x=5,\]then the value of \[ab\] is :-                                                                                             [JEE Main 9-4-2019 Afternoon]

A) \[\frac{2}{5-\pi }\]

B) \[\frac{2}{\pi -5}\]

C) \[\frac{2}{\pi +5}\]               

D) \[\frac{-2}{\pi +5}\]

Correct Answer: A

Solution :

                        \[a|\pi -5|+1=b|5-\pi |+3\]             \[a|(5-\pi )+1=b(5-\pi )+3\]             \[(a-b)(5-\pi )=2\]             \[a-b=\frac{2}{5-\pi }\]