let $f_1 :R\to R, f_2 :\left[0, \infty \right)\to R, f_3 :R\to R and f_4 :R\to [0, \infty )$ be defined by
$f_1\left(x\right)=\left\{\begin{array}{ccc}\left|x\right|& if& x<0\\ e^x& if& x\ge 0\end{array}\right. ;f_2\left(x\right)=x^2;f_3\left(x\right)=\left\{\begin{array}{ccc}\sin x& if& x<0\\ x& if& x\ge 0\end{array}\right. and f_4\left(x\right)=\left\{\begin{array}{ccc}{f}_2\left(f_1\left(x\right)\right)& if& x<0\\ f_2\left(f_1\left(x\right)\right)-1& if& x\ge 0\end{array}\right.$
 

	List – I		List – II
(A)	$f_4$ is	(P)	Onto but not one – one
(B)	$f_3$ is	(Q)	neither continuous nor one-one
(C)	$f_2$ of $f_1$ is	(R)	differentiable but not one-one
(D)	$f_2$ is	(S)	continuous and one-one

• A

  a-q;b-r;c-s;d-p;
• Correct answer
  B

  a-p;b-r;c-q;d-s;
• C

  a-q;b-s;c-r;d-p;
• D

  a-q;b-p;c-r;d-s;

Hence, the correct answer is option: 'B'.