Question

Let $f:\R \rightarrow \R$ and $g:\R \rightarrow\R$ be functions defined by
f(x)=\left\\{ \begin{array}{ll} x|x|\sin(\frac{1}{x}), & x\ne0 \\\ 0, & x = 0, \end{array} \right.\text{and} \ g(x)=\left\\{ \begin{array}{ll} 1-2x, & 0\leq x\leq \frac{1}{2}, \\\ 0, & \text{otherwise.} \end{array} \right.
Let $a,b,c,d \in \R$. Define the function $h:\R\rightarrow\R$ by
$h(x)=af(x)+b(g(x)+g(\frac{1}{2}-x))+c(x-g(x))+d\ g(x), x\in\R$.

Match each entry in List-I to the correct entry in List-II.List - I	List - II
(P)	If a = 0, b = 1, c = 0 and d = 0, then
(Q)	If a = 1, b = 0, c = 0 and d = 0, then
(R)	If a = 0, b = 0, c = 1 and d = 0, then
(S)	If a = 0, b = 0, c = 0 and d = 1, then
	(5)
The correct option is

• A. (P) → (4) (Q) → (3) (R) → (1) (S) → (2)
• B. (P) → (5) (Q) → (2) (R) → (4) (S) → (3)
• C. (P) → (5) (Q) → (3) (R) → (2) (S) → (4)
• D. (P) → (4) (Q) → (2) (R) → (1) (S) → (3)

Answer 1

Answer: (C)

(P) → (5) (Q) → (3) (R) → (2) (S) → (4)

Answer 2

The correct option is (C):(P) → (5) (Q) → (3) (R) → (2) (S) → (4).