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In the following $[x]$ denotes the greatest integer less than or equal to $x$. Match the functions in Column I with the properties Column II.
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The correct answer is:
A-p, q, r; B-p, s; C-r, s; D-p, q
A-p, q, r; B-p, s; C-r, s; D-p, q
(A) $x|x|$ is continuous, differentiable and strictly increasing in $(-1,1)$.
(B) $\sqrt{|x|}$ is continuous in $(-1,1)$ and not differentiable at $x=0$.
(C) $x+[x]$ is strictly increasing in $(-1,1)$ and discontinuous at $x=0$ $\Rightarrow$ not differentiable at $x=0$.
(D) $|x-1|+|x+1|=2$ in $(-1,1)$
The function is continuous and differentiable in $(-1,1)$.
(B) $\sqrt{|x|}$ is continuous in $(-1,1)$ and not differentiable at $x=0$.
(C) $x+[x]$ is strictly increasing in $(-1,1)$ and discontinuous at $x=0$ $\Rightarrow$ not differentiable at $x=0$.
(D) $|x-1|+|x+1|=2$ in $(-1,1)$
The function is continuous and differentiable in $(-1,1)$.
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