Q44 / 66 · JEE Advanced 2007 (Paper 1) · Mathematics

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. Figure

  • A
    A-p, r; B-p, q, s; C-p; D-q, r
  • B
    A-p, s; B-p, r, s; C-p, s; D-q, r
  • Correct answer
    C
    A-p, q, r; B-p, s; C-r, s; D-p, q
  • D
    A-r, s; B-q; C-p; D-p, q, s

Solution

(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 $(-1,1)$.

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

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