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JEE Advanced2007MathematicsContinuity and DifferentiabilityActual

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.

Options

  1. AA-p, r; B-p, q, s; C-p; D-q, r
  2. BA-p, s; B-p, r, s; C-p, s; D-q, r
  3. CA-p, q, r; B-p, s; C-r, s; D-p, q
  4. DA-r, s; B-q; C-p; D-p, q, s

Correct answer

C. A-p, q, r; B-p, s; C-r, s; D-p, q

Step-by-step solution

(A) x|x| is continuous, differentiable and strictly increasing in (-1,1) . (B) |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 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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