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Limits Continuity and Differentiability question

2007 · Shift 1 · Q43
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  2. /JEE Advanced
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  4. /Limits Continuity and Differentiability
  5. /2007 · Shift 1 · Q43

Limits Continuity and Differentiability question

2007 · Shift 1 · Q43

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMCQ+3 / −1

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.

Column I Column II
(A) x∣x∣x|x|x∣x∣ (P) continuous in (−1,1-1,1−1,1).
(B) ∣x∣\sqrt{|x|}∣x∣​ (Q) differentiable in (−1,1-1,1−1,1)
(C) x+[x]x+[x]x+[x] (R) strictly increasing in (−1,1-1,1−1,1)
(D) ∣x−1∣+∣x+1∣|x-1|+|x+1|∣x−1∣+∣x+1∣ (S) not differentiable at least at one point in (−1,1-1,1−1,1)

  1. A
    A - (p), (q), (r), B - (p), (s), C - (r), (s), D - (p), (q)
  2. B
    A - (p), (q), B - (p), (s), C - (r), (s), D - (p)
  3. C
    A - (p), (q), (r), B - (p), C - (r), D - (p), (q)
  4. D
    A - (p), (r), B - (p), (s), C - (r), D - (p), (q)
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