CBSE  /  Class 12  /  Maths  /  Continuity and Differentiability

  • 1. 
    If f (x) = 2x and g (x) = \(\frac{x^2}{2}\) + 1, then’which of the following can be a discontinuous function

  • f(x) + g(x)
  • f(x) – g(x)
  • f(x).g(x)
  • \(\frac{g(x)}{f(x)}\)

  • 2. 
    The function f(x) = \(\frac{4-x^2}{4x-x^3}\) is

  • discontinuous at only one point at x = 0
  • discontinuous at exactly two points
  • discontinuous at exactly three points
  • None of these

  • 3. 
    The set of points where the function f given by f (x) =| 2x – 1| sin x is differentiable is

  • R
  • R = {\(\frac{1}{2}\)}
  • (0, ∞)
  • None of these

  • 4. 
    The function f(x) = cot x is discontinuous on the set

  • {x = nπ, n ∈ Z}
  • {x = 2nπ, n ∈ Z}
  • {x = (2n + 1) \(\frac{π}{2}\) n ∈ Z}
  • {x – \(\frac{nπ}{2}\) n ∈ Z}

  • 5. 
    The function f(x) = e is

  • continuous everywhere but not differentiable at x = 0
  • continuous and differentiable everywhere
  • not continuous at x = 0
  • None of these

  • 6. 
    If f(x) = x² sin\(\frac{1}{x}\), where x ≠ 0, then the value of the function f(x) at x = 0, so that the function is continuous at x = 0 is

  • 0
  • -1
  • 1
  • None of these

  • 7. 
    If f(x) = is continuous at x = \(\frac{π}{2}\), then

  • m = 1, n = 0
  • m = \(\frac{nπ}{2}\) + 1
  • n = \(\frac{mπ}{2}\)
  • m = n = \(\frac{π}{2}\)

  • 8. 
    If y = log(\(\frac{1-x^2}{1+x^2}\)), then \(\frac{dy}{dx}\) is equal to

  • \(\frac{4x^3}{1-x^4}\)
  • \(\frac{-4x}{1-x^4}\)
  • \(\frac{1}{4-x^4}\)
  • \(\frac{-4x^3}{1-x^4}\)

  • 9. 
    Let f(x) = |sin x| Then

  • f is everywhere differentiable
  • f is everywhere continuous but not differentiable at x = nπ, n ∈ Z
  • f is everywhere continuous but no differentiable at x = (2n + 1) \(\frac{π}{2}\) n ∈ Z
  • None of these

  • 10. 
    If y = \(\sqrt{sin x+y}\) then \(\frac{dy}{dx}\) is equal to

  • \(\frac{cosx}{2y-1}\)
  • \(\frac{cosx}{1-2y}\)
  • \(\frac{sinx}{1-xy}\)
  • \(\frac{sinx}{2y-1}\)
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