CBSE  /  Class 12  /  Maths  /  Continuity and Differentiability

  • 1. 
    The derivative of cos(2x² – 1) w.r.t cos x is

  • 2
  • \(\frac{-1}{2\sqrt{1-x^2}}\)
  • \(\frac{2}{x}\)
  • 1 – x²

  • 2. 
    If x = t², y = t³, then \(\frac{d^2y}{dx^2}\)

  • \(\frac{3}{2}\)
  • \(\frac{3}{4t}\)
  • \(\frac{3}{2t}\)
  • \(\frac{3}{4t}\)

  • 3. 
    The value of c in Rolle’s theorem for the function f(x) = x³ – 3x in the interval [o, √3] is

  • 1
  • -1
  • \(\frac{3}{2}\)
  • \(\frac{1}{3}\)

  • 4. 
    For the function f(x) = x + \(\frac{1}{x}\), x ∈ [1, 3] the value of c for mean value theorem is

  • 1
  • √3
  • 2
  • None of these

  • 5. 
    Let f be defined on [-5, 5] as

  • continuous at every x except x = 0
  • discontinuous at everyx except x = 0
  • continuous everywhere
  • discontinuous everywhere

  • 6. 
    Let function f (x) =

  • continuous at x = 1
  • differentiable at x = 1
  • continuous at x = -3
  • All of these

  • 7. 
    If f(x) = \(\frac{\sqrt{4+x}-2}{x}\) x ≠ 0 be continuous at x = 0, then f(o) =

  • \(\frac{1}{2}\)
  • \(\frac{1}{4}\)
  • 2
  • \(\frac{3}{2}\)

  • 8. 
    let f(2) = 4 then f”(2) = 4 then \(_{x→2}^{lim}\) \(\frac{xf(2)-2f(x)}{x-2}\) is given by

  • 2
  • -2
  • -4
  • 3

  • 9. 
    It is given that f'(a) exists, then \(_{x→2}^{lim}\) [/latex] \(\frac{xf(a)-af(x)}{(x-a)}\) is equal to

  • f – af'
  • f'(a)
  • -f’(a)
  • f (a) + af'(a)

  • 10. 
    If f(x) = \(\sqrt{25-x^2}\), then \(_{x→2}^{lim}\)\(\frac{f(x)-f(1)}{x-1}\) is equal to

  • \(\frac{1}{24}\)
  • \(\frac{1}{5}\)
  • –\(\sqrt{24}\)
  • \(\frac{1}{\sqrt{24}}\)
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