CBSE  /  Class 12  /  Maths  /  Continuity and Differentiability

  • 1. 
    If y = ax² + b, then \(\frac{dy}{dx}\) at x = 2 is equal to ax

  • 4a
  • 3a
  • 2a
  • None of these

  • 2. 
    If x sin (a + y) = sin y, then \(\frac{dy}{dx}\) is equal to

  • \(\frac{sin^2(a+y)}{sin a}\)
  • \(\frac{sin a}{sin^2(a+y)}\)
  • \(\frac{sin(a+y)}{sin a}\)
  • \(\frac{sin a}{sin(a+y)}\)

  • 3. 
    If x \(\sqrt{1+y}+y\sqrt{1+x}\) = 0, then \(\frac{dy}{dx}\) =

  • \(\frac{x+1}{x}\)
  • \(\frac{1}{1+x}\)
  • \(\frac{-1}{(1+x)^2}\)
  • \(\frac{x}{1+x}\)

  • 4. 
    If y = x tan y, then \(\frac{dy}{dx}\) =

  • \(\frac{tan x}{x-x^2-y^2}\)
  • \(\frac{y}{x-x^2-y^2}\)
  • \(\frac{tan y}{y-x}\)
  • \(\frac{tan x}{x-y^2}\)

  • 5. 
    If y = (1 + x) (1 + x²) (1 + x) …….. (1 + x), then the value of \(\frac{dy}{dx}\) at x = 0 is

  • 0
  • -1
  • 1
  • None of these

  • 6. 
    If f(x) = \(\frac{5x}{(1-x)^{2/3}}\) + cos² (2x + 1), then f'(0) =

  • 5 + 2 sin 2
  • 5 + 2 cos 2
  • 5 – 2 sin 2
  • 5 – 2 cos 2

  • 7. 
    If sec(\(\frac{x^2-2x}{x^2+1}\)) – y then \(\frac{dy}{dx}\) is equal to

  • \(\frac{y*2}{x^2}\)
  • \(\frac{2y\sqrt{y^2-1}(x^2+x-1)}{(x^2+1)^2}\)
  • \(\frac{(x^2+x-1)}{y\sqrt{y^2-1}}\)
  • \(\frac{x^2-y^2}{x^2+y^2}\)

  • 8. 
    If f(x) = \(\sqrt{1+cos^2(x^2)}\), then the value of f’ (\(\frac{√π}{2}\)) is

  • \(\frac{√π}{6}\)
  • –\(\frac{√π}{6}\)
  • \(\frac{1}{√6}\)
  • \(\frac{π}{√6}\)

  • 9. 
    Differential coefficient of \(\sqrt{sec√x}\) is

  • \(\frac{1}{4√x}\) = sec √x sin √x
  • \(\frac{1}{4√x}\) = (sec√x)sin√x
  • \(\frac{1}{2}\) √x sec√x sin √x. (d) \(\frac{1}{2}\)√x (sec√x)sin√x

  • 10. 
    Let f(x)={\(_{1-cos x, for x ≤ 0}^{sin x, for x > 0}\) and g (x) = e. Then the value of (g o f)’ (0) is

  • 1
  • -1
  • 0
  • None of these
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