CBSE  /  Class 12  /  Maths  /  Continuity and Differentiability

  • 1. 
    If y = (tan x), then \(\frac{dy}{dx}\) is equal to

  • sec x + cos x
  • sec x+ log tan x
  • (tan x)
  • None of these

  • 2. 
    If x= e then \(\frac{dy}{dx}\) is

  • \(\frac{1+x}{1+log x}\)
  • \(\frac{1-log x}{1+log y}\)
  • not defined
  • \(\frac{-y}{(1+log x)^2}\)

  • 3. 
    The derivative of y = (1 – x) (2 – x)…. (n – x) at x = 1 is equal to

  • 0
  • (-1) (n – 1)!
  • n ! – 1
  • (-1)

  • 4. 
    If f(x) = cos x, cos 2 x, cos 4 x, cos 8 x, cos 16 x, then the value of'(\(\frac{π}{4}\)) is

  • 1
  • √2
  • \(\frac{1}{√2}\)
  • 0

  • 5. 
    x. y= 16, then the value of \(\frac{dy}{dx}\) at (2, 2) is

  • -1
  • 0
  • -1
  • None of these

  • 6. 
    If y = e find \(\frac{dy}{dx}\) =

  • \(\frac{y^2}{1-y}\)
  • \(\frac{y^2}{y-1}\)
  • \(\frac{y}{y-1}\)
  • \(\frac{-y}{y-1}\)

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

  • –\(\frac{y}{x}\)
  • \(\frac{y}{x}\)
  • –\(\frac{x}{y}\)
  • \(\frac{x}{y}\)

  • 8. 
    If x = a cosθ, y = a sinθ. then \(\frac{dy}{dx}\) at θ = \(\frac{3π}{4}\) is

  • -1
  • 1
  • -a²
  • a²

  • 9. 
    If x = sin(3t – 4t³) and y = cos(\(\sqrt{1-t^2}\)) then \(\frac{dy}{dx}\) is equal to

  • \(\frac{1}{2}\)
  • \(\frac{2}{5}\)
  • \(\frac{3}{2}\)
  • \(\frac{1}{3}\)

  • 10. 
    If x = e sin t, y = e cos t, t is a parameter, then \(\frac{dy}{dx}\) at (1, 1) is equal to

  • –\(\frac{1}{2}\)
  • –\(\frac{1}{4}\)
  • 0
  • \(\frac{1}{2}\)
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