CBSE  /  Class 12  /  Maths  /  Continuity and Differentiability

  • 1. 
    If y = e, then the value of \(\frac{dy}{dx}\)|is

  • 1
  • 0
  • -1
  • 3e

  • 2. 
    Let f (x) = e, g (x) = sin x and h (x) = f |g(x)|, then \(\frac{h'(x)}{h(x)}\) is equal to

  • e
  • \(\frac{1}{\sqrt{1-x^2}}\)
  • sin x
  • \(\frac{1}{(1-x^2)}\)

  • 3. 
    If y = ae+ be+ c Where a, b, c are parameters, they y’ is equal to

  • ae– be
  • ae+ be
  • -(ae+ be)
  • ae– be

  • 4. 
    If sin y + e= e, then \(\frac{dy}{dx}\) at (1, π) is equal to

  • sin y
  • -x cos y
  • e
  • sin y – x cos y

  • 5. 
    Derivative of the function f (x) = log(Iog,x), x > 7 is

  • \(\frac{1}{x(log5)(log7)(log7-x)}\)
  • \(\frac{1}{x(log5)(log7)}\)
  • \(\frac{1}{x(logx)}\)
  • None of these

  • 6. 
    If y = log x + log y, then \(\frac{dy}{dx}\) is equal to

  • \(\frac{y}{y-1}\)
  • \(\frac{y}{x}\)
  • \(\frac{log_{10}e}{x}\)(\(\frac{y}{y-1}\))
  • None of these

  • 7. 
    If y = log [e(\(\frac{x-1}{x-2}\))\(^{1/2}\)], then \(\frac{dy}{dx}\) is equal to

  • 7
  • \(\frac{3}{x-2}\)
  • \(\frac{3}{(x-1)}\)
  • None of these

  • 8. 
    If y = e, then \(\frac{dy}{dx}\) is equal to

  • \(\frac{1}{2}\) sec² x
  • sec² x
  • sec x tan x
  • e

  • 9. 
    If y = 23 then \(\frac{dy}{dx}\) is equal to dx

  • (log 2) (log 3)
  • (log lg)
  • (log 18²) y²
  • y (log 18)

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

  • –\(\frac{y}{x}\)
  • –\(\frac{x}{y}\)
  • 1 + log (\(\frac{x}{y}\) )
  • \(\frac{1+logx}{1+logy}\)
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