CBSE  /  Class 12  /  Maths  /  Continuity and Differentiability

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

  • \(\frac{x+y}{xy}\)
  • xy
  • \(\frac{x}{y}\)
  • \(\frac{y}{x}\)

  • 2. 
    If ax² + 2hxy + by² = 1, then \(\frac{dy}{dx}\)equals

  • \(\frac{hx+by}{ax+by}\)
  • \(\frac{ax+by}{hx+by}\)
  • \(\frac{ax+hy}{hx+hy}\)
  • \(\frac{-(ax+hy)}{hx+by}\)

  • 3. 
    If sec (\(\frac{x-y}{x+y}\)) = a then \(\frac{dy}{dx}\) is

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

  • 4. 
    If y = tan(\(\frac{sinx+cosx}{cox-sinx}\)) then \(\frac{dy}{dx}\) is equal to

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

  • 5. 
    If y = tan(\(\frac{√x-x}{1+x^{3/2}}\)), then y'(1) is equal to

  • 0
  • (\(\frac{√x-x}{1+x^{3/2}}\))
  • -1
  • –\(\frac{1}{4}\)

  • 6. 
    The differential coefficient of tan(\(\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\)) is

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

  • 7. 
    \(\frac{d}{dx}\)(x\(\sqrt{a^2-x^2}+a^2 sin^{-1}(\frac{x}{a})\)) is equal to

  • \(\sqrt{a^2-x^2}\)
  • 2\(\sqrt{a^2-x^2}\)
  • \(\frac{1}{\sqrt{a^2-x^2}}\)
  • None of these

  • 8. 
    If f(x) = tan(\(\sqrt{\frac{1+sinx}{1-sinx}}\)), 0 ≤ x ≤ \(\frac{π}{2}\), then f'(\(\frac{π}{6}\)) is

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

  • 9. 
    If y = sin(\(\frac{√x-1}{√x+1}\)) + sec(\(\frac{√x+1}{√x-1}\)), x > 0, then \(\frac{dy}{dx}\) is equal to

  • 1
  • 0
  • \(\frac{π}{2}\)
  • None of these

  • 10. 
    If x = exp {tan(\(\frac{y-x^2}{x^2}\))}, then \(\frac{dy}{dx}\) equals

  • 2x [1 + tan (log x)] + x sec² (log x)
  • x [1 + tan (log x)] + sec² (log x)
  • 2x [1 + tan (logx)] + x² sec² (log x)
  • 2x [1 + tan (log x)] + sec² (log x)
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