CBSE  /  Class 12  /  Maths  /  Application of Derivatives

  • 1. 
    The maximum value of sin x . cos x is

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

  • 2. 
    At x = \(\frac{5π}{6}\), f (x) = 2 sin 3x + 3 cos 3x is

  • maximum
  • minimum
  • zero
  • neither maximum nor minimum

  • 3. 
    Maximum slope of the curve y = -x³ + 3x² + 9x – 27 is

  • 0
  • 12
  • 16
  • 32

  • 4. 
    f(x) = x

  • x = e
  • x = \(\frac{1}{e}\)
  • x = 1
  • x = √e

  • 5. 
    The maximum value of (\(\frac{1}{x}\))is

  • e
  • e²
  • e
  • (\(\frac{1}{e}\))

  • 6. 
    If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is

  • a constant
  • proportional to the radius
  • inversely proportional to the radius
  • inversely proportional to the surface area

  • 7. 
    A particle is moving along the curve x = at² + bt + c. If ac = b², then particle would be moving with uniform

  • rotation
  • velocity
  • acceleration
  • retardation

  • 8. 
    The distance Y metres covered by a body in t seconds, is given by s = 3t² – 8t + 5. The body will stop after

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

  • 9. 
    The position of a point in time Y is given by x = a + bt + ct², y = at + bt². Its acceleration at timet Y is

  • b – c
  • b + c
  • 2b – 2c
  • 2\(\sqrt{b^2+c^2}\)

  • 10. 
    The function f(x) = log (1 + x) – \(\frac{2x}{2+x}\) is increasing on

  • (-1, ∞)
  • (-∞, ∞)
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