CBSE  /  Class 12  /  Maths  /  Application of Derivatives

  • 1. 
    The two curves; x³ – 3xy² + 2 = 0 and 3x²y – y³ – 2 = 0 intersect at an angle of

  • \(\frac{π}{4}\)
  • \(\frac{π}{3}\)
  • \(\frac{π}{2}\)
  • \(\frac{π}{6}\)

  • 2. 
    The interval on which the function f (x) = 2x³ + 9x² + 12x – 1 is decreasing is

  • [-1, ∞]
  • [-2, -1]
  • [-∞, -2]
  • [-1, 1]

  • 3. 
    Let the f: R → R be defined by f (x) = 2x + cos x, then f

  • has a minimum at x = 3t
  • has a maximum, at x = 0
  • is a decreasing function
  • is an increasing function

  • 4. 
    y = x (x – 3)² decreases for the values of x given by

  • 1 < x < 3
  • x < 0
  • x > 0
  • 0 < x <\(\frac{3}{2}\)

  • 5. 
    The function f(x) = 4 sin³ x – 6 sin²x + 12 sin x + 100 is strictly

  • increasing in (π, \(\frac{3π}{2}\))
  • decreasing in (\(\frac{π}{2}\), π)
  • decreasing in [\(\frac{-π}{2}\),\(\frac{π}{2}\)]
  • decreasing in [0, \(\frac{π}{2}\)]

  • 6. 
    Which of the following functions is decreasing on(0, \(\frac{π}{2}\))?

  • sin 2x
  • tan x
  • cos x
  • cos 3x

  • 7. 
    The function f(x) = tan x – x

  • always increases
  • always decreases
  • sometimes increases and sometimes decreases
  • never increases

  • 8. 
    If x is real, the minimum value of x² – 8x + 17 is

  • -1
  • 0
  • 1
  • 2

  • 9. 
    The smallest value of the polynomial x³ – 18x² + 96x in [0, 9] is

  • 126
  • 0
  • 135
  • 160

  • 10. 
    The function f(x) = 2x³ – 3x² – 12x + 4 has

  • two points of local maximum
  • two points of local minimum
  • one maxima and one minima
  • no maxima or minima
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