CBSE  /  Class 12  /  Maths  /  Application of Derivatives

  • 1. 
    The sides of an equilateral triangle are increasing at the rate of 2cm/sec. The rate at which the are increases, when side is 10 cm is

  • 10 cm²/s
  • √3 cm²/s
  • 10√3 cm²/s
  • \(\frac{10}{3}\) cm²/s

  • 2. 
    A ladder, 5 meter long, standing oh a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is

  • \(\frac{1}{10}\) radian/sec
  • \(\frac{1}{20}\) radian/sec
  • 20 radiah/sec
  • 10 radiah/sec

  • 3. 
    The curve y – x

  • a vertical tangent (parallel to y-axis)
  • a horizontal tangent (parallel to x-axis)
  • an oblique tangent
  • no tangent

  • 4. 
    The equation of normal to the curve 3x² – y² = 8 which is parallel to the line ,x + 3y = 8 is

  • 3x – y = 8
  • 3x + y + 8 = 0
  • x + 3y ± 8 = 0
  • x + 3y = 0

  • 5. 
    If the curve ay + x² = 7 and x³ = y, cut orthogonally at (1, 1) then the value of a is

  • 1
  • 0
  • -6
  • 6

  • 6. 
    If y = x

  • 0.32
  • 0.032
  • 5.68
  • 5.968

  • 7. 
    The equation of tangent to the curve y (1 + x²) = 2 – x, w here it crosses x-axis is:

  • x + 5y = 2
  • x – 5y = 2
  • 5x – y = 2
  • 5x + y = 2

  • 8. 
    The points at which the tangents to the curve y = x² – 12x +18 are parallel to x-axis are

  • (2, – 2), (- 2, -34)
  • (2, 34), (- 2, 0)
  • (0, 34), (-2, 0)
  • (2, 2),(-2, 34).

  • 9. 
    The tangent to the curve y = e

  • (0, 1)
  • (-\(\frac{1}{2}\), 0)
  • (2, 0)
  • (0, 2)

  • 10. 
    The slope of tangent to the curve x = t² + 3t – 8, y = 2t² – 2t – 5 at the point (2, -1) is

  • \(\frac{22}{7}\)
  • \(\frac{6}{7}\)
  • \(\frac{-6}{7}\)
  • -6
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