12th Standard cbse -- Maths - Application of Derivatives

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Question - 1

 The total revenue Rupees in received from the sale of x units of an article is given by R(x) = 3x² + 36x + 5. The marginal revenue when x = 15 is

  • A 126
  • B 116
  • C 96
  • D 90

Question - 2

The side of an equilateral triangle is increasing at the rate of 2 cm/s. The rate at which area increases when the side is 10 is

  • A 10 cm²/s
  • B \(\sqrt3\) cm²/s
  • C 10 \(\sqrt3\) cm²/s
  • D \(\frac{10}{3}\)cm²/s 

Question - 3

The point(s) on the curve y = x², at which y-coordinate is changing six times as fast as x-coordinate is/are

  • A (2, 4)
  • B (3, 9)
  • C (3, 9), (9, 3)
  • D (6, 2)

Question - 4

The equation of the normal to the curve y = sin x at (0, 0) is

  • A  x = 0
  • B y = 0
  • C  x + y = 0
  • D  x – y = 0

Question - 5

The point on the curve where tangent to the curve y2 = x, makes an angle of 45° clockwise with the x-axis is

  • A \(\left( -\frac { 1 }{ 2 } ,\frac { 1 }{ 4 } \right) \)
  • B \(\left( \frac { 1 }{ 4 } ,-\frac { 1 }{ 2 } \right) \)
  • C (-2, 4)
  • D (4, 2)

Question - 6

The line y = x + 1 is a tangent to the curve y2 = 4x at the point

  • A (-1, 2)
  • B (-1, 2)
  • C (1, -2)
  • D (2, 1)

Question - 7

The curves y = ae-x and y = bex are orthogonal if

  • A  a = b
  • B a = -b
  • C ab = -1
  • D ab = 1

Question - 8

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

  • A 1
  • B 0
  • C -6
  • D 6

Question - 9

The tangent to the curve y = e2x at the point (0, 1) meets the x-axis at

  • A (0, 1)
  • B (2, 0)
  • C (\(-\frac12\), 0)
  • D (-2, 0)

Question - 10

 The angle between the curve y² = x and x² =y at (1, 1) is

  • A  60°
  • B    tan-1\(\frac43\)
  • C    cot-1\(\frac43\)
  • D  90°
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