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Derivative as a Rate Measurer Maths - Derivative as a Rate Measurer

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 78 questions in this chapter.

Question types

Derivative as a Rate Measurer question types

78 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

78
Questions
4
Question groups
5
Question types
Sample Questions

Derivative as a Rate Measurer questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
Each side of equilateral is increasing at the rate of 8cm/hr. The rate of increase of its area when side 2cm, is:
  1. $8\sqrt{3}\text{cm}^{2}/\text{hr}$  
  2. $4\sqrt{3}\text{cm}^{2}/\text{hr}$
  3. $\frac{\sqrt{3}}{8}\text{cm}^{2}/\text{hr}$
  4. $\text{None of these.}$
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Q 2M.C.Q (1 Marks)1 Mark
For what valuse of x is the rate of increase of x3 - 5x2 + 5x + 8 is twice the rate of increase of x?

  1. $-3, -\frac{1}{3}$

  2. $-3, \frac{1}{3}$

  3.   $3, -\frac{1}{3}$ 

  4.  $3, \frac{1}{3}$

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Q 3M.C.Q (1 Marks)1 Mark
In a sphere the rate of change of volume is:

  1.  $\pi$ times the rate of change of radius.

  2.  Surface area times the rate of change of diameter.

  3.  Surface area times the rate of change of radius.

  4.  None of these.

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Q 4M.C.Q (1 Marks)1 Mark
If the rate of change of area of a circle is equal to the rate of change of its diameter, then its radius is equal to:

  1. $\frac{2}{\pi}\ \text{unit}$

  2. $\frac{1}{\pi}\ \text{unit}$

  3. $\frac{\pi}{2}\ \text{unit}$

  4. $\pi \ \text{unit}$

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Q 5M.C.Q (1 Marks)1 Mark
A man of height 6ft walks at a uniform speed of 9ft/sec. from a lamp fixed at 15ft height. The length of his shadow is increasing at the rate of:
  1. $15\text{ft}/\text{sec}.$
  2. $9\text{ft}/\text{sec}.$
  3. $6\text{ft}/\text{sec}.$
  4. None of these. 
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Q 62 Marks2 Marks
Find the rate of change of the volume of a sphere with respect to its surface area when the radius is 2cm.
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Q 72 Marks2 Marks
If a particle moves in a straight line such that the distance travelled in time t is given by s = t3 - 6t2 + 9t + 8. Find the initial velocity of the particle.
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Q 92 Marks2 Marks
The sides of an equilateral triangle are increasing at the rate of 2cm/ sec. How far is the area increasing when the side is 10cms?
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Q 113 Marks3 Marks
A particle moves along the curve y = x3. Find the points on the curve at which the y-coordinate changes three times more rapidly than the x-coordinate.
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Q 123 Marks3 Marks
The volume of a spherical balloon is increasing at the rate of 25cm3/ sec. Find the rate of change of its surface area at the instant when radius is 5cm.
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Q 133 Marks3 Marks
A circular disc of radius 3cm is being heated. Due to expansion, its radius increases at the rate of 0.05cm/ sec. Find the rate at which its area is increasing when radius is 3.2cm.
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Q 143 Marks3 Marks
A balloon which always remains spherical, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon is increasing when the radius is 15cm.
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Q 153 Marks3 Marks
Find the rate of change of the volume of a ball with respect to its radius r. How fast is the volume changing with respect to the radius when the radius is 2cm?
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Q 164 Marks4 Marks
A kite is 120m high and 130m of string is out. If the kite is moving away horizontally at the rate of 52m/ sec, find the rate at which the string is being paid out.
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Q 174 Marks4 Marks
A man 160cm tall, walks away from a source of light situated at the top of a pole 6m high, at the rate of 1.1m/ sec. How fast is the length of his shadow increasing when he is 1m away from the pole?
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Q 184 Marks4 Marks
The length x of a rectangle is decreasing at the rate of 5cm/ minute and the width y is increasing at the rate of 4cm/ minute. When x = 8cm and y = 6cm, find the rates of change of:
  1. The perimeter.
  2. The area of the rectangle.
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Q 194 Marks4 Marks
Water is running into an inverted cone at the rate of $\pi$ cubic metres per minute. The height of the cone is 10 metres, and the radius of its base is 5m. How fast the water level is rising when the water stands 7.5m below the base.
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Q 204 Marks4 Marks
A balloon in the form of a right circular cone surmounted by a hemisphere, having a diametre equal to the height of the cone, is being inflated. How fast is its volume changing with respect to its total height h, when h = 9cm.
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