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Derivative as a Rate Measurer MATHS - Derivative as a Rate Measurer

Rajasthan Board (RBSE) - STD 12 Science - MATHS (Rajasthan - 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
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 2M.C.Q (1 Marks)1 Mark
The radius of the base of a cone is increasing at the rate of 3cm/minute and the altitude is decreasing at the rate of 4cm/minute. The rate of change of lateral surface when the radius = 7cm and altitude 24cm is:
  1. $54\pi \text{cm}^{2}/\text{min}$
  2. $7\pi\text{cm}^{2}/\text{min}$
  3. $27\text{cm}^{2}/\text{min}$​​​​​​​​​​​​​​
  4. $\text{none of these }$​​​​​​​
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Q 3M.C.Q (1 Marks)1 Mark
Side of an equilateral triangle expands at the rate of $2\text{cm}/ \text{sec}.$ The rate of increase of its area when each side is 10cm is:
  1. $10\sqrt{2}\text{cm}^2/\sec.$
  2. $10\sqrt{3}\text{cm}^2/\sec.$
  3. $10\text{cm}^2/\sec.$
  4. $5\text{cm}^2/\sec.$
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Q 4M.C.Q (1 Marks)1 Mark
The equation of motion of a particle is $\text{s} = \text{2t}^2 + \sin\text{2t,}$ where $s$ is in metres and t is in seconds. The velocity of the particle when its acceleration is $2m/\sec^2,$ is:
  • A
    $\pi+\sqrt{3}\text{m}/\text{sec}.$
  • ✓
    $\frac{\pi}{3}+\sqrt{3}\text{m}/\text{sec}.$
  • C
    $\frac{2\pi}{3}+\sqrt{3}\text{m}/\text{sec}.$
  • D
    $\frac{\pi}{3}+\frac{1}{\sqrt{3}}\text{m}/\text{sec}.$ 

Answer: B.

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Q 5M.C.Q (1 Marks)1 Mark
If $s = t^{3 }- 4t^{2 }+ 5$ describes the motion of a particle, then its velocity when the acceleration vanishes, is:
  • A
    $\frac{16}{2}\ \text{unit}/\text{sec}.$
  • B
    $\frac{\text{-32}}{3}\ \text{unit}/\text{sec}.$
  • C
    $\frac{4}{3}\ \text{unit}/\text{sec}.$
  • ✓
    $-\frac{16}{3}\ \text{unit}/\text{sec}.$

Answer: D.

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Q 72 Marks Questions2 Marks
If a particle moves in a straight line such that the distance travelled in time t is given by $s = t^3 - 6t^2 + 9t + 8.$ Find the initial velocity of the particle.
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Q 113 Marks Question3 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 123 Marks Question3 Marks
A man 2 metres high walks at a uniform speed of 5km/-hr away from a lamp-post 6 metres high. Find the rate at which the length of his shadow increases. 
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Q 133 Marks Question3 Marks
A particle moves along the curve $y = x^3.$ 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 143 Marks Question3 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 Marks Question3 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 165 Marks Questions5 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 175 Marks Questions5 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 185 Marks Questions5 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 195 Marks Questions5 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 205 Marks Questions5 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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