Download App

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
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.

View full solution →
Q 2M.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:
  • A
    $15\text{ft}/\text{sec}.$
  • B
    $9\text{ft}/\text{sec}.$
  • ✓
    $6\text{ft}/\text{sec}.$
  • D
    None of these.

Answer: C.

View full solution →
Q 3M.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:
  • ✓
    $54\pi \text{cm}^{2}/\text{min}$
  • B
    $7\pi\text{cm}^{2}/\text{min}$
  • C
    $27\text{cm}^{2}/\text{min}$
  • D
    $\text{none of these }$

Answer: A.

View full solution →
Q 4M.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:
  • A
    $10\sqrt{2}\text{cm}^2/\sec.$
  • ✓
    $10\sqrt{3}\text{cm}^2/\sec.$
  • C
    $10\text{cm}^2/\sec.$
  • D
    $5\text{cm}^2/\sec.$

Answer: B.

View full solution →
Q 5M.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.

View full solution →
Q 82 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.
View full solution →
Q 123 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.
View full solution →
Q 133 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.
View full solution →
Q 143 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?
View full solution →
Q 165 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.
View full solution →
Q 175 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.
View full solution →
Q 185 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.
View full solution →
Q 195 Marks Questions5 Marks
The top of a ladder 6 metres long is resting against a vertical wall on a level pavement, when the ladder begins to slide outwards. At the moment when the foot of the ladder is 4 metres from the wall, it is sliding away from the wall at the rate of 0.5m/ sec. How fast is the top-sliding downwards at this instance?
How far is the foot from the wall when it and the top are moving at the same rate?
View full solution →
Q 205 Marks Questions5 Marks
A man 2 metres high walks at a uniform speed of 6km/h away from a lamp-post 6 metres high. Find the rate at which the length of his shadow increases.
View full solution →
Browse all question groups ↑

Generate a Derivative as a Rate Measurer paper free

Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.

Download App
Generate Paper FreeAll Maths chapters