Important Questions of Application of Derivatives Mathematics | Zigya

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 Multiple Choice QuestionsShort Answer Type

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11.

A ballon which always remain spherical, has a variable diameter 3 over 2 left parenthesis 2 straight x plus 3 right parenthesis. Determine the rate of charge of its volume with respect to x.

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12.

The radius of a circle is increasing at 0.7 cm/sec. What is the rate of increase of its circumference when r = 4.9 cm?

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13.

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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14.

The radius of a circle is increasing uniformly at the rate of 3 cm per second. Find the rate at which the area of the circle is increasing when the radius is 10 cm.

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15. A car starts from a point P at time t = 0 seconds and stops at point Q. The distance x, in metres, covered by it, in t seconds is given by
straight x space equals straight t squared open parentheses 2 minus straight t over 3 close parentheses.
Find the time taken by it to reach Q and also find distance between P and Q.
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16.

A stone is dropped into a quiet lake and waves move in circles at a speed of 4 cm per second. At the instant when the radius of the circular waves is 10 cm, how fast is the enclosed area increasing?

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17. A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of the circular wave is 8 Cm, how fast is the enclosed area increasing?
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18.

The radius of a balloon is increasing at the rate of 10 cm per second. At what rate is the surface area of the balloon increasing when its radius is 15 cm?

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19.

The radius of an air-bubble is increasing at the rate of 1 half cm space per space second. At what rate is the volume of the bubble increasing when the radius is 1 cm?

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20.

An edge of a variable cube is increasing at the rate of 3 cm per second. How fast is the volume of the cube increasing when edge is 10 cm long?

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