A circular disc of radius 3 cm. is heated. Due to expansion its radius increases at the rate of $0.05\text{ cm/s}$. Find the rate at which its area increases when the radius is $3.2\text{ cm}$.
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Applications of Derivatives - ISC Class 12 Mathematics Questions with Answers, Page 5
88 past-paper questions on Applications of Derivatives from ISC Class 12 Mathematics papers (2027-2017), newest first, in full. Questions 81-88 are on this page, 20 to a page. Tap "Show answer" under a question to see its answer.
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An open topped box is to be made by removing equal squares from each corner of a $3\text{ m}$ by $8\text{ m}$ rectangle sheet of aluminium and by folding up the sides. Find the volume of the largest such box.
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Find the intervals in which the function $f(x)$ is strictly increasing where, $f(x) = 10 - 6x - 2x^2$.
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Show that the altitude of a right circular cone of maximum volume that can be inscribed in a sphere of radius $r$ is $\frac{4r}{3}$.
Given: A right circular cone inscribed in a sphere of radius $r$
To show: Altitude of the cone of maximum volume is $\frac{4r}{3}$
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Water is dripping out from a conical funnel of semi-vertical angle $\frac{\pi}{4}$ at the uniform rate of $2\text{ cm}^2/\text{sec}$ in the surface, through a tiny hole at the vertex of the bottom. When the slant height of the water level is $4\text{ cm}$, find the rate of decrease of the slant height of the water.
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If $y - 2x - k = 0$ touches the conic $3x^2 - 5y^2 = 15$, find the value of $k$.
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Find the coordinates of the centre, foci and equation of directrix of the hyperbola
$x^2 - 3y^2 - 4x = 8$.
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Show that the surface area of a closed cuboid with square base and given volume is minimum when it is a cube.
Given: A closed cuboid with square base and given volume $V$.
To show: Surface area is minimum when it is a cube.
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