List of top Mathematics Questions on Rate of Change of Quantities asked in MHT CET

An aeroplane at an altitude of 1 km is flying horizontally at 600 km / hr, passes directly over an observer. Then the rate at which it is approaching the observer when it is 1250 meters away from him is........

A spherical iron ball \(10\) cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of \(50 \text{cm}^3/\text{min}\). When the thickness of ice is \(5\) cm, the rate at which the thickness of ice decreases is...

If the rate of increase of surface area of a spherical balloon is \(5\,\text{cm}^2/\text{sec}\) and rate of increase of volume of a spherical balloon is \(10\,\text{cm}^3/\text{sec}\), then the radius of the balloon at that time is...

A particle is fired straight up from the ground. Its height in feet after \(t\) second is given by \(s(t) = 128t-16t^2\). The velocity of the particle when it hits the ground is...

If a particle moves such that the displacement (s) is proportional to the square of the velocity (v), then its acceleration (a) is

If the side of an equilateral triangle increases at the rate of \(\sqrt{3} \text{cm/sec}\), then the rate of change of increase of its area when the side is \(12 \text{cm}\) is ____

If \(\int \frac{sinx}{sin4x}\,dx = αlog\frac{1+sinx}{1-sinx}+βlog\frac{1+\sqrt{2}sinx}{1-\sqrt{2}sinx}+c\), then the value of \(32(α+β^2) =\)

The coordinates of the points on the curve \(4y = x^2\) that are nearest to the point \((0,5)\) are ...

A spherical snow ball is melting so that its volume is decreasing at the rate of 8 c.c./sec then the rate of change of radius when the radius is 2 cm, is :

A triangle has two fixed vertices A \((a,0)\) and B\((0,b)\) . Let its third vertex C is moving along the line \(x = y\). If \(s\) is the area of triangle ABC, then \(\frac{ds}{dx} =\)

A spherical mothball has initial radius 3 cm. Due to evaporation, the radius of the ball reduces to 1 cm in 4 months. In how many months would the mothball evaporate completely if the volume is lost at a rate proportional to the surface area ?

The surface area of a spherical ball is increasing at the rate of \(4π \text{cm}^2\)/second. The rate at which the radius is increasing when the surface area is \(16π \text{cm}^2\) is

If a spherical balloon has a variable diameter \(3x+\frac{9}{2}\) units, then the rate of change of its volume with respect to \(x\) is

A point on the parabola \(y^2 = \frac{36}{5}x\) at which the ordinate increases at thrice the rate of the abscissa is .....

Gas is being pumped into a spherical balloon at the rate of \(30~ft^3/min\). Find the rate at which the radius increases when the radius becomes \(15~ft\).

Gas is being pumped into a spherical balloon at the rate of $30\text{ ft}^3/\text{min}$. Then the rate at which the radius increases when it reaches the value $15\text{ ft}$ is:

If $x$ and $y$ are sides of two squares such that $y=x-x^{2}$, then the rate of change of area of the second square with respect to that of the first square is}

A spherical balloon is filled with (4500\pi) cubic meters of helium gas. If a leak causes gas to escape at (72\pi) m(^3)/min, then the rate at which the radius decreases 49 minutes after leakage began is

A spherical balloon is filled with (4500\pi) cubic meters of helium gas. If a leak causes gas to escape at (72\pi) m(^3)/min, then the rate at which the radius decreases 49 minutes after leakage began is

A spherical balloon is filled with (4500\pi) cubic meters of helium gas. If a leak causes gas to escape at (72\pi) m(^3)/min, then the rate at which the radius decreases 49 minutes after leakage began is

An object is moving in the clockwise direction around the unit circle $x^{2}+y^{2}=1$. As it passes through the point $(\frac{1}{2},\frac{\sqrt{3{2})$, its y-coordinate is decreasing at the rate of 3 units per sec. The rate at which the x-coordinate changes at this point is

The rate of change of $\sqrt{x^{2}+16}$ with respect to $\frac{x}{x-1}$ at $x=5$ is

The diagonal of a square is changing at the rate of $0.5$ cm/sec. Then the rate of change of area when the area is $400$ cm$^{2}$ is equal to}

A spherical snow ball is forming so that its volume is increasing at the rate of $8\ \text{cm}^3/\text{sec}$. Find the rate of increase of its radius when the radius is $2\ \text{cm}$.

The radius of a circular plate is increasing at the rate of $0.01\ \text{cm/sec}$. When the radius is $12\ \text{cm}$, the rate at which its area increases is