Mathematics · JEE

Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable MCQs for JEE

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Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable JEE MCQs on Goodmarks include 44+ multiple-choice questions with correct answers and step-by-step solutions. Attempt free samples below or unlock the full bank with Pro.

Master Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable through exam-style multiple-choice questions. This page features 44+ JEE MCQs covering Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable, each with verified answers and clear explanations.

Syllabus context

Part of Limit, Continuity and Differentiability in JEE Main Mathematics.

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Q1MathsUnit 7: Limit, Continuity and Differentiability

If the radius of a sphere is measured as

9 \mathrm{cm}

with an error of

0.03 \mathrm{cm}

then, find the approximate error in calculating its volume

Q2MathsUnit 7: Limit, Continuity and Differentiability

If the ratio of base radius and height of a cone is 1: 2 and percentage error in radius is

\lambda \%,

then the error in its volume is

Q3MathsUnit 7: Limit, Continuity and Differentiability

Function

\boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}+\mathbf{2}) \boldsymbol{e}^{-\boldsymbol{x}}

Q4MathsUnit 7: Limit, Continuity and Differentiability

The two curves

x^{3}-3 x y^{2}+2=0

and

\mathbf{3} \boldsymbol{x}^{2} \boldsymbol{y}-\boldsymbol{y}^{3}-\boldsymbol{2}=\mathbf{0}

Q5MathsUnit 7: Limit, Continuity and Differentiability

Equation of normal drawn to the graph of the function defined as

f(x)=\frac{\sin x^{2}}{x}

\boldsymbol{x} \neq \mathbf{0}

and

\boldsymbol{f}(\mathbf{0})=\mathbf{0}

at the origin is?

Q6MathsUnit 7: Limit, Continuity and Differentiability

The point on the curve

y=x^{2}

which is nearest to (3,0) is

Q7MathsUnit 7: Limit, Continuity and Differentiability

For

\boldsymbol{x} \in \boldsymbol{R}

let

\boldsymbol{f}(\boldsymbol{x})=|\sin \boldsymbol{x}|

and

g(x)=\int_{0}^{x} f(t) d t .

Let

p(x)=g(x)-\frac{2}{\pi} x

Then

Q8MathsUnit 7: Limit, Continuity and Differentiability

The normals to the curve

y=x^{2}-x+

1, drawn at the points with the abscissa

\boldsymbol{x}_{1}=\mathbf{0}, \boldsymbol{x}_{2}=-\mathbf{1}

and

\boldsymbol{x}_{3}=\frac{\mathbf{5}}{\mathbf{2}}

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