Mathematics · JEE

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

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Sharpen your mathematics preparation with interactive online practice for Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable. Goodmarks offers 44+ JEE-style MCQs mapped to the official syllabus, each with detailed explanations so you learn from every attempt.

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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How do I practice Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable online for JEE?

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Goodmarks currently has 44+ JEE-aligned MCQs for Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable, with more added regularly.

Is this aligned with the JEE Main syllabus?

Yes. All Mathematics questions on Goodmarks are organised by official JEE Main units and subtopics, including Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable.

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