Mathematics · JEE

Important Questions: 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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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 a curve at which the tangent lines at two distinct points coincide, then the curve cannot be

Q8MathsUnit 7: Limit, Continuity and Differentiability

Mark the correct alternative of the following.

f(x)=1+2 \sin x+3 \cos ^{2} x, 0 \leq x \leq

\frac{2 \pi}{3}

is?

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Important questions test core concepts that appear frequently across JEE Main and Advanced papers — definitions, standard formulas, and classic problem types.

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Key areas include Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable. Prioritise these before moving to edge cases.

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