Mathematics · JEE

Important Questions: Limit, Continuity and Differentiability for JEE

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The most important Limit, Continuity and Differentiability questions for JEE cover conceptual traps, standard results, and numerical patterns from Real-valued functions, algebra of functions, Polynomial, rational, trigonometric, logarithmic and exponential functions, Inverse functions, Graphs of simple functions, and more. Goodmarks provides 70+ high-yield MCQs with full solutions.

Focus on what matters most. These important Limit, Continuity and Differentiability questions cover high-weightage concepts from Real-valued functions, algebra of functions, Polynomial, rational, trigonometric, logarithmic and exponential functions, Inverse functions, Graphs of simple functions, and more — the topics JEE repeats every year.

Subtopics in Limit, Continuity and Differentiability

Real-valued functions, algebra of functions
Polynomial, rational, trigonometric, logarithmic and exponential functions
Inverse functions
Graphs of simple functions
Limits, continuity and differentiability
Differentiation of the sum, difference, product and quotient of two functions
Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions
Derivatives of order upto two
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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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

Let

\boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{3}-\boldsymbol{x}^{2}+\boldsymbol{x}+\mathbf{1}

and

\boldsymbol{g}(\boldsymbol{x})=

\left\{\begin{array}{l}\max \{f(t)\}, \quad 0 \leq t \leq x \quad 0 \leq x \leq 1 \\ 3-x, \quad 1<x \leq 2\end{array}\right.

Then in the interval

[0,2], g(x)

is This question has multiple correct options

Q3MathsUnit 7: Limit, Continuity and Differentiability

5.63 \times 11

is equal to

Q4MathsUnit 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

Q5MathsUnit 7: Limit, Continuity and Differentiability

Function

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

Q6MathsUnit 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}

Q7MathsUnit 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?

Q8MathsUnit 7: Limit, Continuity and Differentiability

If a monomial

\frac{2}{5} x^{2} y^{2},

binomial

2 x+3 y

and a trinomial

2 x+3 y+4 z

are added, then the resultant expression is

a

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Frequently asked questions

What makes a Limit, Continuity and Differentiability question "important" for JEE?

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

Which subtopics in Limit, Continuity and Differentiability are high-weightage?

Key areas include Real-valued functions, algebra of functions, Polynomial, rational, trigonometric, logarithmic and exponential functions, Inverse functions, Graphs of simple functions, and more. Prioritise these before moving to edge cases.

How many important questions should I revise?

Revise 30–50 important MCQs per unit in the last month before JEE. Focus on questions you got wrong at least once.

Can I practise only important questions on Goodmarks?

Pro users can filter by unit and subtopic to target high-yield areas. Free users can attempt sample questions on this page.