Mathematics · JEE

Online Practice: Limit, Continuity and Differentiability for JEE

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Sharpen your mathematics preparation with interactive online practice for Limit, Continuity and Differentiability. Goodmarks offers 70+ JEE-style MCQs mapped to the official syllabus, each with detailed explanations so you learn from every attempt.

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

Free sample questions

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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

How do I practice Limit, Continuity and Differentiability online for JEE?

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How many Limit, Continuity and Differentiability questions are available?

Goodmarks currently has 76+ JEE-aligned MCQs for Limit, Continuity and Differentiability, 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 Real-valued functions, algebra of functions, Polynomial, rational, trigonometric, logarithmic and exponential functions, Inverse functions, Graphs of simple functions, and more.

Do I get solutions after each question?

Every question includes the correct answer and a step-by-step explanation. Free users can practise a random mix; Pro unlocks full subject and topic filters.