Mathematics · JEE

Limit, Continuity and Differentiability MCQs for JEE

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Limit, Continuity and Differentiability JEE MCQs on Goodmarks include 70+ multiple-choice questions with correct answers and step-by-step solutions. Attempt free samples below or unlock the full bank with Pro.

Master Limit, Continuity and Differentiability through exam-style multiple-choice questions. This page features 70+ JEE MCQs covering Real-valued functions, algebra of functions, Polynomial, rational, trigonometric, logarithmic and exponential functions, Inverse functions, Graphs of simple functions, and more, each with verified answers and clear explanations.

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

What type of Limit, Continuity and Differentiability MCQs appear in JEE?

JEE Main tests Limit, Continuity and Differentiability through conceptual and numerical MCQs. Goodmarks mirrors this format with four-option questions and detailed solutions.

How many MCQs should I solve for Limit, Continuity and Differentiability?

Aim for at least 50–100 MCQs per subtopic. Goodmarks has 76+ questions for Limit, Continuity and Differentiability to build speed and accuracy.

Are solutions provided for every MCQ?

Yes. Each MCQ shows the correct option, final answer, and a step-by-step explanation after you submit.

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