Mathematics · JEE

Limit, Continuity and Differentiability Previous Year Questions for JEE

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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

Why practise PYQs for Limit, Continuity and Differentiability?

PYQs reveal recurring concepts, common traps, and the difficulty level JEE expects. Solving them builds exam temperament and time management.

Does Goodmarks have actual JEE past papers?

Our bank includes exam-style MCQs aligned with JEE Main Mathematics syllabus for Limit, Continuity and Differentiability, covering the same topics as previous year papers.

How should I use PYQs for Limit, Continuity and Differentiability?

Solve timed sets, review every explanation, note weak subtopics, then revisit with focused practice on Goodmarks.

Are PYQ solutions step-by-step?

Yes. Every question includes the correct answer and a detailed explanation showing the reasoning.