Mathematics · JEE

Important Questions: Limits, continuity and differentiability for JEE

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The most important Limits, continuity and differentiability questions for JEE cover conceptual traps, standard results, and numerical patterns from Limits, continuity and differentiability. Goodmarks provides 24+ high-yield MCQs with full solutions.

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Q1MathsUnit 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

Q2MathsUnit 7: Limit, Continuity and Differentiability

A polynomial

p(x)

when divided by

x^{2}-

3 x+2

leaves remainder

2 x-3 .

Then

Q3MathsUnit 7: Limit, Continuity and Differentiability

\operatorname{Let} f(x)=\left\{\begin{array}{cc}-1, & -2 \leq x<0 \\ x^{2}-1, & 0<x \leq 2\end{array}

and \right.

\boldsymbol{g}(\boldsymbol{x})=|\boldsymbol{f}(\boldsymbol{x})|+\boldsymbol{f}|\boldsymbol{x}|

then the number of points which

g(x)

is non differentiable, is

Q4MathsUnit 7: Limit, Continuity and Differentiability

The function

f(x)=

\left\{\begin{array}{l}\frac{\cos 3 x-\cos 4 x}{x^{2}}, \text { for } x \neq 0 \\ \frac{7}{2}, \text { for } x=0\end{array}

at \right.

\boldsymbol{x}=\mathbf{0}

Q5MathsUnit 7: Limit, Continuity and Differentiability

Assertion If

f(x)=0

has two distinct positive real roots then number of non- differentiable points of

\boldsymbol{y}=|\boldsymbol{f}(-|\boldsymbol{x}|)|

\mathbf{1}

Reason Graph of

\boldsymbol{y}=\boldsymbol{f}(|\boldsymbol{x}|)

is symmetrical about y-axis

Q6MathsUnit 7: Limit, Continuity and Differentiability

\boldsymbol{f}(\boldsymbol{x})=\cos \boldsymbol{\pi}(|\boldsymbol{x}|+[\boldsymbol{x}]),

then

\boldsymbol{f}(\boldsymbol{x})

is/are (where [.] denotes greatest integer function) This question has multiple correct options

Q7MathsUnit 7: Limit, Continuity and Differentiability

\operatorname{Let} \boldsymbol{f}\left(\frac{\boldsymbol{x}+\boldsymbol{y}}{\mathbf{2}}\right)=\frac{\mathbf{1}}{\mathbf{2}}[\boldsymbol{f}(\boldsymbol{x})+\boldsymbol{f}(\boldsymbol{y})]

for real

x

and

y .

f^{\prime}(0)

exists and equals -1 and

f(0)=1

then the value of

f(2)

Q8MathsUnit 7: Limit, Continuity and Differentiability

Consider the function

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

\left\{\begin{array}{cl}\frac{x+5}{x-2} & \text { if } x \neq 2 \\ 1 & \text { if } x=2\end{array} . \text { Then } f(f(x))

is \right. discontinuous.

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Frequently asked questions

What makes a Limits, 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 Limits, continuity and differentiability. Prioritise these before moving to edge cases.

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

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