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Online Practice: Limits, continuity and differentiability for JEE

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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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How do I practice Limits, continuity and differentiability online for JEE?

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Goodmarks currently has 24+ JEE-aligned MCQs for Limits, 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 Limits, continuity and differentiability.

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