Mathematics · JEE

Limits, continuity and differentiability Mock Test for JEE

31+ syllabus-aligned questions available

Quick answer

A Limits, continuity and differentiability JEE mock test on Goodmarks lets you attempt 31+ timed MCQs with instant feedback. Use it to benchmark speed, accuracy, and readiness for JEE Main Mathematics.

Simulate exam conditions with a Limits, continuity and differentiability mock test. Attempt 31+ timed MCQs, check your score instantly, and review every solution to close gaps before the real exam.

Syllabus context

Part of Limit, Continuity and Differentiability in JEE Main Mathematics.

Free sample questions

Attempt 15 free MCQs for Limits, continuity and differentiability. Unlock 16+ more with Pro.

Unlock full bank

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

Arrange the following limits in the ascending order: (1)

\lim _{x \rightarrow \infty}\left(\frac{1+x}{2+x}\right)^{x+2}

(2)

\lim _{x \rightarrow 0}(1+2 x)^{3 / x}

(3)

\lim _{\boldsymbol{\theta} \rightarrow \mathbf{0}} \frac{\sin \boldsymbol{\theta}}{\mathbf{2} \boldsymbol{\theta}}

(4)

\lim _{x \rightarrow 0} \frac{\log _{e}(1+x)}{x}

Q5MathsUnit 7: Limit, Continuity and Differentiability

Assertion

\lim _{\boldsymbol{x} \rightarrow \mathbf{0}} \frac{\sqrt{1-\cos 2 x}}{\boldsymbol{x}}

does not exist. Reason

|\sin x|=\left\{\begin{array}{cc}\sin x ; & 0<x<\frac{\pi}{2} \\ -\sin x ; & -\frac{\pi}{2}<x<0\end{array}\right.

Q6MathsUnit 7: Limit, Continuity and Differentiability

Let

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

be defined in the interval [-2,2] such that

f(x)=

\left\{\begin{array}{ll}-1, & -2 \leq x \leq 0 \\ x-1, & 0<x \leq 2\end{array} \text { and } g(x)=\right.

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

Test the differentiablity of

g(x)

in (-2,2)

Q7MathsUnit 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}

Q8MathsUnit 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

Q9MathsUnit 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

Q10MathsUnit 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)

Q11MathsUnit 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.

Q12MathsUnit 7: Limit, Continuity and Differentiability

The function

f(x)=\sin ^{-1}(\cos x)

is :

Q13MathsUnit 7: Limit, Continuity and Differentiability

The set of all values of 'a' for which

\lim _{x \rightarrow a}[x]

does not exist is

([x]

denotes greatest integer function)

Q14MathsUnit 7: Limit, Continuity and Differentiability

\boldsymbol{g}(\boldsymbol{x})=\left\{\begin{array}{ll}\mathbf{1} & \boldsymbol{x} \leq-\boldsymbol{2} \\ \frac{\mathbf{1}}{\mathbf{2}} \boldsymbol{x} & -\boldsymbol{2}<\boldsymbol{x}<\mathbf{4} \text { .then } \\ \sqrt{\boldsymbol{x}} & , \boldsymbol{x} \geq \mathbf{4}\end{array}\right.

Q15MathsUnit 7: Limit, Continuity and Differentiability

Which one of the following is correct in respect of the function

\boldsymbol{f}(\boldsymbol{x})=\frac{\boldsymbol{x}^{2}}{|\boldsymbol{x}|}

for

\boldsymbol{x} \neq \mathbf{0}

and

\boldsymbol{f}(\mathbf{0})=\mathbf{0} ?

Want unlimited Limits, continuity and differentiability practice?

Pro unlocks the full question bank, topic filters, and attempt history.

Get started free View Pro plans

Frequently asked questions

How long should a Limits, continuity and differentiability mock test take?

For a topic-level test, aim for 20–30 minutes. For a full subject mock, allow 60–90 minutes to mirror JEE timing.

What is a good score on a Limits, continuity and differentiability mock test?

Aim for 70%+ accuracy initially, then push toward 85%+ as your exam date approaches. Review explanations for every wrong answer.

Does Goodmarks score mock tests automatically?

Yes. Each MCQ is scored instantly with the correct answer and explanation shown after submission.

Can I retake the same mock test?

Pro users can generate new question sets by topic. Reattempting the same questions after a gap is excellent for retention.