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Previous year question hub

Limits Continuity And Differentiability - Calculus - Mathematics Previous Year Questions

Practice Limits Continuity And Differentiability - Calculus - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

60Papers
7Years
127Questions
1Topics

Limits Continuity And Differentiability question pattern

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Difficulty distribution

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Not classified 127 100%

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Multiple Choices 127 100%

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Mathematics
127 Qs

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Calculus
127 Qs

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Limits Continuity And Differentiability
127 Qs

Paper coverage

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MHT CET 2025 21ST APRIL EVENING SHIFT
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MHT CET 2025 25TH APRIL MORNING SHIFT
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MHT CET 2025 19TH APRIL EVENING SHIFT
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MHT CET 2025 19TH APRIL MORNING SHIFT
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MHT CET 2022 11TH AUGUST EVENING SHIFT
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MHT CET 2019 2ND MAY EVENING SHIFT
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Included previous year papers

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PaperYear / sessionQuestions in this viewOpen
MHT CET 2025 19TH APRIL EVENING SHIFT20252View paper
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MHT CET 2023 10TH MAY EVENING SHIFT20233View paper
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MHT CET 2023 11TH MAY EVENING SHIFT20232View paper
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MHT CET 2023 9TH MAY EVENING SHIFT20232View paper
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MHT CET 2022 11TH AUGUST EVENING SHIFT20222View paper
MHT CET 2021 20TH SEPTEMBER EVENING SHIFT20212View paper
MHT CET 2021 20TH SEPTEMBER MORNING SHIFT20212View paper
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MHT CET 2021 23RD SEPTEMBER EVENING SHIFT20211View paper
MHT CET 2021 23th September Morning Shift20212View paper
MHT CET 2021 24TH SEPTEMBER EVENING SHIFT20212View paper
MHT CET 2021 24TH SEPTEMBER MORNING SHIFT20212View paper
MHT CET 2020 16TH OCTOBER EVENING SHIFT20202View paper
MHT CET 2020 16TH OCTOBER MORNING SHIFT20201View paper
MHT CET 2020 19TH OCTOBER EVENING SHIFT20201View paper
MHT CET 2019 2ND MAY EVENING SHIFT20193View paper
MHT CET 2019 2ND MAY MORNING SHIFT20192View paper
MHT CET 2019 3RD MAY MORNING SHIFT20192View paper

All Limits Continuity And Differentiability previous year questions

Practice every matching question in batches of 20, with every available option.

1
2019 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2019 2ND MAY EVENING SHIFT

If the function $f(x)=\frac{\left(e^{k x}-1\right) \tan k x}{4 x^2}, x \neq 0$

$$\qquad \qquad=16 \qquad x=0$$

is continuous at $x=0$, then $k=\ldots \ldots$

A
$\pm \frac{1}{8}$
B
$\pm 4$
C
$\pm 2$
D
$\pm 8$
Open complete paper
2
2019 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2019 2ND MAY EVENING SHIFT

If function

$$\begin{aligned} f(x) & =x-\frac{|x|}{x}, x<0 \\ & =x+\frac{|x|}{x}, x>0 \\ & =1, \quad x=0, \text { then } \end{aligned}$$

A
$\lim _\limits{x \rightarrow 0^{-}} f(x)$ does not exist
B
$\lim _\limits{x \rightarrow 0^{+}} f(x)$ does not exist
C
$f(x)$ is continuous at $x=0$
D
$\lim _\limits{x \rightarrow 0^{-}} f(x) \neq \lim _\limits{x \rightarrow 0^{+}} f(x)$
Open complete paper
3
2019 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2019 2ND MAY EVENING SHIFT

If $f(x)=[x]$, where $[x]$ is the greatest integer not greater than $x$, then $f^{\prime}\left(1^{+}\right)=$ ...........

A
1
B
2
C
0
D
$-$1
Open complete paper
4
2019 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2019 2ND MAY MORNING SHIFT

If the function $f(x)=\frac{\log (1+a x)-\log (1-b x)}{x}$ $x \neq 0$ is continuous at $x=0$ then, $f(0)=\ldots \ldots$

A
$\log a-\log b$
B
$a+b$
C
$\log a+\log b$
D
$a-b$
Open complete paper
5
2019 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2019 2ND MAY MORNING SHIFT

Which of the following function is not continuous at $x=0$ ?

A
\(\begin{aligned} f(x) & =(1+2 x)^{1 / x}, & & x \neq 0 \\ & =e^2, & & x=0 \end{aligned}\)
B
\(\begin{aligned} f(x) & =\sin x-\cos x, & & x \neq 0 \\ & =-1, & & x=0 \end{aligned}\)
C
\(\begin{array}{rlr} f(x) & =\frac{e^{1 / x}-1}{e^{1 / x}+1}, & x \neq 0 \\ & =-1, & x=0 \end{array}\)
D
\(\begin{array}{rlr} f(x) & =\frac{e^{5 x}-e^{2 x}}{\sin 3 x}, & x \neq 0 \\ & =1, & x=0 \end{array}\)
Open complete paper
6
2019 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2019 3RD MAY MORNING SHIFT

If $f(x)$ is continuous at $x=3$, where

$$\begin{aligned} f(x) & =a x+1, & \text { for } x \leq 3 \\ & =b x+3 & , \text { for } x>3 \text { then } \end{aligned}$$

A
$a+b=\frac{-2}{3}$
B
$a-b=\frac{-2}{3}$
C
$a-b=\frac{2}{3}$
D
$a+b=\frac{2}{3}$
Open complete paper
7
2019 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2019 3RD MAY MORNING SHIFT

\(\begin{aligned} & \text { If } f(x)=\left[\tan \left(\frac{\pi}{4}+x\right)\right]^{\frac{1}{x}}, \quad x \neq 0 \\ & =k \text {, } \qquad x=0 \text { is continuous }\\ & x=0 \end{aligned}\) Then $k=$

A
$e^2$
B
1
C
$e$
D
$e^{-2}$
Open complete paper
8
2020 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2020 16TH OCTOBER EVENING SHIFT

The function \(f(x)=\frac{x+1}{9 x+x^3}\) is

A
discontinuous at exactly two points
B
discontinuous at exactly one point
C
continuous for all real values of \(x\)
D
discontinuous at exactly three points
Open complete paper
9
2020 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2020 16TH OCTOBER EVENING SHIFT

If \(f(x)=\frac{|x|}{x}\), for \(x \neq 0\) \(=1\), for \(x=0\), then tre function is

A
differentiable but not continuous at \(x=0\)
B
continuous and differentiable at \(x=0\)
C
neither continuous nor differentiable at \(x=0\)
D
continuous but not differentiable at \(x=0\)
Open complete paper
10
2020 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2020 16TH OCTOBER MORNING SHIFT

The points of discontinuity of the function

$$\begin{aligned} f(x) & =\frac{1}{x-1}, \text { if } 0 \leq x \leq 2 \\ & =\frac{x+5}{x+3} \text { if } 2< x \leq 4 \end{aligned}$$

in its domain are

A
\(x=1, x=2\)
B
\(x=0, x=2\)
C
\(x=2\) only
D
\(x=4\) only
Open complete paper
11
2020 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2020 19TH OCTOBER EVENING SHIFT

If $f(x)=\frac{1-\sin x+\cos x}{1+\sin x+\cos x}$, for $x \neq \pi$ is continuous at $x=\pi$, then $f(\pi)=$

A
1
B
$-$1
C
0
D
2
Open complete paper
12
2021 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2021 20TH SEPTEMBER EVENING SHIFT

If \(f(x) = {{{4^{x - \pi }} + {4^{x - \pi }} - 2} \over {{{(x - \pi )}^2}}}\), for \(x \ne \pi\), is continuous at \(x=\pi\), then k =

A
\(2\log2\)
B
\((\log2)^2\)
C
\(-(\log2)^2\)
D
\(8(\log2)^2\)
Open complete paper
13
2021 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2021 20TH SEPTEMBER EVENING SHIFT

If \(a=\lim _\limits{n \rightarrow \infty} \frac{1+2+3+\ldots+n}{n^2}\) and \(b=\lim _\limits{n \rightarrow \infty} \frac{1^2+2^2+3^2+\ldots+n^2}{n^3}\), then

A
a = b
B
2a = 3b
C
a = 2b
D
3a = 2b
Open complete paper
14
2021 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2021 20TH SEPTEMBER MORNING SHIFT

$$\mathop {\lim }\limits_{x \to \infty } \left( {\sqrt {{x^2} + 5x - 7} - x} \right) =$$

A
\({7 \over 2}\)
B
5
C
\({5 \over 2}\)
D
6
Open complete paper
15
2021 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2021 20TH SEPTEMBER MORNING SHIFT

If f(x) = |x|, for x \(\in\) (\(-1,2\)), then f is discontinuous at (where [x] represents floor function)

A
x = \(-1,0,1,2\)
B
x = \(-1,0,1\)
C
x = 0, 1
D
x = 2
Open complete paper
16
2021 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2021 21TH SEPTEMBER EVENING SHIFT

If \(\lim _\limits{x \rightarrow 5} \frac{x^k-5^k}{x-5}=500\), then the value of \(k\), where \(k \in N\) is

A
5
B
3
C
4
D
6
Open complete paper
17
2021 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2021 21TH SEPTEMBER EVENING SHIFT

$$\begin{aligned} & \text { } f(x)=\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x} \text {, if } 1 \leq x<0 \\ & =\frac{2 x+1}{x-2} \quad \text {, if } 0 \leq x \leq 1 \\ \end{aligned}$$

is continuous in the interval \([-1,1]\), then \(p=\)

A
1
B
\(-\)1
C
\(\frac{-1}{2}\)
D
\(\frac{1}{2}\)
Open complete paper
18
2021 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2021 21TH SEPTEMBER MORNING SHIFT

$$\begin{aligned} & \text { If the function } \mathrm{f}(\mathrm{x})=1+\sin \frac{\pi}{2}, \quad-\infty<\mathrm{x} \leq 1 \\ & =\mathrm{ax}+\mathrm{b}, \quad 1<\mathrm{x}<3 \\ & =6 \tan \frac{x \pi}{12}, \quad 3 \leq x<6 \\ \end{aligned}$$

is continuous in \((-\infty, 6)\), then the values of \(\mathrm{a}\) and \(\mathrm{b}\) are respectively.

A
1, 1
B
2, 1
C
0, 2
D
2, 0
Open complete paper
19
2021 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2021 21TH SEPTEMBER MORNING SHIFT

$$\lim _\limits{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^2+x-3}=$$

A
\(\frac{1}{5}\)
B
\(\frac{1}{10}\)
C
\(\frac{-1}{10}\)
D
\(\frac{-1}{5}\)
Open complete paper
20
2021 · Mathematics · Calculus · Limits Continuity And Differentiability
MHT CET 2021 22TH SEPTEMBER EVENING SHIFT

Let

$$\begin{aligned} f(x) & =x+a \sqrt{2} \sin x & & , 0 \leq x<\frac{\pi}{4} \\ & =2 x \cot x+b & & \frac{\pi}{4} \leq x<\frac{\pi}{2} \\ & =a \cos 2 x-b \sin x & & \frac{\pi}{2} \leq x \leq \pi \end{aligned}$$

If \(\mathrm{f}(\mathrm{x})\) is continuous for \(0 \leq \mathrm{x} \leq \pi\), then

A
\(a=\frac{\pi}{6}, b=\frac{\pi}{12}\)
B
\(\mathrm{a}=\frac{-\pi}{6}, \mathrm{~b}=\frac{-\pi}{12}\)
C
\(a=\frac{-\pi}{6}, b=\frac{\pi}{12}\)
D
\(a=\frac{\pi}{6}, b=\frac{-\pi}{12}\)
Open complete paper

Showing 20 of 127 questions