Limits, Continuity and Differentiability PYQs - Last 5 Years
KCET / Mathematics / Calculus / 15 recent questions
MathematicsCalculus2022-2026
Practice 15 KCET Mathematics questions from Limits, Continuity and Differentiability. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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Mathematics / Calculus
2022-2026
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15 in last 5 years15 in last 10 years
Last 5 Years Limits, Continuity and Differentiability Questions
Showing 15 of 15 filtered questions.
1Limits Continuity And Differentiability
If $f(x) = \begin{cases} ax + 7 & \text{if } x < 1 \\ 3x - 1 & \text{if } x = 1 \\ \dfrac{b}{x + 3} & \text{if } x > 1 \end{cases}$ is continuous at $x = 1$, then
MCQ+1 / -02026
2Limits Continuity And Differentiability
If $\lim\limits_{x \to 3}\left(\dfrac{x^2 - ax - 3b}{x - 3}\right) = 5$, then $a + b = $
MCQ+1 / -02026
3Limits Continuity And Differentiability
If $f(x) = \begin{cases} x^2 - 1 & \text{if } x \geq 2 \\ x + 1 & \text{if } x < 2 \end{cases}$, then $\lim\limits_{x \to 1} f(x) + \lim\limits_{x \to 2} f(x) = $
MCQ+1 / -02026
4Limits Continuity And Differentiability
Match the following:
In the following, $[\mathrm{x}]$ denotes the greatest integer less than or equal to x .
Column - I
Column - II
(a)
x
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x
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x
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x
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x|x|
(i)
continuo...
In the following, $[\mathrm{x}]$ denotes the greatest integer less than or equal to x .
Column - I
Column - II
(a)
x
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x
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x
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x
|
x|x|
(i)
continuo...
MCQ+1 / -02025
5Limits Continuity And Differentiability
$$ \text { A function } f(x)=\left\{\begin{array}{cl} \frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}, & \text { if } x \neq 0 \\ 0, & \text { if } x=0 \end{array}\right. $$
MCQ+1 / -02025
6Limits Continuity And Differentiability
The function $f(x)=\left\{\begin{array}{ll}e^x+a x & , x<0 \\ b(x-1)^2 & , x \geq 0\end{array}\right.$ is differentiable at $x=0$. Then
MCQ+1 / -02025
7Limits Continuity And Differentiability
$\lim _{x \rightarrow 1} \frac{x^4-\sqrt{x}}{\sqrt{x}-1}$ is
MCQ+1 / -02025
8Limits Continuity And Differentiability
The function $f(x)=|\cos x|$ is
MCQ+1 / -02024
9Limits Continuity And Differentiability
\(\lim _\limits{n \rightarrow \infty}\left(\frac{n}{n^2+1^2}+\frac{n}{n^2+2^2}+\frac{n}{n^2+3^2}+\ldots+\frac{1}{5 n}\right)=\)
MCQ+1 / -02024
10Limits Continuity And Differentiability
Let $f(x)=\left|\begin{array}{ccc}\cos x & x & 1 \\ 2 \sin x & x & 2 x \\ \sin x & x & x\end{array}\right|$. Then, $\lim _\limits{x \rightarrow 0} \frac{f(x)}{x^2}$ is
MCQ+1 / -02024
11Limits Continuity And Differentiability
$\lim \limits_{x \rightarrow \frac{\pi}{4}} \frac{\sqrt{2} \cos x-1}{\cot x-1}$ is equal to
MCQ+1 / -02024
12Limits Continuity And Differentiability
The function \(f(x)=\cot x\) is discontinuous on every point of the set
MCQ+1 / -02023
13Limits Continuity And Differentiability
If \(\lim _\limits{x \rightarrow 0} \frac{\sin (2+x)-\sin (2-x)}{x}=A \cos B\), then the values of \(A\) and \(B\) respectively are
MCQ+1 / -02023
14Limits Continuity And Differentiability
\(\lim _\limits{y \rightarrow 0} \frac{\sqrt{3+y^3}-\sqrt{3}}{y^3}=\)
MCQ+1 / -02022
15Limits Continuity And Differentiability
If $$f(x)=\left\{\begin{array}{cc}x^2-1, & 0< x<2 \\ 2 x+3, & 2 \leq x<3\end{array}\right.$$,
the quadratic equation whose roots are \(\lim _\limits{x \rightarrow 2^{-}} f(x)\) and \(\lim _\limits{x \rightarrow 2^{+}} f(x)\) is
the quadratic equation whose roots are \(\lim _\limits{x \rightarrow 2^{-}} f(x)\) and \(\lim _\limits{x \rightarrow 2^{+}} f(x)\) is
MCQ+1 / -02022