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Syllabus: Limits, Continuity, and Differentiability, Maxima and minima, Mean value theorem, Integration.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1 &1&1&1&1&1&0&1&1&1&0&0.9&1
\\\hline\textbf{2 Marks Count} & 0 &0&0&0&0&0&1&0&0&0&0&0.1&1
\\\hline\textbf{Total Marks} & 1 &1&1&1&1&1&2&1&1&1&\bf{1}&\bf{1.1}&\bf{2}\\\hline
\end{array}}}$$

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Recent questions in Calculus

2 votes
1 answer
573
TIFR-2014-Maths-A-3
Let $f: \mathbb{R} \to \mathbb{R}$ be a differentiable function such that $\displaystyle \lim_{x \to +\infty} f'(x)=1$, then $f$ is bounded $f$ is increasing $f$ is unbounded $f'$ is bounded
Let $f: \mathbb{R} \to \mathbb{R}$ be a differentiable function such that $\displaystyle \lim_{x \to +\infty} f'(x)=1$, then$f$ is bounded $f$ is increasing $f$ is unboun...
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1 votes
0 answers
574
TIFR-2011-Maths-B-6
Suppose $f_{n}(x)$ is a sequence of continuous functions on the closed interval $[0, 1]$ converging to $0$ point wise. Then the integral $\int_{0}^{1} f_{n}(x) \text{d}x$ converges to 0.
Suppose $f_{n}(x)$ is a sequence of continuous functions on the closed interval $[0, 1]$ converging to $0$ point wise. Then the integral $\int_{0}^{1} f_{n}(x) \text{d}x...
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1 votes
0 answers
575
TIFR-2011-Maths-B-4
A bounded continuous function on $\mathbb{R}$ is uniformly continuous.
A bounded continuous function on $\mathbb{R}$ is uniformly continuous.
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3 votes
2 answers
576
TIFR-2011-Maths-A-25
The function $f(x) = \begin{cases} 0 & \text{if x is rational} \\ x& \text{if x is irrational} \end{cases}$ is not continuous anywhere on the real line.
The function$f(x)= \begin{cases}0 & \text{if x is rational} \\ x& \text{if x is irrational} \end{cases}$is not continuous anywhere on the real line.
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1 votes
1 answer
577
TIFR-2011-Maths-A-21
Any continuous function from the open unit interval $(0, 1)$ to itself has a fixed point.
Any continuous function from the open unit interval $(0, 1)$ to itself has a fixed point.
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1 votes
1 answer
578
TIFR-2011-Maths-A-19
The derivative of the function $\int_{0}^{\sqrt{x}} e^{-t^{2}}dt$ at $x = 1$ is $e^{-1}$ .
The derivative of the function$\int_{0}^{\sqrt{x}} e^{-t^{2}}dt$at $x = 1$ is $e^{-1}$ .
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1 votes
1 answer
579
TIFR-2011-Maths-A-15
If $A, B$ are closed subsets of $[0,\infty)$, then $A + B = \left\{x + y | x \in A, y \in B\right\}$ is closed in $[0,\infty)$
If $A, B$ are closed subsets of $[0,\infty)$, then$A + B = \left\{x + y | x \in A, y \in B\right\}$is closed in $[0,\infty)$
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1 votes
1 answer
580
TIFR-2011-Maths-A-14
$\log x$ is uniformly continuous on $( \frac{1}{2}, \infty)$.
$\log x$ is uniformly continuous on $( \frac{1}{2}, \infty)$.
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1 votes
0 answers
582
TIFR-2011-Maths-A-6
The function $f_{n}(x)= n \sin (x/n)$ Does not converge for any $x$ as $n \rightarrow \infty$ Converges to the constant function $1$ as $n \rightarrow \infty$ Converges to the function $x$ as $n \rightarrow \infty$ Does not converge for all $x$ as $n \rightarrow \infty$
The function $f_{n}(x)= n \sin (x/n)$Does not converge for any $x$ as $n \rightarrow \infty$Converges to the constant function $1$ as $n \rightarrow \infty$Converges to t...
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2 votes
1 answer
583
TIFR-2011-Maths-A-5
The differential equation $\frac{dy}{dx}= y^{1/3}, y(0)=0$ has A unique solution No nontrivial solution Finite number of solutions Infinite number of solutions
The differential equation$\frac{dy}{dx}= y^{1/3}, y(0)=0$ hasA unique solutionNo nontrivial solution Finite number of solutionsInfinite number of solutions
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1 votes
2 answers
584
TIFR-2011-Maths-A-2
$\lim_{x \rightarrow 0} \sin \left(1/x^{2}\right)$ equals. $1$ $0$ $\infty$ Oscillates
$\lim_{x \rightarrow 0} \sin \left(1/x^{2}\right)$ equals.$1$$0$$\infty$Oscillates
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1 votes
1 answer
585
Which book is best for calculus?
Between Higher engineering mathematics and Gilbert Strang which one is more appropriate for GATE?
Between Higher engineering mathematics and Gilbert Strang which one is more appropriate for GATE?
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2 votes
0 answers
586
bijection, surjection please confirm the ans
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1 votes
2 answers
589
Find absolute minimum
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1 votes
2 answers
590
improper integral
http://www.questionpapers.net.in/Question%20Papers/gate-question-papers-download/gate-question-papers-download-civil-engineering-2007.pdf question 25....plz give it proper solution
http://www.questionpapers.net.in/Question%20Papers/gate-question-papers-download/gate-question-papers-download-civil-engineering-2007.pdfquestion 25....plz give it proper...
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