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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

3 votes
1 answer
603
TIFR-2015-Maths-A-8
Let $f(x)=\frac{e^{\frac{-1}{x}}}{x}$, where $x \in (0, 1)$. Then on $(0, 1)$. $f$ is uniformly continuous. $f$ is continuous but not uniformly continuous. $f$ is unbounded. $f$ is not continuous.
Let $f(x)=\frac{e^{\frac{-1}{x}}}{x}$, where $x \in (0, 1)$. Then on $(0, 1)$.$f$ is uniformly continuous.$f$ is continuous but not uniformly continuous.$f$ is unbounded....
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0 votes
1 answer
605
maxima-minima query
consider the following function f(x) = x3 /3+ x2 /2 -6x+1000 find the intervals on which f is increasing. Is my solution right approach for this kind of numerical?? Caption
consider the following function f(x) = x3 /3+ x2 /2 -6x+1000find the intervals on which f is increasing.Is my solution right approach for this kind of numerical?? Caption...
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2 votes
1 answer
608
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
609
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
610
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
611
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
612
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
613
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
614
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
615
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
617
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
618
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
619
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
620
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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