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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1} &\textbf{2024-2} &\textbf{2023} &\textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &1&1&2& 1 &1&1&1&1.16&2
\\\hline\textbf{2 Marks Count} &0&0&0& 0 &0&0&0&0&0
\\\hline\textbf{Total Marks} & 1&1&2&1 &1&1&\bf{1}&\bf{1.16}&\bf{2}\\\hline
\end{array}}}$$

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Hot questions in Calculus

#61
6.6k
views
2 answers
17 votes
GATE CSE 2007 | Question: 1
Consider the following two statements about the function $f(x)=\left\vert x\right\vert$:P. $f(x)$ is continuous for all real values of $x$.Q. $f(x)$ is differentiable for...
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#62
1.1k
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2 answers
7 votes
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 8
Choose the CORRECT statement -The function $f(x)=\exp \left(-x^{2}\right)-1$ has the root $x=0$.If a function $f$ is differentiable on $[-1,1]$, then there is a point $x$...
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#63
5.6k
views
6 answers
13 votes
GATE CSE 1998 | Question: 1.4
Consider the function $y=|x|$ in the interval $[-1, 1]$. In this interval, the function iscontinuous and differentiablecontinuous but not differentiabledifferentiable but...
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#64
5.8k
views
3 answers
27 votes
GATE CSE 1995 | Question: 1.21
In the interval $[0, \pi]$ the equation $x=\cos x$ has No solutionExactly one solutionExactly two solutionsAn infinite number of solutions
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#65
14.3k
views
4 answers
62 votes
GATE CSE 2012 | Question: 9
Consider the function $f(x) = \sin(x)$ in the interval $x =\left[\frac{\pi}{4},\frac{7\pi}{4}\right]$. The number and location(s) of the local minima of this function are...
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#66
590
views
3 answers
2 votes
ISI2016-MMA-27
Consider the function $f(x) = \dfrac{e^{- \mid x \mid}}{\text{max}\{e^x, e^{-x}\}}, \: \: x \in \mathbb{R}$. Then$f$ is not continuous at some points$f$ is continuous eve...
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#67
646
views
1 answers
7 votes
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 15
Suppose $f$ is twice differentiable with$$f^{\prime \prime}(x)=7 x-2, \quad f^{\prime}(-2)=0, \quad \text { and } \quad f(-2)=-2 .$$Find $f(0)$.$-337 / 6$$-74 / 3$$23 / 9...
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#68
458
views
2 answers
0 votes
ISI2016-PCB-A-2
Let $n$ be a fixed positive integer. For any real number $x,$ if for some integer $q,$ $$x=qn+r, \: \: \: 0 \leq r < n,$$ then we define $x \text{ mod } n=r$.Specify the...
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#69
550
views
1 answers
0 votes
ISI2016-MMA-24
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a strictly increasing function. Then which one the following is always true?The limits $\lim_{x \rightarrow a+} f(x) $ and $...
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#70
693
views
1 answers
5 votes
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 6
Suppose that the derivative of a function $h$ is given by:$$h^{\prime}(x)=x(x-1)^{2}(x-2)$$On what interval(s) is $h$ increasing?$(-\infty, 0)$$(-\infty, 0)$ and $(2, \in...
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#71
592
views
1 answers
8 votes
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 19
The equation $x^{5}+x+1=0$ has a solution in the interval$[0,1]$$[-1,0]$$[-2,-1]$$[1,2]$
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#72
770
views
1 answers
6 votes
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 13
Suppose $g(x)$ is a polynomial function such that $g(-1)=4$ and $g(2)=7$. Then there is a number $c$ between $-1$ and $2$ such that$g(c)=1$$g^{\prime}(c)=1$$g(c)=0$$g^{\p...
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#73
518
views
1 answers
6 votes
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 18
Let $f$ be differentiable for all $x$. If $f(1)=-2$ and $f^{\prime}(x) \geq 2$ for $x \in[1,6]$, then$f(6) \geq 8$$f(6)<8$$f(6)<5$$f(6)=5$
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#74
8.0k
views
5 answers
24 votes
GATE IT 2008 | Question: 31
If $f(x)$ is defined as follows, what is the minimum value of $f(x)$ for $x \in (0, 2]$ ?$$f(x) = \begin{cases} \frac{25}{8x} &\text{ when } x \leq \frac{3}{2} \\ x+ \fr...
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#75
543
views
1 answers
5 votes
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 4
The function $f(x)=\cos x-x$is an even functionis an odd functionis neither an even nor an odd functionNone of these
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#76
573
views
1 answers
4 votes
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 16
The sum of three positive numbers is $12$ and two of them are equal. Find the largest possible product.$86$$64$$48$$72$
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#77
677
views
1 answers
8 votes
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 12
Which of the following is/are FALSE?The absolute maximum value of $f(x)=\dfrac{1}{x}$ on the interval $[2,4]$ is $2.$If $f(x)$ is a continuous function and $f(3)=2$ and $...
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#78
451
views
0 answers
0 votes
Gate@Zeal 2022 Test Series
Answer -3.7
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#79
2.3k
views
4 answers
12 votes
TIFR CSE 2011 | Part A | Question: 14
The limit $$\lim_{x \to 0} \frac{d}{dx}\,\frac{\sin^2 x}{x}$$ is$0$$2$$1$$\frac{1}{2}$None of the above
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#80
806
views
2 answers
1 votes
GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 1
Evaluate the limit$$\lim _{x \rightarrow 0} \frac{1-\cos x}{\sin ^{2} x}$$$1$$\frac{1}{2}$$2$$0$
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