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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\hline \textbf{Year}& \textbf{2026 - 1}& \textbf{2026 - 2}& \textbf{2025 - 1}& \textbf{2025 - 2}& \textbf{2024 - 1}& \textbf{2024 - 2}& \textbf{2023}& \textbf{2022}& \textbf{2021 - 1}& \textbf{2021 - 2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}\\\hline \textbf{1 Mark Count}&1&1&1&1&1&1&2&1&1&1&1&1.1&2\\\hline \textbf{2 Marks Count}&1&1&0&0&0&0&0&0&0&0&0&0.2&1\\\hline \textbf{Total Marks}&3&3&1&1&1&1&2&1&1&1&\bf{1}&\bf{1.5}&\bf{3}\\\hline \end{array}}}$$

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Recent questions in Calculus

3 3 votes
3 3 answers
155
155 views
what is the mistake here
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5 5 votes
1 1 answer
608
608 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Arc Length
Find the length of the curve $x=\cos t,\ y=t+\sin t,\ 0\le t\le \pi$.
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7 7 votes
1 1 answer
490
490 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Chain Rule
Find $\dfrac{dy}{dx}$ where $$y=\int_{x^2}^{\sin x}\sqrt{1+t^4}dt$$$\cos x\sqrt{1+\sin^4x}-2x\sqrt{1+x^8}$ $\cos x\sqrt{1+\sin^4x}+2x\sqrt{1+x^8}$ $\sqrt{1+\sin^4x}-\sqrt...
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4 4 votes
1 1 answer
334
334 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Initial Value Integration
Find $f(x)$ if $f'(x)=6x^2+\sec^2 x$ and $f(0)=4$.$f(x)=2x^3+\tan x+4$ $f(x)=2x^3-\tan x+4$ $f(x)=6x^3+\tan x+4$ $f(x)=2x^3+\tan x-4$
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3 3 votes
1 1 answer
288
288 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Area Between Curves
Find the area of the region bounded by the lines $x=-1$, $x=2$, $y=0$, and the curve $y=x^3-x^2-2x$.$\frac{5}{12}$ $\frac{8}{3}$ $\frac{37}{12}$ $\frac{11}{4}$
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1 1 vote
1 1 answer
277
277 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Applications of Integration
The volume of the solid generated by revolving the region bounded by the curves $y=x^2$ and $y=x+2$ about the $x$-axis is:$\frac{72}{5}$ $\frac{72\pi}{5}$ $\frac{36\pi}{5...
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0 0 votes
1 1 answer
270
270 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Arc Length
The length of the curve $y=\frac{1}{3}\left((x-1)^2+2\right)^{3/2}$ for $-1\leq x\leq2$ is:$5$ $6$ $\dfrac{20}{3}$ $8$
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0 0 votes
1 1 answer
198
198 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Area Between Curves
The area of the region between the curves $y=x^2-2x$ and $y=2x-x^2$ for $x\in[-1,3]$ is:$4$ $\frac{16}{3}$ $\frac{20}{3}$ $8$
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2 2 votes
1 1 answer
214
214 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Inflection Points
The point of inflection of the function $y=e^x(\sin x-\cos x)$ in $[0,\pi]$ is:$x=\dfrac{\pi}{4}$ $x=\dfrac{3\pi}{4}$ $x=\dfrac{\pi}{4},\dfrac{3\pi}{4}$ No point of infle...
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2 2 votes
1 1 answer
266
266 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Continuity & Differentiability
The function $$f(x)=\begin{cases}x\sin\left(\frac{1}{x}\right),&x\neq0\\\\0,&x=0\end{cases}$$ at $x=0$ is:Continuous and differentiable Continuous but not differentiable ...
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3 3 votes
1 1 answer
195
195 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | One-Sided Derivatives
Let $f:\mathbb{R}\to\mathbb{R}$ be an even function. Suppose the left derivative of $f$ at $x=3$ exists and is equal to $-6$. Which of the following is necessarily true?T...
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1 1 vote
1 1 answer
249
249 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Sequence Limits
Let $(v_n)$ be a sequence defined by $v_1=2$ and $v_{n+1}=\frac{1}{2}\left(v_n+\frac{8}{v_n}\right)$ for $n\geq1$. If $(v_n)$ converges, then $\lim_{n\to\infty}v_n$ is:$2...
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2 2 votes
1 1 answer
220
220 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Absolute Value Integrals
Find the value of $$\int_{-2}^{3}|x^3-3x^2-4x+12|dx$$$\dfrac{125}{4}$ $\dfrac{131}{4}$ $32$ $\dfrac{119}{4}$
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1 1 vote
1 1 answer
198
198 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Inflection Points
The point(s) of inflection of the curve $$y=\frac{2}{5}x^6-\frac{9}{5}x^5-3x^4+22x^3-36x^2+5x+1$$ is/are:$x=-2,1,3$ $x=-2$ and $x=3$ only $x=1$ only None of the above
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1 1 vote
1 1 answer
212
212 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Definite Integration
Evaluate $$I=\int_0^{\frac{\pi}{2}}\frac{\cos x}{\sqrt{1+\sin x}\left(1+\sqrt{1+\sin x}\right)}dx$$$2\ln\left(\frac{1+\sqrt2}{2}\right)$ $\ln\left(\frac{1+\sqrt2}{2}\righ...
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2 2 votes
1 1 answer
218
218 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Pointwise Differentiability
At the point $x=1$, the function $f(x)=\begin{cases}(x-1)^2\sin\left(\frac{1}{x-1}\right),&x\neq1\\\\0,&x=1\end{cases}$ is:not continuous continuous but not differ...
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0 0 votes
1 1 answer
222
222 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Improper Integrals
Evaluate $$I=\int_0^1 \frac{x^2}{(1-x^2)^{3/2}}dx$$$\frac{\pi}{4}$ $1$ $2$ The integral diverges
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1 1 vote
1 1 answer
193
193 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Integration
Let $f(x)=\left|x-\lfloor x\rfloor-\frac{1}{2}\right|$, where $\lfloor x\rfloor$ denotes the greatest integer less than or equal to $x$. The value of $\int_{0.2}^{2.75} f...
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0 0 votes
1 1 answer
140
140 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Related Rates
A $20\text{ ft}$ ladder leans against a vertical wall. The base of the ladder is sliding away from the wall at $2\text{ ft/s}$. A point $P$ on the ladder is $6\text{ ft}$...
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1 1 vote
1 1 answer
168
168 views
GO Classes DPP | GATE CS, DA | Calculus & Optimization | Definite Integration
Let $f:[0,1]\to\mathbb{R}$ be continuous and satisfy $f(x)=x^2+\int_0^1 (x+t)f(t)dt$ for every $x\in[0,1]$. Which of the following is $f(x)$?$x^2-5x-\frac{17}{6}$ $x^2+5x...
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