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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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Most viewed questions in Calculus

12 votes
6 answers
41
GATE CSE 1998 | Question: 1.4
Consider the function $y=|x|$ in the interval $[-1, 1]$. In this interval, the function is continuous and differentiable continuous but not differentiable differentiable but not continuous neither continuous nor differentiable
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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3 votes
3 answers
42
ISRO2018-15
The domain of the function $\log (\log \sin(x))$ is: $0<x<$\pi$ $2n$\pi$<$x$<$(2n+1)$\pi$, for $n$ in $N$ Empty set None of the above
The domain of the function $\log (\log \sin(x))$ is:$0<x<$$\pi$$2n$$\pi$$<$$x$$<$$(2n+1)$$\pi$, for $n$ in $N$Empty setNone of the above
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8 votes
2 answers
43
GATE CSE 2023 | Question: 18
Let $\qquad f(x)=x^{3}+15 x^{2}-33 x-36$ be a real-valued function. Which of the following statements is/are $\text{TRUE}?$ $f(x)$ does not have a local maximum. $f(x)$ has a local maximum. $f(x)$ does not have a local minimum. $f(x)$ has a local minimum.
Let $$\qquad f(x)=x^{3}+15 x^{2}-33 x-36$$be a real-valued function.Which of the following statements is/are $\text{TRUE}?$$f(x)$ does not have a local maximum.$f(x)$ has...
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19 votes
4 answers
44
GATE CSE 2014 Set 1 | Question: 46
The function $f(x) =x \sin x$ satisfies the following equation: $f''(x) + f(x) +t \cos x = 0$The value of $t$ is______.
The function $f(x) =x \sin x$ satisfies the following equation: $$f''(x) + f(x) +t \cos x = 0$$The value of $t$ is______.
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10 votes
1 answer
46
ISRO2016-3
$\displaystyle{}\lim_{x\rightarrow 0}\frac{\sqrt{1+x}-\sqrt{1-x}}{x}$ is given by $0$ $-1$ $1$ $\frac{1}{2}$
$\displaystyle{}\lim_{x\rightarrow 0}\frac{\sqrt{1+x}-\sqrt{1-x}}{x}$ is given by$0$$-1$$1$$\frac{1}{2}$
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3 votes
2 answers
47
Lagrange 's Mean Value Theorem 2
If f ' (x) =$\frac{8}{x^{}2+3x+4}$ and f(0) =1 then the lower and upper bounds of f(1) estimated by Langrange 's Mean Value Theorem are ___
If f ' (x) =$\frac{8}{x^{}2+3x+4}$ and f(0) =1 then the lower and upper bounds of f(1) estimated by Langrange 's Mean Value Theorem are ___
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0 votes
2 answers
48
GATE CSE 2023 | Memory Based Question: 11
Let $f(x)=x^3+15 x^2-33 x-36$ be a real valued function. Which statement is/are TRUE? $f(x)$ has a local maximum. $f(x)$ does NOT have a local maximum. $f(x)$ has a local minimum. $f(x)$ does NOT have a local minimum.
Let $f(x)=x^3+15 x^2-33 x-36$ be a real valued function. Which statement is/are TRUE?$f(x)$ has a local maximum.$f(x)$ does NOT have a local maximum.$f(x)$ has a local mi...
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5 votes
3 answers
49
ISRO-2013-49
What is the least value of the function $f(x) = 2x^{2}-8x-3$ in the interval $[0, 5]$? $-15$ $7$ $-11$ $-3$
What is the least value of the function $f(x) = 2x^{2}-8x-3$ in the interval $[0, 5]$?$-15$$7$$-11$$-3$
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13 votes
1 answer
50
GATE CSE 1998 | Question: 8
Find the points of local maxima and minima, if any, of the following function defined in $0\leq x\leq 6$. $x^3-6x^2+9x+15$ Integrate $\int_{-\pi}^{\pi} x \cos x dx$
Find the points of local maxima and minima, if any, of the following function defined in $0\leq x\leq 6$. $$x^3-6x^2+9x+15$$Integrate $$\int_{-\pi}^{\pi} x \cos x dx$$
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15 votes
3 answers
51
GATE CSE 1993 | Question: 02.1
$\displaystyle \lim_{x \to 0} \frac{x(e^x - 1) + 2(\cos x -1)}{x(1 - \cos x)}$ is __________
$\displaystyle \lim_{x \to 0} \frac{x(e^x - 1) + 2(\cos x -1)}{x(1 - \cos x)}$ is __________
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4 votes
2 answers
52
GATE CSE 1993 | Question: 02.6
The value of the double integral $\int^{1}_{0} \int_{0}^{\frac{1}{x}} \frac {x}{1+y^2} dxdy$ is_________.
The value of the double integral $\int^{1}_{0} \int_{0}^{\frac{1}{x}} \frac {x}{1+y^2} dxdy$ is_________.
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3 votes
1 answer
53
Gate_EE_2006
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15 votes
6 answers
55
TIFR CSE 2010 | Part A | Question: 7
The limit of $\dfrac{10^{n}}{n!}$ as $n \to \infty$ is. $0$ $1$ $e$ $10$ $\infty$
The limit of $\dfrac{10^{n}}{n!}$ as $n \to \infty$ is.$0$$1$$e$$10$$\infty$
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2 votes
3 answers
56
limit
limx->0 (cot x)1/logx ? ans: 0(m getting 1/e)
limx->0 (cot x)1/logx ?ans: 0(m getting 1/e)
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1 votes
1 answer
57
GATE CSE 1993 | Question: 01.7
The function $f\left(x,y\right) = x^2y - 3xy + 2y +x$ has no local extremum one local minimum but no local maximum one local maximum but no local minimum one local minimum and one local maximum
The function $f\left(x,y\right) = x^2y - 3xy + 2y +x$ hasno local extremumone local minimum but no local maximumone local maximum but no local minimumone local minimum an...
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0 votes
1 answer
60
Lagrange 's Mean Value Theorem
Question: The value of $\zeta$ of $f(b) - f(a) = (b-a) \cdot f'(\zeta)$ for the function $f(x) = Ax^2 + Bx +C$ in the interval $[a,b]$ is _______ My Attempt : STEP 1: $f(x)$ is polynomial function therefore continuous STEP 2: $f(x)$ is ... How to proceed further?
Question:The value of $\zeta$ of $f(b) - f(a) = (b-a) \cdot f'(\zeta)$ for the function $f(x) = Ax^2 + Bx +C$ in the interval $[a,b]$ is _______My Attempt :STEP 1: $f(x)...
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