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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

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151
ISI2017-MMA-25
For $a,b \in \mathbb{R}$ and $b > a$ , the maximum possible value of the integral $\int_{a}^{b}(7x-x^{2}-10)dx$ is $\frac{7}{2}\\$ $\frac{9}{2}\\$ $\frac{11}{2}\\$ none of these
For $a,b \in \mathbb{R}$ and $b a$ , the maximum possible value of the integral $\int_{a}^{b}(7x-x^{2}-10)dx$ is$\frac{7}{2}\\$$\frac{9}{2}\\$$\frac{11}{2}\\$none of the...
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1 votes
1 answer
152
Doubt
A polynomial of degree 4 with real coefficients A) Can possibly have no extrema and no zero crossings B) May have up to four extrema and up to 3 zero crossings C) Cannot have more than three extrema and more than four zero crossings D) Will have an equal number of extrema and zero crossings
A polynomial of degree 4 with real coefficientsA) Can possibly have no extrema and no zero crossingsB) May have up to four extrema and up to 3 zero crossingsC) Cannot hav...
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0 votes
2 answers
154
ISI2017-MMA-4
Let $S\subseteq \mathbb{R}$. Consider the statement “There exists a continuous function $f:S\rightarrow S$ such that $f(x) \neq x$ for all $x \in S.$ ” This statement is false if $S$ equals $[2,3]$ $(2,3]$ $[-3,-2] \cup [2,3]$ $(-\infty,\infty)$
Let $S\subseteq \mathbb{R}$. Consider the statement “There exists a continuous function $f:S\rightarrow S$ such that $f(x) \neq x$ for all $x \in S.$ ”This statement ...
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0 votes
0 answers
155
Shortcut Method to find Maxima and Minima in Calculus
https://www.youtube.com/watch?v=tyiQLindzCE This is a great video but covers formula for cubic root what about for any given equation x^n,what would be the solution?
https://www.youtube.com/watch?v=tyiQLindzCEThis is a great video but covers formula for cubic root what about for any given equation x^n,what would be the solution?
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4 votes
1 answer
156
Calculus
It should be 1 and 3 ?? please correct me if I'm wrong.
It should be 1 and 3 ?? please correct me if I'm wrong.
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0 votes
0 answers
157
Mathematics GATE 2018 EE: 43
Let $f(x) = 3x^{3} - 7x^{2} + 5x + 6$. The maximum value of $f(x)$ over the the interval $[ 0 , 2 ]$ is_________(Upto $1$ decimal place)
Let $f(x) = 3x^{3} - 7x^{2} + 5x + 6$. The maximum value of $f(x)$ over the the interval $[ 0 , 2 ]$ is_________(Upto $1$ decimal place)
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0 votes
0 answers
158
calculus differentiation question
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0 votes
1 answer
159
GradeUp quiz-Maxima minima
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1 votes
3 answers
161
NIELIT 2017 DEC Scientific Assistant A - Section B: 10
The function $f\left ( x \right )=\dfrac{x^{2}-1}{x-1}$ at $x=1$ is : Continuous and differentiable Continuous but not differentiable Differentiable but not continuous Neither continuous nor differentiable
The function $f\left ( x \right )=\dfrac{x^{2}-1}{x-1}$ at $x=1$ is :Continuous and differentiableContinuous but not differentiableDifferentiable but not continuousNeith...
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1 votes
1 answer
162
Finding Maxima Minima
The greatest value of the function f(x) = 2 sin x + sin 2x on the interval [ 0,3pi/2 ] is ____
The greatest value of the function f(x) = 2 sin x + sin 2x on the interval [ 0,3pi/2 ] is ____
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2 votes
1 answer
164
Limit question
$\lim_{x\rightarrow0}\frac{x^{2}+1}{x(x-1)}=?$
$\lim_{x\rightarrow0}\frac{x^{2}+1}{x(x-1)}=?$
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0 votes
1 answer
165
Area between curves
The area between the parabola $x^2 = 8y$ and the straight line y= 8 is . I am getting $128√2$.
The area between the parabola $x^2 = 8y$ and the straight line y= 8 is .I am getting $128√2$.
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1 votes
1 answer
166
GATE CSE 1995 | Question: 2.18
The solution of differential equation $y''+3y'+2y=0$ is of the form $C_1e^x+C_2e^{2x}$ $C_1e^{-x}+C_2e^{3x}$ $C_1e^{-x}+C_2e^{-2x}$ $C_1e^{-2x}+C_2e^{-x}$
The solution of differential equation $y''+3y'+2y=0$ is of the form$C_1e^x+C_2e^{2x}$$C_1e^{-x}+C_2e^{3x}$$C_1e^{-x}+C_2e^{-2x}$$C_1e^{-2x}+C_2e^{-x}$
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0 votes
1 answer
167
ISRO 2012- [Mech] Calculus
The approximate value of y(0.1) from dy/dx = $x^2$y-1, y(0) =1 is (a) 0.900 (b) 1.001 (c) 0.802 (d) 0.994
The approximate value of y(0.1) from dy/dx = $x^2$y-1, y(0) =1 is(a) 0.900(b) 1.001(c) 0.802(d) 0.994
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0 votes
1 answer
168
order and degree
The order and degree of the differential equation (A) 3 and 2 (B) 2 and 3 (C) 3 and 3 (D) 3 and 1
The order and degree of the differential equation(A) 3 and 2 (B) 2 and 3(C) 3 and 3 (D) 3 and 1
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2 votes
1 answer
169
ISI2018-MMA-29
Let $f$ be a continuous function with $f(1) = 1$. Define $F(t)=\int_{t}^{t^2}f(x)dx$. The value of $F’(1)$ is $-2$ $-1$ $1$ $2$
Let $f$ be a continuous function with $f(1) = 1$. Define $$F(t)=\int_{t}^{t^2}f(x)dx$$.The value of $F’(1)$ is$-2$$-1$$1$$2$
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