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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 answered questions in Calculus

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641
ISI2016-MMA-21
Let $A=\{1, 2, 3, 4, 5, 6, 7, 8 \}$. How many functions $f: A \rightarrow A$ can be defined such that $f(1)< f(2) < f(3)$? $\begin{pmatrix} 8 \\ 3 \end{pmatrix}$ $\begin{pmatrix} 8 \\ 3 \end{pmatrix} 5^8$ $\begin{pmatrix} 8 \\ 3 \end{pmatrix} 8^5$ $\frac{8!}{3!}$
Let $A=\{1, 2, 3, 4, 5, 6, 7, 8 \}$. How many functions $f: A \rightarrow A$ can be defined such that $f(1)< f(2) < f(3)$?$\begin{pmatrix} 8 \\ 3 \end{pmatrix}$$\begin{pm...
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642
ISI2016-MMA-23
Given that $\int_{-\infty}^{\infty} e^{-x^2/2} dx = \sqrt{2 \pi}$, what is the value of $\int_{- \infty}^{\infty} \mid x \mid ^{-1/2} e^{- \mid x \mid} dx$? $0$ $\sqrt{\pi}$ $2 \sqrt{\pi}$ $\infty$
Given that $\int_{-\infty}^{\infty} e^{-x^2/2} dx = \sqrt{2 \pi}$, what is the value of $\int_{- \infty}^{\infty} \mid x \mid ^{-1/2} e^{- \mid x \mid} dx$?$0$$\sqrt{\pi}...
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643
limit
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644
limit
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645
definite integral when infinity is multiplied by zero
in this question, infinity is multiplied by zero generally infinity multiplied by zero gives undefined result.
in this question, infinity is multiplied by zero generally infinity multiplied by zero gives undefined result.
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646
vectors x1= 5i-2j+k and x2=4i-j+2k are transformed into y1=ax1 and y2=ax2.
vectors x1= 5i-2j+k and x2=4i-j+2k are transformed into y1=ax1 and y2=ax2.
vectors x1= 5i-2j+k and x2=4i-j+2k are transformed into y1=ax1 and y2=ax2.
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647
limit
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648
Find sequence's sum?
What is sum of the following series 1+ √2+ √3 +√4.....+√n ? Asymptotic answer will be okay too.
What is sum of the following series1+ √2+ √3 +√4.....+√n ?Asymptotic answer will be okay too.
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649
What is sum of the sequence?
What is sum of the series 1+ √2+ √3 +√4.....+√n ? Assymptotic answer will be okay too.
What is sum of the series1+ √2+ √3 +√4.....+√n ?Assymptotic answer will be okay too.
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650
Integration
$f\left ( x \right )=$\int_{-2}^{2}x^{-\frac{2}{7}}dx$ Is this function f(x) is continuous, bounded and differentiable? (In exam hall is it possible to draw the graph for this function f(x), or some other procedure to follow to ans this)
$f\left ( x \right )=$$\int_{-2}^{2}x^{-\frac{2}{7}}dx$Is this function f(x) is continuous, bounded and differentiable?(In exam hall is it possible to draw the graph for ...
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651
Integration
Evaluate $\Large\int_3^7 \sqrt[4]{(x-3)(7-x)} dx$
Evaluate $\Large\int_3^7 \sqrt[4]{(x-3)(7-x)} dx$
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652
Multiple integration
Evaluate $\Large\int_1^4\Large\int_\sqrt{y}^2(x^{2}+y^{2})dA $ by changing the order of integration
Evaluate $\Large\int_1^4\Large\int_\sqrt{y}^2(x^{2}+y^{2})dA $ by changing the order of integration
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653
ISI2017-MMA-25
For $a,b \in \mathbb{R}$ and $b > a$ , the maximum possible value of the integral $\int_{a}^{b}(7x-x^{2}-10)dx$ is $\frac{7}{2}\\$ $\frac{9}{2}\\$ $\frac{11}{2}\\$ none of these
For $a,b \in \mathbb{R}$ and $b a$ , the maximum possible value of the integral $\int_{a}^{b}(7x-x^{2}-10)dx$ is$\frac{7}{2}\\$$\frac{9}{2}\\$$\frac{11}{2}\\$none of the...
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654
Calculus Integration
$I=\int_{3}^{7}((x-3)(7-x))^{\frac{1}{4}}dx$
$I=\int_{3}^{7}((x-3)(7-x))^{\frac{1}{4}}dx$
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655
General Math
What is value of $\log _{2}10$? In general calculator $\ln _{2}10$ is giving 2.3.... But it should be 3. something right?
What is value of $\log _{2}10$?In general calculator $\ln _{2}10$ is giving 2.3....But it should be 3. somethingright?
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656
Maths calculus
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657
Problems in Calculus Of One Variable by I.A. Maron
Prove that 0.101001000...1000....01 is irrational. can i get the exact solution.
Prove that 0.101001000...1000....01 is irrational.can i get the exact solution.
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1 votes
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658
Mathematics GATE 2018 EE: 34
The number of roots of the polynomial, $s^{7} + s^{6} + 7s^{5} + 14s^{4} + 31s^{3} + 7s^{2}+ 25s + 200$, in the open left half of the complex plane is $3$ $4$ $5$ $6$
The number of roots of the polynomial, $s^{7} + s^{6} + 7s^{5} + 14s^{4} + 31s^{3} + 7s^{2}+ 25s + 200$, in the open left half of the complex plane is$3$$4$$5$$6$
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659
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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660
Differentiation confusion
Please show the steps how to differentiate u function equation and obtain this answer after differentating .please tell totally confused.
Please show the steps how to differentiate u function equation and obtain this answer after differentating .please tell totally confused.
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