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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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Recent questions in Calculus

1 votes
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282
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}$$\begin{pm...
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283
ISI2016-MMA-23
Given that $\int_{-\infty}^{\infty} e^{-x^2/2} dx = \sqrt{2 \pi}$, what is the value of $\int_{- \infty}^{\infty} \mid x \mid ^{-1/2} e^{- \mid x \mid} dx$? $0$ $\sqrt{\pi}$ $2 \sqrt{\pi}$ $\infty$
Given that $\int_{-\infty}^{\infty} e^{-x^2/2} dx = \sqrt{2 \pi}$, what is the value of $\int_{- \infty}^{\infty} \mid x \mid ^{-1/2} e^{- \mid x \mid} dx$?$0$$\sqrt{\pi}...
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286
limit
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287
limit
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288
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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289
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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0 votes
1 answer
290
integration
now if we use sin^2 x=(1-cos2x)/2 then we are not getting solution like this please check
now if we use sin^2 x=(1-cos2x)/2then we are not getting solution like this please check
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291
limit
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292
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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0 answers
293
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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0 votes
1 answer
294
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
295
NIELIT2017 STA-set-c-119
The function $f(x)=\frac{x^2 -1}{x-1}$ at $x=1$ is: Continuous and Differentiable Continuous but not Differentiable Differentiable but not Continuous Neither Continuous nor Differentiable
The function $f(x)=\frac{x^2 -1}{x-1}$ at $x=1$ is:Continuous and Differentiable Continuous but not DifferentiableDifferentiable but not ContinuousNeither Continuous nor ...
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1 answer
296
lt x→0(3cosx+2sin3x)^(1/x)
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1 votes
1 answer
298
MadeEasy Test Series: Calculus - Functions
Consider the following function $f(x)=\frac{x}{2x+1} , \, x\not= -\frac{1}{2}$ ... is defined on $R \rightarrow R-\{ \frac{1}{2} \}$, then it will be a bijection. Please let me know what's correct?
Consider the following function$f(x)=\frac{x}{2x+1} , \, x\not= -\frac{1}{2}$Is the function a bijection?Yes, this is a one-to-one function.For onto, let's suppose functi...
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1 votes
1 answer
299
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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300
Calculus-Self Doubt
Is the function $f(x)=\frac{1}{x^{\frac{1}{3}}}$ continous in the interval [-1 0) ?
Is the function $f(x)=\frac{1}{x^{\frac{1}{3}}}$ continous in the interval [-1 0) ?
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