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

$$\small{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}&1&1&0&1&1&1&0&0.8&1
\\\hline\textbf{2 Marks Count}&0&0&1&0&0&0&0&0.2&1
\\\hline\textbf{Total Marks}&1&1&2&1&1&1&\bf{1}&\bf{1.2}&\bf{2}\\\hline
\end{array}}}$$

Recent questions in Calculus

2 votes
2 answers
1
Suppose that $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function on the interval $[-3, 3]$ and a differentiable function in the interval $(-3,3)$ such that for every $x$ in the interval, $f’(x) \leq 2$. If $f(-3)=7$, then $f(3)$ is at most __________
asked Feb 18 in Calculus Arjun 366 views
0 votes
2 answers
2
Consider the following expression. $\displaystyle \lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}$ The value of the above expression (rounded to 2 ddecimal places) is ___________.
asked Feb 18 in Calculus Arjun 348 views
0 votes
0 answers
3
The limit $\underset{n\rightarrow \infty }{\lim}\:n^{2}\int_{0}^{1}\:\frac{1}{\left ( 1+x^{2} \right )^{n}}\:dx$ is equal to $1$ $0$ $+\infty$ $1/2$
asked Aug 30, 2020 in Calculus soujanyareddy13 242 views
0 votes
0 answers
4
A solution for the differential equation $x’(t) + 2x(t) = \delta(t)$ with initial condition $x(\overline{0}) = 0$ $e^{-2t}u(t)$ $e^{2t}u(t)$ $e^{-t}u(t)$ $e^{t}u(t)$
asked Aug 28, 2020 in Calculus Lakshman Patel RJIT 93 views
2 votes
2 answers
5
The function $f(x)=x^{5}-5x^{4}+5x^{3}-1$ has one minima and two maxima two minima and one maxima two minima and two maxima one minima and one maxima
asked Apr 2, 2020 in Calculus Lakshman Patel RJIT 157 views
0 votes
1 answer
6
0 votes
1 answer
7
0 votes
0 answers
8
$\displaystyle \lim_{x \rightarrow a}\frac{1}{x^{2}-a^{2}} \displaystyle \int_{a}^{x}\sin (t^{2})dt=$? $2a \sin (a^{2})$ $2a$ $\sin (a^{2})$ None of the above
asked Apr 2, 2020 in Calculus Lakshman Patel RJIT 58 views
0 votes
1 answer
9
$\displaystyle \lim_{x \rightarrow 0}\frac{1}{x^{6}} \displaystyle \int_{0}^{x^{2}}\frac{t^{2}dt}{t^{6}+1}=$? $1/4$ $1/3$ $1/2$ $1$
asked Apr 2, 2020 in Calculus Lakshman Patel RJIT 79 views
0 votes
1 answer
10
A ladder $13$ feet long rests against the side of a house. The bottom of the ladder slides away from the house at a rate of $0.5$ ft/s. How fast is the top of the ladder sliding down the wall when the bottom of the ladder is $5$ feet from the house? $\dfrac{5}{24} \text{ ft/s} \\$ $\dfrac{5}{12} \text{ ft/s} \\$ $-\dfrac{5}{24} \text {ft/s} \\$ $-\dfrac{5}{12} \text{ ft/s}$
asked Apr 2, 2020 in Calculus Lakshman Patel RJIT 79 views
0 votes
1 answer
13
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
asked Mar 31, 2020 in Calculus Lakshman Patel RJIT 272 views
0 votes
1 answer
14
0 votes
1 answer
16
0 votes
1 answer
17
0 votes
1 answer
18
0 votes
0 answers
20
Differential equation, $\dfrac{d^2x}{dt^2}+10\dfrac{dx}{dt}+25x=0$ will have a solution of the form $(C_1+C_2t)e^{-5t}$ $C_1e^{-2t}$ $C_1e^{-5t}+C_2e^{5t}$ $C_1e^{-5t}+C_2e^{2t}$ where $C_1$ and $C_2$ are constants.
asked Mar 31, 2020 in Calculus Lakshman Patel RJIT 82 views
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