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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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Recent questions in Calculus

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421
[Linear Algebra]
What is the effect of elementary operations on eigen vectors ? I know eigen values are not preserved with elementary operations,so as eigen vectors are generated by eigen values so they should change,But i am not sure.
What is the effect of elementary operations on eigen vectors ?I know eigen values are not preserved with elementary operations,so as eigen vectors are generated by eigen ...
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0 votes
1 answer
422
Calculus maxima minima
True / false ? In continuous function if we have three stationary points then always it will be case that either one is maxima and two are minima or one is minima and two are maxima ? I think it is true but i am concerned about constant fucntion
True / false ?In continuous function if we have three stationary points then always it will be case that either one is maxima and two are minima orone is minima and two a...
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1 votes
1 answer
423
[Engineering Maths] Calculus
What can we say about e^-x ? a. Function is increasing at increasing rate b. Function is decreasing at increasing rate c. Function is increasing at decreasing rate d. Function is decreasing at decreasing rate
What can we say about e^-x ?a. Function is increasing at increasing rateb. Function is decreasing at increasing ratec. Function is increasing at decreasing rated. Functi...
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1 votes
1 answer
424
gate-2018
I am not good in calculus. Can anyone suggest me any maths books, for practicing calculus(useful for gate)
I am not good in calculus. Can anyone suggest me any maths books, for practicing calculus(useful for gate)
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0 votes
1 answer
425
maths
Q.9 (B) 4 (C) 7 (D) 8 Consider the function f(x) = sin(x) in the interval x  [π/4, 7π/4]. The number and location(s) of the local minima of this function are (A) One, at π/2 (B) One, at 3π/2 (C) Two, at π/2 and 3π/2 (D) Two, at π/4 and 3π/2
Q.9(B) 4(C) 7(D) 8Consider the function f(x) = sin(x) in the interval x  [π/4, 7π/4]. The number and location(s) of thelocal minima of this function are(A) One, at �...
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7 votes
1 answer
426
ISI-2017 MMA
Let $S \subseteq R$. Consider the statement: "There exists a continuous function $f:S \rightarrow S$ such that $f(x) \neq x$ for all $x$ belongs to $S$." This statement is false if $S$ equals $[2,3]$ $[2,3]$ $[-3,-2] \cup [2,3]$ $(-\infty \text{ to} +\infty)$
Let $S \subseteq R$. Consider the statement:"There exists a continuous function $f:S \rightarrow S$ such that $f(x) \neq x$ for all $x$ belongs to $S$."This statement is ...
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4 votes
2 answers
427
Generating Function-Rosen
Find the coefficient of x10 $\left ( 1+x^{2}+x^{4}+........ \right )\left ( 1+x^{4}+x^{8}+..... \right )\left ( 1+x^{6}+x^{12}..... \right )$
Find the coefficient of x10$\left ( 1+x^{2}+x^{4}+........ \right )\left ( 1+x^{4}+x^{8}+..... \right )\left ( 1+x^{6}+x^{12}..... \right )$
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1 votes
1 answer
428
Calculus
The interval in which $f(x) = \cot^{-1}x + x$ increases, is (a) $R$ (b)$(0,\infty )$ (c)$R-[n-\pi]$ (d)None of these
The interval in which $f(x) = \cot^{-1}x + x$ increases, is(a) $R$(b)$(0,\infty )$(c)$R-[n-\pi]$(d)None of these
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1 votes
2 answers
430
PGEE 2017
$\int_{-3}^{3} \left | X+1 \right |dx$
$\int_{-3}^{3} \left | X+1 \right |dx$
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5 votes
1 answer
432
ISI2004-MIII: 23
If $\textit{f}(x)=x^{2}$ and $g(x)=x \sin x +\cos x$ then $f$ and $g$ agree at no point $f$ and $g$ agree at exactly one point $f$ and $g$ agree at exactly two point $f$ and $g$ agree at more then two point
If $\textit{f}(x)=x^{2}$ and $g(x)=x \sin x +\cos x$ then$f$ and $g$ agree at no point$f$ and $g$ agree at exactly one point$f$ and $g$ agree at exactly two point$f$ and ...
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6 votes
1 answer
433
ISI2004-MIII: 22
If $\textit{f}(x)=\frac{\sqrt{3}\sin x}{2+\cos x}$ then the range of $\textit{f}(x)$ is the interval $\left[-1,\frac{\sqrt{3}}{2}\right]$ the interval $\left[\frac{-\sqrt{3}}{2},1\right]$ the interval $\left[-1,1\right]$ none of the above
If $\textit{f}(x)=\frac{\sqrt{3}\sin x}{2+\cos x}$ then the range of $\textit{f}(x)$ isthe interval $\left[-1,\frac{\sqrt{3}}{2}\right]$the interval $\left[\frac{-\sqrt{3...
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5 votes
3 answers
434
ISI2004-MIII: 13
Let $X =\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\ldots+\frac{1}{3001}$. Then $X< 1$ $X>\frac{3}{2}$ $1< X< \frac{3}{2}$ none of the above
Let $X =\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\ldots+\frac{1}{3001}$. Then$X< 1$$X>\frac{3}{2}$$1< X< \frac{3}{2}$none of the above
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9 votes
2 answers
435
ISI2004-MIII: 12
The maximum possible value of $xy^2z^3$ subjected to condition $x,y,z \geq 0$ and $x+y+z=3$ is $1$ $\frac{9}{8}$ $\frac{9}{4}$ $\frac{27}{16}$
The maximum possible value of $xy^2z^3$ subjected to condition $x,y,z \geq 0$ and $x+y+z=3$ is$1$$\frac{9}{8}$$\frac{9}{4}$$\frac{27}{16}$
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0 votes
1 answer
436
From Question bank
How to solve such type of problems which involve finding the Domain of the Function ?
How to solve such type of problems which involve finding the Domain of the Function ?
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0 votes
1 answer
437
From a Question bank
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1 votes
1 answer
438
ISRO 2015- Differential equation [EE]
The solution of the differential equation (d y /dx)=ky , Y(0)= C is (a) x =ce-xy (b) y= cekx (c) x =ke cy (d) y= ce-kx
The solution of the differential equation (d y /dx)=ky , Y(0)= C is(a) x =ce-xy(b) y= cekx(c) x =ke cy(d) y= ce-kx
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0 votes
2 answers
439
ISRO 2013- Integration [EE]
The integrating factor of equation sec 2 y dy/dx + x tan y = x3 is a) $[e]^{x^2/2}$ b) $[e]^ {-x^2/2}$ c) $[e]^{x/2}$ d)$ [e]^{-x/2}$
The integrating factor of equation sec 2 y dy/dx + x tan y = x3 isa) $[e]^{x^2/2}$b) $[e]^ {-x^2/2}$c) $[e]^{x/2}$d)$ [e]^{-x/2}$
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1 votes
2 answers
440
ISRO 2013- Area under curve [EE]
The area bounded by the curves $y^2$ = 9x, x - y + 2 = 0 is given by a) 1 b) 1/2 C) 3/2 d) 5/4
The area bounded by the curves $y^2$ = 9x, x - y + 2 = 0 is given bya) 1b) 1/2C) 3/2d) 5/4
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