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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

1 votes
2 answers
151
Differential calculus
If f(x) = |x-1| + |x-2| is not derivable at x = (a) x = 0 (b) x = 1,2 (c) x = 3 (d) none
If f(x) = |x-1| + |x-2| is not derivable at x =(a) x = 0(b) x = 1,2(c) x = 3(d) none
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1 votes
2 answers
152
Continuity and Differentiability
If the function f(x) =[(x-2)3 ​​​​​​​/a] sin(x-2) + acos(x-2), [.] denotes greatest integer function, is continuous & differentiable in (4,6) then find ‘a’ range: (A) a ϵ (-∞,∞) (B) a ϵ [64, ∞) (C) a ϵ [128, ∞) (D) Not defined
If the function f(x) =[(x-2)3 ​​​​​​​/a] sin(x-2) + acos(x-2), [.] denotes greatest integer function, is continuous & differentiable in (4,6) then find ‘...
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4 votes
2 answers
153
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
2 answers
155
PGEE 2017
$\int_{-3}^{3} \left | X+1 \right |dx$
$\int_{-3}^{3} \left | X+1 \right |dx$
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9 votes
2 answers
156
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
2 answers
157
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
158
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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0 votes
2 answers
159
ISRO 2013- Calculus [Mech]
Lim x $\rightarrow$0 $\frac{x^{2}+ x - Sin x}{x^{2}}$ (a) 0 (b) ∞ (c) 1 (d) None of these
Lim x $\rightarrow$0 $\frac{x^{2}+ x - Sin x}{x^{2}}$(a) 0(b) ∞(c) 1(d) None of these
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0 votes
2 answers
160
ISRO 2009-ECE Engineering Mathematics
There is a function f(x), such that f(0) = 1 and f ' (0)= -1 and f(x) is positive for all values of x. Then, a) f"(x) < 0 for all x b) -1 < f'' (x) < 0 for all x c) -2 < f '' (x) < -1 for all x d) None of the above
There is a function f(x), such that f(0) = 1 and f ' (0)= -1 and f(x) is positive for all values of x. Then,a) f"(x) < 0 for all xb) -1 < f'' (x) < 0 for all xc) -2 < f ...
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2 votes
2 answers
161
ISRO 2010-ECE Calculus
What does the following integral evaluate to? a) 5 π /16 b) 5 π /8 c) 0 d) 5 π /32
What does the following integral evaluate to?a) 5 π /16b) 5 π /8c) 0d) 5 π /32
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0 votes
2 answers
164
Integration
what is the integration of this funcion? f(x)=1−|x| where −1≤x≤1
what is the integration of this funcion? f(x)=1−|x| where −1≤x≤1
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1 votes
2 answers
166
CMI2016-B-7ai
Consider the funciton $M$ defined as follows: $M(n) = \begin{cases} n-10 & \text{ if } n > 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$ Compute the following$: M(101)$
Consider the funciton $M$ defined as follows:$M(n) = \begin{cases} n-10 & \text{ if } n 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$Compute the following$: M(...
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2 votes
2 answers
167
CMI2016-B-7aii
Consider the funciton $M$ defined as follows: $M(n) = \begin{cases} n-10 & \text{ if } n > 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$ Compute the following$: M(99)$
Consider the funciton $M$ defined as follows:$M(n) = \begin{cases} n-10 & \text{ if } n 100 \\ M(M(n+11)) & \text{ if } n \leq 100 \end{cases}$Compute the following$: M(...
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1 votes
2 answers
170
Targate
How to solve this?
How to solve this?
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