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Hot questions in Calculus
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1
GATE2014128
The line integral of function $F$ = $yzi$, in the counterclockwise direction, along the circle $x^2$+$y^2$ = $1$ at $z$ = $1$ is $2\pi$ $\pi$ $\pi$ $2\pi$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
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9.2k
points)
gate2014ee1
lineintegral
circleequation
quadraticfunction
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votes
0
answers
2
GATE201513
If the sum of the diagonal elements of a $2 \times 2$ matrix is $6$, then the maximum possible value of determinant of the matrix is ________
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Feb 12, 2017
in
Calculus
by
makhdoom ghaya
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9.2k
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gate2015ee1
diagonalelements
determinant
matrix
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votes
0
answers
3
GATE2015226
The volume enclosed by the surface $f(x, y) = e^{x}$ over the triangle bounded by the lines $x = y; x = 0; y = 1$ in the $xy$ plane is ________.
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Feb 12, 2017
in
Calculus
by
makhdoom ghaya
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9.2k
points)
gate2015ee2
lineequations
3dsystem
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votes
0
answers
4
GATE201512
If a continuous function $f(x)$ does not have a root in the interval $[a, b]$, then which one of the following statements is TRUE? $f(a) . f(b)=0$ $f(a) . f(b) < 0$ $f(a) . f(b) > 0$ $f(a) / f(b) \leq 0$
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Feb 12, 2017
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Calculus
by
makhdoom ghaya
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9.2k
points)
gate2015ee1
continuousfunction
roots
interval
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votes
0
answers
5
GATE201346
A function $y=5x^2+10x$ is defined over an open interval $x$ = $(1, 2)$ . At least at one point in this interval, $\frac{\mathrm{dy} }{\mathrm{d} x}$ is exactly $20$ $25$ $30$ $35$
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Feb 12, 2017
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Calculus
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piyag476
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1.5k
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gate2013ee
directionalderivatives
gausss
theorem
0
votes
0
answers
6
GATE201350
The state variable formulation of a system is given as $\begin{vmatrix} x^\cdot_1 \\ x^\cdot_2 \end{vmatrix}=\begin{vmatrix} 2 & 0\\ 0 & 1 \end{vmatrix}\begin{vmatrix} x_1\\ x_2 \end{vmatrix}+\begin{vmatrix} 1\\ 1 \end{vmatrix}u$ , $x_1(0)=0$ , $x_2(0)=0$ and $y=\begin{vmatrix} 1 & 0 \end{vmatrix}\begin{vmatrix} x_1\\ x_2 \end{vmatrix}$ The system is
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Feb 12, 2017
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Calculus
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piyag476
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1.5k
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gate2013ee
matrix
adjoint
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0
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7
GATE2014218
The state transition matrix for the system $\begin{bmatrix} \dot{x_1}\\ \dot{x_2} \end{bmatrix}=\begin{bmatrix} 1 & 0\\ 1 & 1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$ ... $\begin{bmatrix} e^t &te^t \\ 0&e^t \end{bmatrix}$
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Feb 12, 2017
in
Calculus
by
makhdoom ghaya
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9.2k
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gate2014ee2
state
transition
matrix
0
votes
0
answers
8
GATE2014228
The minimum value of the function $f(x)=x^33x^224x+100$ in the interval $[3,3]$ is $20$ $28$ $16$ $32$
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Feb 12, 2017
in
Calculus
by
makhdoom ghaya
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9.2k
points)
gate2014ee2
linearfunctions
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votes
0
answers
9
GATE20152GA5
Consider a function $f(x) = 1  x$ on $1 \leq x \leq 1$. The value of $x$ at which the function attains a maximum, and the minimum value of the function are: $0, 1$ $1, 0$ $0, 1$ $1, 2$
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Feb 12, 2017
in
Calculus
by
makhdoom ghaya
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9.2k
points)
gate2015ee2
maxima
minima
0
votes
0
answers
10
GATE2014326
Integration of the complex function $f(z)=\frac{z^2}{z^21}$ , in the counterclockwise direction, around $z1$ = $1$, is $\pi i$ 0 $\pi i$ 2$\pi i$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.2k
points)
gate2014ee3
complexfunctions
integration
0
votes
0
answers
11
GATE201629
The value of the line integral $\int_{c}^{} (2xy^{2}dx+2x^{2}y dy+dz)$ along a path joining the origin $(0, 0, 0)$ and the point $(1, 1, 1)$ is $0$ $2$ $4$ $6$
asked
Jan 30, 2017
in
Calculus
by
makhdoom ghaya
(
9.2k
points)
gate2016ee2
compositefunctions
additivity
space
riemannsum
0
votes
0
answers
12
GATE20161GA10
Choose the correct expression for $f(x)$ given in the graph. $f(x) = 1  x  1$ $f(x) = 1 + x  1$ $f(x) = 2  x  1$ $f(x) = 2 + x  1$
asked
Jan 30, 2017
in
Calculus
by
makhdoom ghaya
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9.2k
points)
gate2016ee1
compositefunctions
arrowdiagram
shifting
0
votes
0
answers
13
GATE20162GA5
If $9y−6 =3$, then $y^{2}4y/3$ is . $0$ $+1/3$ $1/3$ undefined
asked
Jan 30, 2017
in
Calculus
by
makhdoom ghaya
(
9.2k
points)
gate2016ee2
linearequation
quadraticequation
mode
0
votes
0
answers
14
GATE201619
The value of $\int_{\infty}^{+\infty} e^{t} \delta (2t2){d}t$, where $\delta (t)$ is the Dirac delta function, is $\frac{1}{2e}$ $\frac{2}{e}$ $\frac{1}{e^{2}}$ $\frac{1}{2e^{2}}$
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Jan 30, 2017
in
Calculus
by
makhdoom ghaya
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9.2k
points)
gate2016ee1
pauldirac
operationalcalculus
weaklimit
0
votes
0
answers
15
GATE2016229
The value of the integral $2\int_{\infty}^{\infty} (\frac{\sin2\pi t}{\pi t}) \text{d}t$ is equal to $0$ $0.5$ $1$ $2$
asked
Jan 30, 2017
in
Calculus
by
makhdoom ghaya
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9.2k
points)
gate2016ee2
theoremofintegral
definiteintegral
0
votes
0
answers
16
GATE2016129
Let $A$ be a $4 \times 3$ real matrix with rank $2$. Which one of the following statement is TRUE? Rank of $A^{T} A$ is less than $2$. Rank of $A^{T} A$ is equal to $2$. Rank of $A^{T} A$ is greater than $2$. Rank of $A^{T} A$ can be any number between $1$ and $3$.
asked
Jan 30, 2017
in
Calculus
by
makhdoom ghaya
(
9.2k
points)
gate2016ee1
numberofnonzerorows
gaussreduction
gausselimination
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