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Recent questions and answers in Calculus
0
votes
1
answer
1
GATE Electrical 2020 | Question: 1
$ax^{3}+bx^{2}+cx+d$ is a polynomial on real $\text{x}$ over real coefficients $\text{a, b, c, d}$ wherein $a\neq 0.$ Which of the following statements is true? $\text{d}$ can be chosen to ensure that $\text{x = 0}$ is a root for any ... $\text{a, b, c, d}$ can be chosen to ensure that all roots are complex. $\text{c}$ alone cannot ensure that all roots are real.
Adarsh Joshi
answered
in
Calculus
Mar 17, 2021
by
Adarsh Joshi
150
points
gate2020-ee
calculus
polynomials
0
votes
0
answers
2
GATE Electrical 2021 | Question: 3
Let $f\left ( x \right )$ be a real-valued function such that ${f}'\left ( x_{0} \right )=0$ for some $x _{0} \in\left ( 0,1 \right ),$ and ${f}''\left ( x \right )> 0$ for all $x \in \left ( 0,1 \right )$ ... $(0,1)$ one local maximum in $(0,1)$ exactly one local minimum in $(0,1)$ two distinct local minima in $(0,1)$
Arjun
asked
in
Calculus
Feb 20, 2021
by
Arjun
9.3k
points
gateee-2021
calculus
maxima-minima
0
votes
0
answers
3
GATE Electrical 2021 | Question: 5
Which one of the following vector functions represents a magnetic field $\overrightarrow{B}$? $\text{($\hat{X}, \hat{Y}$ and $\hat{Z}$ are unit vectors along x-axis, y-axis, and z-axis, respectively)}$ $10x\hat{X}+20y\hat{Y}-30z\hat{Z}$ $10y\hat{X}+20x\hat{Y}-10z\hat{Z}$ $10z\hat{X}+20y\hat{Y}-30x\hat{Z}$ $10x\hat{X}-30z\hat{Y}+20y\hat{Z}$
Arjun
asked
in
Calculus
Feb 20, 2021
by
Arjun
9.3k
points
gateee-2021
calculus
field-vectors
0
votes
0
answers
4
GATE Electrical 2021 | Question: 13
Suppose the circles $x^{2}+y^{2}=1$ and $\left ( x-1\right )^{2}+\left ( y-1 \right )^{2}=r^{2}$ intersect each other orthogonally at the point $\left ( u,v \right )$. Then $u+v=$ _______________.
Arjun
asked
in
Calculus
Feb 20, 2021
by
Arjun
9.3k
points
gateee-2021
numerical-answers
calculus
curves
0
votes
0
answers
5
GATE Electrical 2021 | Question: 26
In the open interval $\left ( 0,1 \right )$, the polynomial $p\left ( x \right) =x^{4}-4x^{3}+2$ has two real roots one real root three real roots no real roots
Arjun
asked
in
Calculus
Feb 20, 2021
by
Arjun
9.3k
points
gateee-2021
calculus
polynomials
0
votes
0
answers
6
GATE Electrical 2021 | Question: 28
Let $\left ( -1 -j \right ), \left ( 3 -j \right ), \left ( 3 + j \right )$ and $\left ( -1+ j \right )$ be the vertices of a rectangle $C$ in the complex plane. Assuming that $C$ is traversed in counter-clockwise direction, the value of the contour integral $\oint _{C}\dfrac{dz}{z^{2}\left ( z-4 \right )}$ is $j\pi /2$ $0$ $-j\pi /8$ $j\pi /16$
Arjun
asked
in
Calculus
Feb 20, 2021
by
Arjun
9.3k
points
gateee-2021
calculus
contour-plots
0
votes
0
answers
7
GATE Electrical 2020 | Question: 2
Which of the following is true for all possible non-zero choices of integers $m,n;m\neq n,$ or all possible non-zero choices of real numbers $p,q;p\neq q,$ ...
go_editor
asked
in
Calculus
Feb 28, 2020
by
go_editor
1.9k
points
gate2020-ee
calculus
definite-integral
0
votes
0
answers
8
GATE Electrical 2020 | Question: 26
For real numbers, $\text{x}$ and $\text{y}$, with $y=3x^{2}+3x+1$, the maximum and minimum value of $\text{y}$ for $\text{x}$ $\in \left [ -2,0 \right ]$ are respectively, ______. $7$ and $1/4$ $7$ and $1$ $-2$ and $-1/2$ $1$ and $1/4$
go_editor
asked
in
Calculus
Feb 28, 2020
by
go_editor
1.9k
points
gate2020-ee
calculus
maxima-minima
0
votes
0
answers
9
GATE Electrical 2020 | Question: 27
The vector function expressed by $F=a_{x}\left ( 5y-k_{1} z\right )+a_{y}\left ( 3z+k_{2}x \right )+a_{z}\left ( k_{3} y-4x\right )$ represents a conservative field, where $a_{x}, a_{y},a_{z}$ are unit vectors along $x, y$ and $z$ directions, respectively. The values of constants ... $k_{1}=3, k_{2}=8,k_{3}=5$ $k_{1}=4, k_{2}=5,k_{3}=3$ $k_{1}=0, k_{2}=0,k_{3}=0$
go_editor
asked
in
Calculus
Feb 28, 2020
by
go_editor
1.9k
points
gate2020-ee
calculus
field-vectors
0
votes
0
answers
10
GATE Electrical 2019 | Question: 18
If $f=2x^{3}+3y^{2}+4z$, the value of line integral $\int_{c} \text{grad}f \cdot d \textbf{r}$ evaluated over contour $C$ formed by the segments $(-3,-3,2)\rightarrow(2,-3,2)\rightarrow(2,6,2) \rightarrow(2,6,-1) $ is___________.
Arjun
asked
in
Calculus
Feb 12, 2019
by
Arjun
9.3k
points
gate2019-ee
numerical-answers
calculus
line-integral
0
votes
0
answers
11
GATE Electrical 2019 | Question: 28
A periodic function $f(t)$, with a period of $2 \pi$, is represented as its Fourier series, $f(t) = a_0 + \sum_{n=1}^{\infty }a_n \cos nt + \sum_{n=1}^{\infty} b_n \sin nt.$ ... $a_1 = \frac{A}{2}; \: b_1 = 0$ $a_1 = 0; \: b_1 = \frac{A}{\pi}$ $a_1 = 0;b_1 = \frac{A}{2}$
Arjun
asked
in
Calculus
Feb 12, 2019
by
Arjun
9.3k
points
gate2019-ee
calculus
fourier-series
0
votes
0
answers
12
GATE Electrical 2019 | Question: 39
If $\textbf{A}= 2x \textbf{i} + 3y \textbf{j} +4z \textbf{k}$ and $u=x^2+y^2+z^2$, then $\text{div} \big(u \textbf{A} \big)$ at $(1,1,1)$ is _______
Arjun
asked
in
Calculus
Feb 12, 2019
by
Arjun
9.3k
points
gate2019-ee
numerical-answers
calculus
divergence
0
votes
0
answers
13
GATE Electrical 2012 | Question: 38
The direction of vector $\textbf{A}$ is radically outward from the origin, with $\mid \textbf{A} \mid k r ^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla \cdot \textbf{A} = 0$ is $-2$ $2$ $1$ $0$
Andrijana3306
asked
in
Calculus
Mar 24, 2018
by
Andrijana3306
1.4k
points
gate2012-ee
differential-equations
0
votes
0
answers
14
GATE Electrical 2012 | Question: 27
The maximum value of $f(x) = x^3-9x^2+24x+5$ in the interval $[1,6]$ is $21$ $25$ $41$ $46$
Andrijana3306
asked
in
Calculus
Mar 24, 2018
by
Andrijana3306
1.4k
points
gate2012-ee
calculus
maxima-minima
0
votes
0
answers
15
GATE Electrical 2018 | Question: 43
Let $f(x) = 3x^3-7x^2+5x+6$. The maximum value of $f(x)$ over the interval $[0,2]$ is ________ (up to one decimal place).
Arjun
asked
in
Calculus
Feb 19, 2018
by
Arjun
9.3k
points
gate2018-ee
numerical-answers
calculus
maxima-minima
0
votes
0
answers
16
GATE Electrical 2018 | Question: 42
As shown in the figure, $C$ is the arc from the point $(3,0)$ to the point $(0,3)$ on the circle $x^2+y^2=9$. The value of the integral $\int_C (y^2+2yx) dx +(2xy+x^2)dy$ is ________ (up to $2$ decimal places).
Arjun
asked
in
Calculus
Feb 19, 2018
by
Arjun
9.3k
points
gate2018-ee
numerical-answers
calculus
definite-integral
0
votes
0
answers
17
GATE Electrical 2018 | Question: 18
Let $f$ be a real-valued function of a real variable defined as $f(x)=x – [x]$, where $[x]$ denotes the largest integer less than or equal to $x$. The value of $\int_{0.25}^{1.25} f(x) dx$ is _______ (up to $2$ decimal places).
Arjun
asked
in
Calculus
Feb 19, 2018
by
Arjun
9.3k
points
gate2018-ee
numerical-answers
calculus
definite-integral
0
votes
0
answers
18
GATE Electrical 2018 | Question: 12
The value of the directional derivative of the function $\Phi (x,y,z) = xy^2 +yz^2+zx^2$ at the point $(2,-1,1)$ in the direction of the vector $\textbf{p}= \textbf{i} +2 \textbf{j} + 2 \textbf{k}$ is $1$ $0.95$ $0.93$ $0.9$
Arjun
asked
in
Calculus
Feb 19, 2018
by
Arjun
9.3k
points
gate2018-ee
calculus
directional-derivatives
0
votes
0
answers
19
GATE Electrical 2018 | Question: 11
Let $f$ be a real-valued function of a real variable defined as $f(x)=x^2$ for $x \geq 0$, and $f(x)=-x^2$ for $x<0$. Which one of the following statements is true? $f(x)$ is discontinuous at $x=0$ $f(x)$ ... is differentiable but its first derivative is not continuous at $x=0$ $f(x)$ is differentiable but its first derivative is not differentiable at $x=0$
Arjun
asked
in
Calculus
Feb 19, 2018
by
Arjun
9.3k
points
gate2018-ee
calculus
continuity-and-differentiability
0
votes
0
answers
20
GATE Electrical 2017 Set 2 | Question: 26
Let $ g(x)= \begin{cases} -x & \ x \leq 1 \\ x+1 & \ x \geq 1 \end{cases}$ and $ f(x)= \begin{cases} 1-x & \ x \leq 0 \\ x^{2} & \ x > 0 \end{cases}$. Consider the composition of $f$ and $g$ ... $(f {\circ} g) (x)$ present in the interval $(-\infty, 0)$ is: $0$ $1$ $2$ $4$
Arjun
asked
in
Calculus
Feb 27, 2017
by
Arjun
9.3k
points
gate2017-ee-2
calculus
continuity
0
votes
0
answers
21
GATE Electrical 2017 Set 2 | Question: 27
The value of the contour integral in the complex plane $\oint \frac{z^{3}-2z+3}{z-2} dz$ along the contour $\mid z \mid =3$, taken counter- clockwise is $-18 \pi i$ $0$ $14 \pi i$ $48 \pi i$
Arjun
asked
in
Calculus
Feb 27, 2017
by
Arjun
9.3k
points
gate2017-ee-2
calculus
contour-integral
0
votes
0
answers
22
GATE Electrical 2017 Set 2 | Question: 19
Let $x$ and $y$ be integers satisfying the following equations $2x^{2}+y^{2}=34$ $x+2y=11$ The value of $(x+y)$ is _______.
Arjun
asked
in
Calculus
Feb 27, 2017
by
Arjun
9.3k
points
gate2017-ee-2
numerical-answers
calculus
curves
0
votes
0
answers
23
GATE Electrical 2017 Set 2 | Question: 20
Let $y^{2}-2y+1=x$ and $\sqrt{x}+y=5$. The value of $x+\sqrt{y}$ equals _________. (Give the answer up to three decimal places).
Arjun
asked
in
Calculus
Feb 27, 2017
by
Arjun
9.3k
points
gate2017-ee-2
numerical-answers
calculus
curves
0
votes
0
answers
24
GATE Electrical 2017 Set 2 | Question: 18
Consider a function $f(x, y, z)$ given by $f(x, y, z)=(x^{2}+y^{2}-2z^{2})(y^{2}+z^{2})$ The partial derivative of this function with respect to $x$ at the point, $x=2, y=1$ and $z=3$ is _______.
Arjun
asked
in
Calculus
Feb 27, 2017
by
Arjun
9.3k
points
gate2017-ee-2
numerical-answers
calculus
derivatives
partial-derivatives
0
votes
0
answers
25
GATE Electrical 2017 Set 2 | Question: 3
The figures show diagramatic representations of vector fields $\vec{X}, \vec{Y}, \text{and} \vec{Z}$ ... $\bigtriangledown . \vec{X}=0,\bigtriangledown \times \vec{Y} = 0, \bigtriangledown \times \vec{Z}=0$
Arjun
asked
in
Calculus
Feb 27, 2017
by
Arjun
9.3k
points
gate2017-ee-2
calculus
field-vectors
0
votes
0
answers
26
GATE Electrical 2017 Set 1 | Question: 28
Consider the line integral $I=\int_{c} (x^{2}+iy^{2})dz$, where $z=x+iy$. The line $c$ is shown in the figure below. The value of $I$ is $\frac{1}{2}i \\ $ $\frac{2}{3}i \\ $ $\frac{3}{4}i \\ $ $\frac{4}{5}i$
Arjun
asked
in
Calculus
Feb 27, 2017
by
Arjun
9.3k
points
gate2017-ee-1
calculus
line-integral
0
votes
0
answers
27
GATE Electrical 2017 Set 1 | Question: 26
A function $f(x)$ is defined as $f(x)= \begin{cases} e^{x}, & x < 1 \\ \text{In } x+ax^{2}+bx, & x\geq 1 \end{cases}$, where $x \in \mathbb{R}$ Which one of the following statement is TRUE? $f(x)$ is NOT differentiable at $x=1$ ... for all values of $a$ and $b$ such that $a+b=e$. $f(x)$ is differentiable at $x=1$ for all values of $a$ and $b$.
Arjun
asked
in
Calculus
Feb 27, 2017
by
Arjun
9.3k
points
gate2017-ee-1
calculus
continuity-and-differentiability
0
votes
0
answers
28
GATE Electrical 2017 Set 1 | Question: 17
Let $I= c\int \int _{R} xy^{2} dxdy$, where $R$ is the region shown in the figure and $c= 6 \times 10^{-4}$. The value of $I$ equals _________. (Give the answer up to two decimal places.)
Arjun
asked
in
Calculus
Feb 27, 2017
by
Arjun
9.3k
points
gate2017-ee-1
numerical-answers
calculus
double-integral
0
votes
0
answers
29
GATE Electrical 2017 Set 1 | Question: 2
For a complex number $z,\displaystyle{} \lim_{z \rightarrow i} \frac{z^{2}+1}{z^{3}+2z-i (z^{2}+2)}$ is $-2i$ $-i$ $i$ $2i$
Arjun
asked
in
Calculus
Feb 27, 2017
by
Arjun
9.3k
points
gate2017-ee-1
calculus
limits
complex-number
0
votes
0
answers
30
GATE Electrical 2013 | Question: 46
A function $y=5x^2+10x$ is defined over an open interval $x$ = $(1, 2)$ . At least at one point in this interval, $\dfrac{\mathrm{dy} }{\mathrm{d} x}$ is exactly $20$ $25$ $30$ $35$
piyag476
asked
in
Calculus
Feb 12, 2017
by
piyag476
1.5k
points
gate2013-ee
calculus
derivatives
0
votes
0
answers
31
GATE Electrical 2013 | Question: 24
Given a vector field $\textbf{F}=y^2x \textbf{a}_x-yz \textbf{a}_y-x^2 \textbf{a}_z$ the line integral $\int \textbf{F} \cdot d \textbf{l}$ evaluated along a segment on the $x$-axis from $x=1$ to $x=2$ is $-2.33$ $0$ $2.33$ $7$
piyag476
asked
in
Calculus
Feb 12, 2017
by
piyag476
1.5k
points
gate2013-ee
calculus
field-vector
integral
0
votes
0
answers
32
GATE Electrical 2014 Set 3 | Question: 3
Let $\nabla .(fv)=x^2y+y^2z+z^2x$ , where $f$ and $v$ are scalar and vector fields respectively. If $v=yi+zj+xk$ then $v.\Delta f$ is $x^2y+y^2z+z^2x$ $2xy+2yz+2zx$ $x+y+z$ $0$
makhdoom ghaya
asked
in
Calculus
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-3
calculus
field-vectors
0
votes
0
answers
33
GATE Electrical 2014 Set 2 | Question: 26
To evaluate the double integral $\displaystyle \int_{0}^{8} \bigg (\int_{(y/2)}^{y/2+1} \bigg (\dfrac{2x-y}{2} \bigg)dx \bigg)dy$ , we make the substitution $u=\bigg (\dfrac{2x-y}{2} \bigg)$ and $v=\dfrac{y}{2}$ ... $\displaystyle \int_{0}^{4} \bigg (\int_{0}^{2}u \: du \bigg ) dv$
makhdoom ghaya
asked
in
Calculus
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-2
calculus
definite-integral
double-integral
0
votes
0
answers
34
GATE Electrical 2014 Set 2 | Question: 28
The minimum value of the function $f(x)=x^3-3x^2-24x+100$ in the interval $[-3,3]$ is $20$ $28$ $16$ $32$
makhdoom ghaya
asked
in
Calculus
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-2
calculus
maxima-minima
0
votes
0
answers
35
GATE Electrical 2014 Set 2 | Question: 3
Minimum of the real valued function $f(x)=(x-1)^{2/3}$ occurs at $x$ equal to $-\infty$ $0$ $1$ $\infty$
makhdoom ghaya
asked
in
Calculus
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-2
calculus
maxima-minima
0
votes
0
answers
36
GATE Electrical 2014 Set 1 | Question: 28
The line integral of function $F = yzi$, in the counterclockwise direction, along the circle $x^2+y^2 = 1$ at $z = 1$ is $-2\pi$ $-\pi$ $\pi$ $2\pi$
makhdoom ghaya
asked
in
Calculus
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-1
calculus
line-integral
circle-equation
0
votes
0
answers
37
GATE Electrical 2014 Set 1 | Question: 17
In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of only one root at the origin Imaginary roots only positive real roots only negative real roots
makhdoom ghaya
asked
in
Calculus
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-1
calculus
polynomial
routh-hurwitz-array
0
votes
0
answers
38
GATE Electrical 2014 Set 1 | Question: 2
Let $f(x)=xe^{-x}$ . The maximum value of the function in the interval $(0,\infty)$ is $e^{-1}$ $e$ $1-e^{-1}$ $1+e^{-1}$
makhdoom ghaya
asked
in
Calculus
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-1
calculus
maxima-minima
0
votes
0
answers
39
GATE Electrical 2015 Set 2 | Question: 26
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 ________.
makhdoom ghaya
asked
in
Calculus
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2015-ee-2
calculus
volume-integral
numerical-answers
0
votes
0
answers
40
GATE Electrical 2015 Set 2 | Question: 3
Match the following. ... $P-4; Q-1; R-3; S-2$ $P-4; Q-3; R-1; S-2$ $P-3; Q-4; R-2; S-1$
makhdoom ghaya
asked
in
Calculus
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2015-ee-2
calculus
divergence
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