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GATE Mechanical 2021 Set 2 | Question: 11
For a two-dimensional, incompressible flow having velocity components $u$ and $v$ in the $x$ and $y$ directions, respectively, the expression $\frac{\partial \left ( u^{2} \right )}{\partial x}+\frac{\partial \left ( uv \right )}{\partial y}$ can ... $u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}$
For a two-dimensional, incompressible flow having velocity components $u$ and $v$ in the $x$ and $y$ directions, respectively, the expression$$\frac{\partial \left ( u^{2...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Calculus
gateme-2021-set2
calculus
partial-derivatives
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 13
A two dimensional flow has velocities in $x$ and $y$ directions given by $u = 2xyt$ and $v = -y^{2}t$, where $\text{t}$ denotes time. The equation for streamline passing through $x=1,\:y=1$ is $x^{2}y=1$ $xy^{2}=1$ $x^{2}y^{2}=1$ $x/y^{2}=1$
A two dimensional flow has velocities in $x$ and $y$ directions given by $u = 2xyt$ and $v = -y^{2}t$, where $\text{t}$ denotes time. The equation for streamline passing ...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Calculus
gateme-2021-set2
calculus
derivatives
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 19
Value of $\left ( 1+i \right )^{8}$, where $i=\sqrt{-1}$, is equal to $4$ $16$ $4i$ $16i$
Value of $\left ( 1+i \right )^{8}$, where $i=\sqrt{-1}$, is equal to$4$$16$$4i$$16i$
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Calculus
gateme-2021-set2
calculus
complex-variables
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 26
The value of $\int_{0}^{^{\pi }/_{2}}\int_{0}^{\cos\theta }r\sin\theta \:dr\:d\theta$ is $0$ $\frac{1}{6}$ $\frac{4}{3}$ $\pi$
The value of $\int_{0}^{^{\pi }/_{2}}\int_{0}^{\cos\theta }r\sin\theta \:dr\:d\theta$ is $0$$\frac{1}{6}$$\frac{4}{3}$$\pi$
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Calculus
gateme-2021-set2
calculus
definite-integrals
double-interals
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 1 | Question: 2
The value of $\displaystyle{} \lim_{x \rightarrow 0} \left( \frac{1 – \cos x}{x^{2}}\right)$ is $\frac{1}{4}$ $\frac{1}{3}$ $\frac{1}{2}$ $1$
The value of $\displaystyle{} \lim_{x \rightarrow 0} \left( \frac{1 – \cos x}{x^{2}}\right)$ is$\frac{1}{4}$$\frac{1}{3}$$\frac{1}{2}$$1$
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Calculus
gateme-2021-set1
calculus
limits
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 1 | Question: 27
Let $\text{C}$ represent the unit circle centered at origin in the complex plane, and complex variable, $z=x+iy$. The value of the contour integral $\oint _{C}\dfrac{\cosh \:3z}{2z}\:dz$ (where integration is taken counter clockwise) is $0$ $2$ $\pi i$ $2 \pi i$
Let $\text{C}$ represent the unit circle centered at origin in the complex plane, and complex variable, $z=x+iy$. The value of the contour integral $\oint _{C}\dfrac{\cos...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Calculus
gateme-2021-set1
calculus
complex-variables
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 1 | Question: 34
Let $f\left ( x \right )=x^{2}-2x+2$ be a continuous function defined on $x \in \left [ 1,3 \right ]$. The point $x$ at which the tangent of $f\left ( x \right )$ becomes parallel to the straight line joining $f\left ( 1 \right )$ and $f\left ( 3 \right )$ is $0$ $1$ $2$ $3$
Let $f\left ( x \right )=x^{2}-2x+2$ be a continuous function defined on $x \in \left [ 1,3 \right ]$. The point $x$ at which the tangent of $f\left ( x \right )$ becomes...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Calculus
gateme-2021-set1
calculus
maxima-minima
+
–
0
answers
0
votes
GATE2020-ME-2: 27
The function $f(z)$ of complex variable $z=x+iy$, where $i=\sqrt{-1}$, is given as $f(z)=(x^3-3xy^2)+i \: v(x,y)$. For this function to be analytic, $v(x,y)$ should be $(3xy^2-y^3) +$ constant $(3x^2y^2-y^3) +$ constant $(x^3-3x^2 y) +$ constant $(3x^2y-y^3) +$ constant
The function $f(z)$ of complex variable $z=x+iy$, where $i=\sqrt{-1}$, is given as $f(z)=(x^3-3xy^2)+i \: v(x,y)$. For this function to be analytic, $v(x,y)$ should be$(3...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Calculus
gateme-2020-set2
calculus
complex-variables
analytic-functions
+
–
0
answers
0
votes
GATE2020-ME-2: 26
The directional derivative of $f(x,y,z) = xyz$ at point $(-1,1,3)$ in the direction of vector $\hat{i} – 2 \hat{j} +2 \hat{k}$ is $3\hat{i} – 3 \hat{j} - \hat{k} \\$ $- \dfrac{7}{3} \\$ $\dfrac{7}{3} \\ $ $7$
The directional derivative of $f(x,y,z) = xyz$ at point $(-1,1,3)$ in the direction of vector $\hat{i} – 2 \hat{j} +2 \hat{k}$ is$3\hat{i} – 3 \hat{j} - \hat{k} \\$$-...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Calculus
gateme-2020-set2
calculus
vector-identities
directional-derivatives
+
–
0
answers
0
votes
GATE2020-ME-2: 3
Let $I=\displaystyle \int_{x=0}^1 \int_{y=0}^{x^2} xy^2 dy \: dx$. Then, $I$ may also be expressed as $\displaystyle \int_{y=0}^1 \int_{x=0}^{\sqrt{y}} xy^2 dx \: dy$ $\displaystyle \int_{y=0}^1 \int_{x=\sqrt{y}}^1 yx^2 dx \: dy$ $\displaystyle \int_{y=0}^1 \int_{x=\sqrt{y}}^1 xy^2 dx \: dy$ $\displaystyle \int_{y=0}^1 \int_{x=0}^{\sqrt{y}} yx^2 dx \: dy$
Let $I=\displaystyle \int_{x=0}^1 \int_{y=0}^{x^2} xy^2 dy \: dx$. Then, $I$ may also be expressed as$\displaystyle \int_{y=0}^1 \int_{x=0}^{\sqrt{y}} xy^2 dx \: dy$$\dis...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Calculus
gateme-2020-set2
calculus
definite-integrals
double-interals
+
–
0
answers
0
votes
GATE2020-ME-1: 2
The value of $\displaystyle{}\lim_{x \to \infty}\left ( \dfrac{1 -e^{-c\left ( 1-x \right )}}{1-x\:e^{-c\left ( 1-x \right )}} \right )$ is $\text{c} \\$ $\text{c + 1} \\$ $\dfrac{c}{c+1} \\$ $\dfrac{c+1}{c}$
The value of $\displaystyle{}\lim_{x \to \infty}\left ( \dfrac{1 -e^{-c\left ( 1-x \right )}}{1-x\:e^{-c\left ( 1-x \right )}} \right )$ is$\text{c} \\$$\text{c + 1} \\$$...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Calculus
gateme-2020-set1
calculus
limits
+
–
0
answers
0
votes
GATE2020-ME-1: 4
Which of the following function $f(z)$, of the complex variable $z,$ is NOT analytic at all the points of the complex plane? $f\left ( z \right )=z^{2}$ $f\left ( z \right )=e^{z}$ $f\left ( z \right )=\sin z$ $f\left ( z \right )=\log z$
Which of the following function $f(z)$, of the complex variable $z,$ is NOT analytic at all the points of the complex plane?$f\left ( z \right )=z^{2}$$f\left ( z \right ...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Calculus
gateme-2020-set1
calculus
complex-variables
+
–
0
answers
0
votes
GATE2020-ME-1: 27
A vector field is defined as ... shell formed by two concentric spheres with origin as the center, and internal and external radii of $1$ and $2$, respectively, is $0$ $2\pi$ $4\pi$ $8\pi$
A vector field is defined as $$\overrightarrow{f}\left ( x,y,z \right )=\dfrac{x}{\left [ x^{2}+y^{2}+z^{2} \right ]^{\frac{3}{2}}}\widehat{i}\:+\:\dfrac{y}{\left [ x^{2}...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Calculus
gateme-2020-set1
calculus
vector-identities
+
–
0
answers
0
votes
GATE2020-ME-1: 36
An analytic function of a complex variable $z=x + iy \left ( i=\sqrt{-1} \right )$ is defined as $f\left ( z \right )=x^{2}-y^{2}+i\psi \left ( x,y \right ),$ where $\psi \left ( x,y \right )$ is a real function. The value of the imaginary part of $f(z)$ at $z=\left ( 1+i \right )$ is __________ (round off to $2$ decimal places).
An analytic function of a complex variable $z=x + iy \left ( i=\sqrt{-1} \right )$ is defined as$$f\left ( z \right )=x^{2}-y^{2}+i\psi \left ( x,y \right ),$$where $\psi...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Calculus
gateme-2020-set1
numerical-answers
calculus
complex-variables
analytic-functions
+
–
0
answers
0
votes
GATE2019 ME-2: 28
The derivative of $f(x)= \cos x$ can be estimated using the approximation $f'(x)=\dfrac{f(x+h)-f(x-h)}{2h}$. The percentage error is calculated as $\bigg( \dfrac{\text{Exact value - Approximate value}}{\text{Exact value}} \bigg) \times 100$. The percentage error in the derivative of $f(x)$ ... $> 0.1 \% \text{ and } <1 \%$ $> 1 \% \text{ and } <5 \%$ $>5 \%$
The derivative of $f(x)= \cos x$ can be estimated using the approximation $f’(x)=\dfrac{f(x+h)-f(x-h)}{2h}$. The percentage error is calculated as $\bigg( \dfrac{\text{...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2019-set2
calculus
derivatives
+
–
0
answers
0
votes
GATE2019 ME-2: 26
Given a vector $\overrightarrow{u} = \dfrac{1}{3} \big(-y^3 \hat{i} + x^3 \hat{j} + z^3 \hat{k} \big)$ and $\hat{n}$ as the unit normal vector to the surface of the hemipshere $(x^2+y^2+z^2=1; \: z \geq 0)$ ... $S$ is $- \dfrac{\pi}{2} \\$ $\dfrac{\pi}{3} \\$ $\dfrac{\pi}{2} \\$ $\pi$
Given a vector $\overrightarrow{u} = \dfrac{1}{3} \big(-y^3 \hat{i} + x^3 \hat{j} + z^3 \hat{k} \big)$ and $\hat{n}$ as the unit normal vector to the surface of the hemi...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2019-set2
calculus
vector-identities
+
–
1
answers
0
votes
GATE2019 ME-2: 4
An analytic function $f(z)$ of complex variable $z=x+iy$ may be written as $f(z)=u(x,y)+iv(x,y)$. Then $u(x,y)$ and $v(x,y)$ ...
An analytic function $f(z)$ of complex variable $z=x+iy$ may be written as $f(z)=u(x,y)+iv(x,y)$. Then $u(x,y)$ and $v(x,y)$ must satisfy$\dfrac{\partial u}{ \partial x} ...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
retagged
Mar 5, 2021
Calculus
gateme-2019-set2
calculus
partial-derivatives
complex-variables
analytic-functions
+
–
0
answers
0
votes
GATE2019 ME-2: 2
The directional derivative of the function $f(x,y)=x^2+y^2$ along a line directed from $(0,0)$ to $(1,1)$, evaluated at the point $x=1, y=1$ is $\sqrt{2}$ $2$ $2 \sqrt{2}$ $4 \sqrt{2}$
The directional derivative of the function $f(x,y)=x^2+y^2$ along a line directed from $(0,0)$ to $(1,1)$, evaluated at the point $x=1, y=1$ is$\sqrt{2}$$2$$2 \sqrt{2}$$4...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
retagged
Mar 5, 2021
Calculus
gateme-2019-set2
calculus
directional-derivatives
+
–
0
answers
0
votes
GATE2019 ME-1: 2
A parabola $x=y^2$ with $0 \leq x \leq 1$ is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by $360^{\circ}$ around x-axis is $\dfrac{\pi}{4} \\$ $\dfrac{\pi}{2} \\$ ${\pi} \\$ $2 \pi$
A parabola $x=y^2$ with $0 \leq x \leq 1$ is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by $360^{\circ}$ around x-axis ...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2019-set1
calculus
area-under-curve
+
–
1
answers
0
votes
GATE2019 ME-1: 51
The value of the following definite integral is __________ (round off to three decimal places) $\int_1^e (x \: \ln \: x) dx$
The value of the following definite integral is __________ (round off to three decimal places)$$\int_1^e (x \: \ln \: x) dx$$
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2019-set1
numerical-answers
calculus
definite-integrals
+
–
0
answers
0
votes
GATE2018-1-27
The value of the integral over the closed surface $S$ bounding a volume $V$, where $\overrightarrow{r} = x \hat{i} + y \hat{j}+z \hat{k}$ is the position vector and $\overrightarrow{n}$ is the normal to the surface $S$, is $V$ $2V$ $3V$ $4V$
The value of the integralover the closed surface $S$ bounding a volume $V$, where $\overrightarrow{r} = x \hat{i} + y \hat{j}+z \hat{k}$ is the position vector and $\over...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2018-set1
calculus
surface-integral
vector-identities
+
–
0
answers
0
votes
GATE2018-1-4
$F(z)$ is a function of the complex variable $z=x+iy$ given by $F(z)+ i \: z + k \: Re(z) + i \: Im(z)$. For what value of $k$ will $F(z)$ satisfy the Cauchy-Riemann equations? $0$ $1$ $-1$ $y$
$F(z)$ is a function of the complex variable $z=x+iy$ given by $F(z)+ i \: z + k \: Re(z) + i \: Im(z)$. For what value of $k$ will $F(z)$ satisfy the Cauchy-Riemann equa...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2018-set1
calculus
complex-variables
euler-cauchy-equations
+
–
0
answers
0
votes
GATE2018-1-3
According to the Mean Value Theorem, for a continuous function $f(x)$ in the interval $[a,b]$, there exists a value $\xi$ in this interval such that $\int_a^b f(x) dx = $ $f(\xi)(b-a)$ $f(b)(\xi-a)$ $f(a)(b-\xi)$ $0$
According to the Mean Value Theorem, for a continuous function $f(x)$ in the interval $[a,b]$, there exists a value $\xi$ in this interval such that $\int_a^b f(x) dx = $...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2018-set1
calculus
mean-value-theorems
definite-integrals
+
–
0
answers
0
votes
GATE2018-2-28
For a position vector $\overrightarrow{r} = x \hat{i}+y \hat{j} + z\hat{k}$ the norm of the vector can be defined as $\mid \overrightarrow{r} \mid = \sqrt{x^2+y^2+z^2}$. Given a function $\phi =\text{ln} \mid \overrightarrow{r} \mid$, its ... $\dfrac{\overrightarrow{r}}{\overrightarrow{r} \cdot \overrightarrow{r} } \\ $ $\dfrac{\overrightarrow{r}}{\mid \overrightarrow{r} \mid^3} $
For a position vector $\overrightarrow{r} = x \hat{i}+y \hat{j} + z\hat{k}$ the norm of the vector can be defined as $\mid \overrightarrow{r} \mid = \sqrt{x^2+y^2+z^2}$. ...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
retagged
Mar 5, 2021
Calculus
gateme-2018-set2
calculus
vector-identities
+
–
0
answers
0
votes
GATE2018-2-26
Let $z$ be a complex variable. For a counter-clockwise integration around a unit circle $C$, centered at origin, $\oint_C \frac{1}{5z-4} dz=A \pi i$, the value of $A$ is $2/5$ $1/2$ $2$ $4/5$
Let $z$ be a complex variable. For a counter-clockwise integration around a unit circle $C$, centered at origin, $$\oint_C \frac{1}{5z-4} dz=A \pi i$$, the value of $A$ i...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2018-set2
calculus
complex-variables
+
–
0
answers
0
votes
GATE2018-2-2
The divergence of the vector field $\overrightarrow{u}=e^x(\cos \: y\hat{i}+\sin \: y \hat{j})$ is $0$ $e^x \cos y + e^x \sin y$ $2e^x \cos y$ $2e^x \sin y$
The divergence of the vector field $\overrightarrow{u}=e^x(\cos \: y\hat{i}+\sin \: y \hat{j})$ is$0$$e^x \cos y + e^x \sin y$$2e^x \cos y$$2e^x \sin y$
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
edited
Mar 5, 2021
Calculus
gateme-2018-set2
calculus
divergence-and-curl
+
–
0
answers
0
votes
GATE2018-2-1
The Fourier cosine series for an even function $f(x)$ is given by $ f(x)=a_0 + \Sigma_{n=1}^\infty a_n \cos (nx).$ The value of the coefficient $a_2$ for the function $f(x)=\cos ^2 (x)$ in $[0, \pi]$ is $-0.5$ $0.0$ $0.5$ $1.0$
The Fourier cosine series for an even function $f(x)$ is given by $$ f(x)=a_0 + \Sigma_{n=1}^\infty a_n \cos (nx).$$ The value of the coefficient $a_2$ for the function $...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
edited
Mar 5, 2021
Calculus
gateme-2018-set2
calculus
fourier-series
+
–
1
answers
0
votes
GATE2017 ME-2: 29
If $f(z)=(x^{2}+ay^{2})+i bxy$ is a complex analytic function of $z=x+iy$, where $i=\sqrt{-1}$, then $a=-1, b=-1$ $a=-1, b=2$ $a=1, b= 2$ $a=2, b=2$
If $f(z)=(x^{2}+ay^{2})+i bxy$ is a complex analytic function of $z=x+iy$, where $i=\sqrt{-1}$, then$a=-1, b=-1$$a=-1, b=2$$a=1, b= 2$$a=2, b=2$
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2017-set2
calculus
complex-variables
+
–
0
answers
0
votes
GATE2017 ME-2: 26
The surface integral $\int \int _{s} F.n $ dS over the surface $S$ of the sphere $x^{2}+y^{2}+z^{2}=9$, where $F=(x+y) i+(x+z) j+(y+z)k$ and $n$ is the unit outward surface normal, yields ________.
The surface integral $\int \int _{s} F.n $ dS over the surface $S$ of the sphere $x^{2}+y^{2}+z^{2}=9$, where $F=(x+y) i+(x+z) j+(y+z)k$ and $n$ is the unit outward surfa...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2017-set2
numerical-answers
calculus
surface-integral
+
–
0
answers
0
votes
GATE2017 ME-2: 2
The divergence of the vector $-yi+xj$ is ________.
The divergence of the vector $-yi+xj$ is ________.
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2017-set2
numerical-answers
calculus
vector-identities
divergence-and-curl
+
–
0
answers
0
votes
GATE2017 ME-1: 28
A parametric curve defined by $x= \cos \left ( \dfrac{\Pi u}{2} \right ), y= \sin \left ( \dfrac{\Pi u}{2} \right )$ in the range $0 \leq u \leq 1$ is rotated about the $X$-axis by $360$ degrees. Area of the surface generated is $\dfrac{\Pi }{2} \\$ $\pi \\$ $2 \pi \\$ $4 \pi$
A parametric curve defined by $x= \cos \left ( \dfrac{\Pi u}{2} \right ), y= \sin \left ( \dfrac{\Pi u}{2} \right )$ in the range $0 \leq u \leq 1$ is rotated about the $...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2017-set1
calculus
area-under-curve
+
–
0
answers
0
votes
GATE2017 ME-1: 27
For the vector $\vec{V}=2yz\hat{i}+3xz \hat{j}+4xy \hat{k}$, the value of $\bigtriangledown$. $(\bigtriangledown \times \vec{V})$ is ________.
For the vector $\vec{V}=2yz\hat{i}+3xz \hat{j}+4xy \hat{k}$, the value of $\bigtriangledown$. $(\bigtriangledown \times \vec{V})$ is ________.
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2017-set1
numerical-answers
calculus
vector-identities
+
–
0
answers
0
votes
GATE2017 ME-1: 2
The value of $\displaystyle{}\lim_{x \rightarrow 0}\dfrac{x^{3}-\sin(x)}{x}$ is $0$ $3$ $1$ $-1$
The value of $\displaystyle{}\lim_{x \rightarrow 0}\dfrac{x^{3}-\sin(x)}{x}$ is$0$$3$$1$$-1$
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
edited
Mar 5, 2021
Calculus
gateme-2017-set1
calculus
limits
+
–
0
answers
0
votes
GATE2016-3-53
A point P $(1, 3,−5)$ is translated by $2\hat{i}+3\hat{j}-4\hat{k}$ and then rotated counter clockwise by $90^\circ $ about the $z$-axis. The new position of the point is $(−6, 3,−9)$ $(−6,−3,−9)$ $(6, 3,−9)$ $(6, 3, 9)$
A point P $(1, 3,−5)$ is translated by $2\hat{i}+3\hat{j}-4\hat{k}$ and then rotated counter clockwise by $90^\circ $ about the $z$-axis. The new position of the point...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2016-set3
calculus
vector-identities
+
–
0
answers
0
votes
GATE2016-3-28
$\displaystyle{}\lim_{x\rightarrow \infty }\sqrt{x^2+x-1}-x$ is $0$ $\infty$ $1/2$ $-\infty$
$\displaystyle{}\lim_{x\rightarrow \infty }\sqrt{x^2+x-1}-x$ is$0$$\infty$$1/2$$-\infty$
Lakshman Bhaiya
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Lakshman Bhaiya
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Calculus
gateme-2016-set3
calculus
limits
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GATE2016-3-27
The value of the line integral $\oint_{c}^{ }\overline{F}.{\overline{r}}'ds$ ,where $C$ is a circle of radius $\dfrac{4}{\sqrt{\pi }}$ units is ________ Here, $\overline{F}(x,y)=y\hat{i}+2x\hat{j}$ ... $x-y$ Cartesian reference. In evaluating the line integral, the curve has to be traversed in the counter-clockwise direction.
The value of the line integral $\oint_{c}^{ }\overline{F}.{\overline{r}}'ds$ ,where $C$ is a circle of radius $\dfrac{4}{\sqrt{\pi }}$ units is ________Here, $\overline{F...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2016-set3
numerical-answers
calculus
vector-identities
initial-and-boundary-value-problems
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–
0
answers
0
votes
GATE2016-3-2
$\displaystyle{}\lim_{x\rightarrow 0}\dfrac{\log_e(1+4x)}{e^{3x}-1}$ is equal to $0 \\$ $\dfrac{1}{12} \\$ $\dfrac{4}{3} \\$ $1$
$\displaystyle{}\lim_{x\rightarrow 0}\dfrac{\log_e(1+4x)}{e^{3x}-1}$ is equal to$0 \\$$\dfrac{1}{12} \\$$\dfrac{4}{3} \\$$1$
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2016-set3
calculus
limits
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–
0
answers
0
votes
GATE2016-2-27
The value of $\oint_{\Gamma }^{ }\dfrac{3z-5}{(z-1)(z-2)}dz$ along a closed path $\Gamma$ is equal to $(4\pi i)$ , where $z=x+iy$ and $i=\sqrt{-1}$. The correct path $\Gamma$ is
The value of $\oint_{\Gamma }^{ }\dfrac{3z-5}{(z-1)(z-2)}dz$ along a closed path $\Gamma$ is equal to $(4\pi i)$ , where $z=x+iy$ and $i=\sqrt{-1}$. The correct path $\G...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2016-set2
calculus
initial-and-boundary-value-problems
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0
answers
0
votes
GATE2016-2-26
A scalar potential $\varphi$ has the following gradient: $\bigtriangledown \varphi =yz\hat{i}+xz\hat{j}+xy\hat{k}$ . Consider the integral $\int_{c}^{ }\bigtriangledown \varphi .d\overrightarrow{r}$ on the curve $\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}$. The curve $C$ ... . The value of the integral is ________
A scalar potential $\varphi$ has the following gradient: $\bigtriangledown \varphi =yz\hat{i}+xz\hat{j}+xy\hat{k}$ . Consider the integral $\int_{c}^{ }\bigtriangledown \...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2016-set2
numerical-answers
calculus
integrals
vector-identities
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0
answers
0
votes
GATE2016-2-4
A function of the complex variable $z= x+iy$, is given as $f(x,y) =u(x,y) +iv(x,y)$ , where $u(x,y) = 2kxy$ and $ v(x,y) =x^2 −y^2$. The value of $k$, for which the function is analytic, is _____
A function of the complex variable $z= x+iy$, is given as $f(x,y) =u(x,y) +iv(x,y)$ , where $u(x,y) = 2kxy$ and $ v(x,y) =x^2 −y^2$. The value of $k$, for which the fun...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 5, 2021
Calculus
gateme-2016-set2
numerical-answers
calculus
complex-variables
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