GO Mechanical
Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Recent activity in Engineering Mathematics
1
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 3
The mean and variance, respectively, of a binomial distribution for $n$ independent trails with the probability of success as $p$, are $\sqrt{np},np\left ( 1-2p \right )$ $\sqrt{np},\sqrt{np\left ( 1-p \right )}$ $np,np$ $np, np\left ( 1-p \right )$
The mean and variance, respectively, of a binomial distribution for $n$ independent trails with the probability of success as $p$, are$\sqrt{np},np\left ( 1-2p \right )$$...
ShouvikSVK
280
points
ShouvikSVK
answered
Jan 22, 2022
Probability and Statistics
gateme-2021-set2
probability-and-statistics
probability
binomial-distribution
+
–
1
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 1
Consider an $n \times n$ matrix $\text{A}$ and a non-zero $n \times 1$ vector $p.$ Their product $Ap=\alpha ^{2}p$, where $\alpha \in \Re$ and $\alpha \notin \left \{ -1,0,1 \right \}$. Based on the given information, the eigen value of $A^{2}$ is: $\alpha$ $\alpha ^{2}$ $\surd{\alpha }$ $\alpha ^{4}$
Consider an $n \times n$ matrix $\text{A}$ and a non-zero $n \times 1$ vector $p.$ Their product $Ap=\alpha ^{2}p$, where $\alpha \in \Re$ and $\alpha \notin \left \{ -1...
ShouvikSVK
280
points
ShouvikSVK
answered
Jan 21, 2022
Linear Algebra
gateme-2021-set2
linear-algebra
matrices
eigen-values
+
–
1
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 2
If the Laplace transform of a function $f(t)$ is given by $\frac{s+3}{\left ( s+1 \right )\left ( s+2 \right )}$, then $f(0)$ is $0$ $\frac{1}{2}$ $1$ $\frac{3}{2}$
If the Laplace transform of a function $f(t)$ is given by $\frac{s+3}{\left ( s+1 \right )\left ( s+2 \right )}$, then $f(0)$ is$0$$\frac{1}{2}$$1$$\frac{3}{2}$
Hashtag
140
points
Hashtag
answered
Jun 20, 2021
Differential Equations
gateme-2021-set2
differential-equations
laplace-transforms
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 8
A $\text{PERT}$ network has $9$ activities on its critical path. The standard deviation of each activity on the critical path is $3$. The standard deviation of the critical path is $3$ $9$ $27$ $81$
A $\text{PERT}$ network has $9$ activities on its critical path. The standard deviation of each activity on the critical path is $3$. The standard deviation of the critic...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Probability and Statistics
gateme-2021-set2
probability-and-statistics
statistics
mode-and-standard-deviation
+
–
0
answers
0
votes
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$$\frac{\partial \left ( u^{2...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Calculus
gateme-2021-set2
calculus
partial-derivatives
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 13
A two dimensional flow has velocities in $x$ and $y$ directions given by $u = 2xyt$ and $v = -y^{2}t$, where $\text{t}$ denotes time. The equation for streamline passing through $x=1,\:y=1$ is $x^{2}y=1$ $xy^{2}=1$ $x^{2}y^{2}=1$ $x/y^{2}=1$
A two dimensional flow has velocities in $x$ and $y$ directions given by $u = 2xyt$ and $v = -y^{2}t$, where $\text{t}$ denotes time. The equation for streamline passing ...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Calculus
gateme-2021-set2
calculus
derivatives
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 18
Value of $\int_{4}^{5.2} \ln x\: dx$ using Simpson’s one-third rule with interval size $0.3$ is $1.83$ $1.60$ $1.51$ $1.06$
Value of $\int_{4}^{5.2} \ln x\: dx$ using Simpson’s one-third rule with interval size $0.3$ is$1.83$$1.60$$1.51$$1.06$
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Numerical Methods
gateme-2021-set2
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
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 2 | Question: 27
Let the superscript $\text{T}$ represent the transpose operation. Consider the function $f(x)=\frac{1}{2}x^TQx-r^Tx$, where $x$ and $r$ are $n \times 1$ vectors and $\text{Q}$ is a symmetric $n \times n$ matrix. The stationary point of $f(x)$ is $Q^{T}r$ $Q^{-1}r$ $\frac{r}{r^{T}r}$ $r$
Let the superscript $\text{T}$ represent the transpose operation. Consider the function $f(x)=\frac{1}{2}x^TQx-r^Tx$, where $x$ and $r$ are $n \times 1$ vectors and $\tex...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Linear Algebra
gateme-2021-set2
linear-algebra
matrix-algebra
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 28
Consider the following differential equation $\left ( 1+y \right )\frac{dy}{dx}=y.$ The solution of the equation that satisfies condition $y(1)=1$ is $2ye^{y}=e^{x}+e$ $y^{2}e^{y}=e^{x}$ $ye^{y}=e^{x}$ $\left ( 1+y \right )e^{y}=2e^{x}$
Consider the following differential equation$$\left ( 1+y \right )\frac{dy}{dx}=y.$$The solution of the equation that satisfies condition $y(1)=1$ is$2ye^{y}=e^{x}+e$$y^{...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Differential Equations
gateme-2021-set2
differential-equations
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 2 | Question: 35
Find the positive real root of $x^3-x-3=0$ using Newton-Raphson method. lf the starting guess $(x_{0})$ is $2,$ the numerical value of the root after two iterations $(x_{2})$ is ______ ($\textit{round off to two decimal places}$).
Find the positive real root of $x^3-x-3=0$ using Newton-Raphson method. lf the starting guess $(x_{0})$ is $2,$ the numerical value of the root after two iterations $(x_{...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Numerical Methods
gateme-2021-set2
numerical-methods
newton-raphson-method
numerical-answers
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 1 | Question: 1
If $y(x)$ satisfies the differential equation $(\sin x) \dfrac{\mathrm{d}y }{\mathrm{d} x} + y \cos x = 1,$ subject to the condition $y(\pi/2) = \pi/2,$ then $y(\pi/6)$ is $0$ $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\frac{\pi}{2}$
If $y(x)$ satisfies the differential equation $(\sin x) \dfrac{\mathrm{d}y }{\mathrm{d} x} + y \cos x = 1,$subject to the condition $y(\pi/2) = \pi/2,$ then $y(\pi/6)$ is...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Differential Equations
gateme-2021-set1
differential-equations
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 1 | Question: 2
The value of $\displaystyle{} \lim_{x \rightarrow 0} \left( \frac{1 – \cos x}{x^{2}}\right)$ is $\frac{1}{4}$ $\frac{1}{3}$ $\frac{1}{2}$ $1$
The value of $\displaystyle{} \lim_{x \rightarrow 0} \left( \frac{1 – \cos x}{x^{2}}\right)$ is$\frac{1}{4}$$\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: 3
The Dirac-delta function $\left ( \delta \left ( t-t_{0} \right ) \right )$ for $\text{t}$, $t_{0} \in \mathbb{R}$ ... $0$ $\infty$ $e^{sa}$ $e^{-sa}$
The Dirac-delta function $\left ( \delta \left ( t-t_{0} \right ) \right )$ for $\text{t}$, $t_{0} \in \mathbb{R}$, has the following property$$\int_{a}^{b}\varphi \left ...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Differential Equations
gateme-2021-set1
differential-equations
laplace-transforms
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 1 | Question: 4
The ordinary differential equation $\dfrac{dy}{dt}=-\pi y$ subject to an initial condition $y\left ( 0 \right )=1$ ... ___________________. $0< h< \frac{2}{\pi }$ $0< h< 1$ $0< h< \frac{\pi }{2}$ for all $h> 0$
The ordinary differential equation $\dfrac{dy}{dt}=-\pi y$ subject to an initial condition $y\left ( 0 \right )=1$ is solved numerically using the following scheme:$$\fra...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Differential Equations
gateme-2021-set1
differential-equations
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 1 | Question: 5
Consider a binomial random variable $\text{X}$. If $X_{1},X_{2},\dots ,X_{n}$ are independent and identically distributed samples from the distribution of $\text{X}$ with sum $Y=\sum_{i=1}^{n}X_{i}$, then the distribution of $\text{Y}$ as $n\rightarrow \infty$ can be approximated as Exponential Bernoulli Binomial Normal
Consider a binomial random variable $\text{X}$. If $X_{1},X_{2},\dots ,X_{n}$ are independent and identically distributed samples from the distribution of $\text{X}$ with...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Probability and Statistics
gateme-2021-set1
probability-and-statistics
probability
random-variables
normal-distribution
+
–
0
answers
0
votes
GATE Mechanical 2021 Set 1 | Question: 26
Consider a vector $\text{p}$ in $2$-dimensional space. Let its direction (counter-clockwise angle with the positive $\text{x}$-axis) be $\theta$. Let $\text{p}$ be an eigenvector of a $2\times2$ matrix $\text{A}$ ... ${p}'=\theta ,\left \| {p}' \right \|= \left \| p \right \|/\lambda$
Consider a vector $\text{p}$ in $2$-dimensional space. Let its direction (counter-clockwise angle with the positive $\text{x}$-axis) be $\theta$. Let $\text{p}$ be an ei...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Linear Algebra
gateme-2021-set1
linear-algebra
eigen-values
eigen-vectors
+
–
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: 33
Customers arrive at a shop according to the Poisson distribution with a mean of $10$ customers/hour. The manager notes that no customer arrives tor the first $3$ minutes after the shop opens. The probability that a customer arrives within the next $3$ minutes is $0.39$ $0.86$ $0.50$ $0.61$
Customers arrive at a shop according to the Poisson distribution with a mean of $10$ customers/hour. The manager notes that no customer arrives tor the first $3$ minutes ...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Apr 11, 2021
Probability and Statistics
gateme-2021-set1
probability-and-statistics
probability
poisson-distribution
+
–
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
+
–
1
answers
0
votes
GATE2020-ME-2: 36
A fair coin is tossed $20$ times. The probability that ‘head’ will appear exactly $4$ times in the first ten tosses, and ‘tail’ will appear exactly $4$ times in the next ten tosses is _________ (round off to $3$ decimal places)
A fair coin is tossed $20$ times. The probability that ‘head’ will appear exactly $4$ times in the first ten tosses, and ‘tail’ will appear exactly $4$ times in t...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Probability and Statistics
gateme-2020-set2
numerical-answers
probability-and-statistics
probability
+
–
0
answers
0
votes
GATE2020-ME-2: 35
For the integral $\displaystyle \int_0 ^{\pi/2} (8+4 \cos x) dx$, the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the end points, is ________ (round off to one decimal place).
For the integral $\displaystyle \int_0 ^{\pi/2} (8+4 \cos x) dx$, the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the end poin...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Numerical Methods
gateme-2020-set2
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
numerical-answers
+
–
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: 19
Let $\textbf{I}$ be a $100$ dimensional identity matrix and $\textbf{E}$ be the set of its distinct (no value appears more than once in $\textbf{E})$ real eigen values. The number of elements in $\textbf{E}$ is _________
Let $\textbf{I}$ be a $100$ dimensional identity matrix and $\textbf{E}$ be the set of its distinct (no value appears more than once in $\textbf{E})$ real eigen values. T...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
retagged
Mar 6, 2021
Linear Algebra
gateme-2020-set2
numerical-answers
linear-algebra
eigen-values
+
–
0
answers
0
votes
GATE2020-ME-2: 4
The solution of $\dfrac{d^2y}{dt^2}-y=1,$ which additionally satisfies $y \bigg \vert_{t=0} = \dfrac{dy}{dt} \bigg \vert_{t=0}=0$ in the Laplace $s$-domain is $\dfrac{1}{s(s+1)(s-1)} \\$ $\dfrac{1}{s(s+1)} \\$ $\dfrac{1}{s(s-1)} \\$ $\dfrac{1}{s-1} \\$
The solution of $$\dfrac{d^2y}{dt^2}-y=1,$$ which additionally satisfies $y \bigg \vert_{t=0} = \dfrac{dy}{dt} \bigg \vert_{t=0}=0$ in the Laplace $s$-domain is$\dfrac{1}...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Differential Equations
gateme-2020-set2
differential-equations
laplace-transforms
+
–
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$$\dis...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Calculus
gateme-2020-set2
calculus
definite-integrals
double-interals
+
–
1
answers
0
votes
GATE2020-ME-2: 2
A matrix $P$ is decomposed into its symmetric part $S$ and skew symmetric part $V$ ... $\begin{pmatrix} -2 & 9/2 & -1 \\ -1 & 81/4 & 11 \\ -2 & 45/2 & 73/4 \end{pmatrix}$
A matrix $P$ is decomposed into its symmetric part $S$ and skew symmetric part $V$. If $$S= \begin{pmatrix} -4 & 4 & 2 \\ 4 & 3 & 7/2 \\ 2 & 7/2 & 2 \end{pmatrix}, \: \: ...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
retagged
Mar 6, 2021
Linear Algebra
gateme-2020-set2
linear-algebra
matrices
+
–
0
answers
0
votes
GATE2020-ME-2: 1
The sum of two normally distributed random variables $X$ and $Y$ is always normally distributed normally distributed, only if $X$ and $Y$ are independent normally distributed, only if $X$ and $Y$ have the same standard deviation normally distributed, only if $X$ and $Y$ have the same mean
The sum of two normally distributed random variables $X$ and $Y$ isalways normally distributednormally distributed, only if $X$ and $Y$ are independentnormally distribute...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
retagged
Mar 6, 2021
Probability and Statistics
gateme-2020-set2
probability-and-statistics
probability
normal-distribution
+
–
0
answers
0
votes
GATE2020-ME-1: 1
Multiplication of real valued square matrices of same dimension is associative commutative always positive definite not always possible to compute
Multiplication of real valued square matrices of same dimension isassociativecommutativealways positive definitenot always possible to compute
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Linear Algebra
gateme-2020-set1
linear-algebra
matrices
+
–
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: 3
The Laplace transform of a function $f(t)$ is $L( f )=\dfrac{1}{(s^{2}+\omega ^{2})}.$ Then, $f(t)$ is $f\left ( t \right )=\dfrac{1}{\omega ^{2}}\left ( 1-\cos\:\omega t \right ) \\$ $f\left ( t \right )=\dfrac{1}{\omega}\cos\:\omega t \\$ $f\left ( t \right )=\dfrac{1}{\omega}\sin\:\omega t \\$ $f\left ( t \right )=\dfrac{1}{\omega^{2}}\left ( 1-\sin\:\omega t \right )$
The Laplace transform of a function $f(t)$ is $L( f )=\dfrac{1}{(s^{2}+\omega ^{2})}.$ Then, $f(t)$ is$f\left ( t \right )=\dfrac{1}{\omega ^{2}}\left ( 1-\cos\:\omega t ...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Differential Equations
gateme-2020-set1
differential-equations
laplace-transforms
+
–
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}$$f\left ( z \right ...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Calculus
gateme-2020-set1
calculus
complex-variables
+
–
0
answers
0
votes
GATE2020-ME-1: 19
For three vectors $\overrightarrow{A}=2\widehat{j}-3\widehat{k},\:\overrightarrow{B}=-2\widehat{i}+\widehat{k}\:\:\text{and}\:\overrightarrow{C}=3\widehat{i}-\widehat{j},\:\text{where}\:\widehat{i},\:\widehat{j}\:\text{and}\:\widehat{k}$ are ... system, the value of $\left ( \overrightarrow{A}.\left ( \overrightarrow{B}\times \overrightarrow{C} \right )+6 \right )$ is __________.
For three vectors $\overrightarrow{A}=2\widehat{j}-3\widehat{k},\:\overrightarrow{B}=-2\widehat{i}+\widehat{k}\:\:\text{and}\:\overrightarrow{C}=3\widehat{i}-\widehat{j},...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Engineering Mathematics
gateme-2020-set1
numerical-answers
engineering-mathematics
+
–
0
answers
0
votes
GATE2020-ME-1: 26
The evaluation of the definite integral $\int ^{1.4}_{ – 1}x \mid x \mid dx$ by using Simpson’s $1/3^{rd}$ (one - third) rule with step size $h=0.6$ yields $0.914$ $1.248$ $0.581$ $0.592$
The evaluation of the definite integral $\int ^{1.4}_{ – 1}x \mid x \mid dx$ by using Simpson’s $1/3^{rd}$ (one - third) rule with step size $h=0.6$ yields$0.914$$1.2...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Numerical Methods
gateme-2020-set1
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
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 $$\overrightarrow{f}\left ( x,y,z \right )=\dfrac{x}{\left [ x^{2}+y^{2}+z^{2} \right ]^{\frac{3}{2}}}\widehat{i}\:+\:\dfrac{y}{\left [ x^{2}...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Calculus
gateme-2020-set1
calculus
vector-identities
+
–
0
answers
0
votes
GATE2020-ME-1: 35
Consider two exponentially distributed random variables $\text{X and Y}$, both having a mean of $0.50$. Let $Z=X+Y$ and $r$ be the correlation between $\text{X and Y}$.If the variance of $Z$ equals $0$, then the value of $r$ is __________ (roundoff to $2$ decimal places).
Consider two exponentially distributed random variables $\text{X and Y}$, both having a mean of $0.50$. Let $Z=X+Y$ and $r$ be the correlation between $\text{X and Y}$.If...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
recategorized
Mar 6, 2021
Engineering Mathematics
gateme-2020-set1
numerical-answers
engineering-mathematics
differential-equation
random-variables
+
–
0
answers
0
votes
GATE2020-ME-1: 36
An analytic function of a complex variable $z=x + iy \left ( i=\sqrt{-1} \right )$ is defined as $f\left ( z \right )=x^{2}-y^{2}+i\psi \left ( x,y \right ),$ where $\psi \left ( x,y \right )$ is a real function. The value of the imaginary part of $f(z)$ at $z=\left ( 1+i \right )$ is __________ (round off to $2$ decimal places).
An analytic function of a complex variable $z=x + iy \left ( i=\sqrt{-1} \right )$ is defined as$$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
+
–
1
answers
0
votes
GATE2019 ME-2: 1
In matrix equation $[A] \{X\}=\{R\}$, $[A] = \begin{bmatrix} 4 & 8 & 4 \\ 8 & 16 & -4 \\ 4 & -4 & 15 \end{bmatrix} \{X\} = \begin{Bmatrix} 2 \\ 1 \\ 4 \end{Bmatrix} \text{ and} \{ R \} = \begin{Bmatrix} 32 \\ 16 \\ 64 \end{Bmatrix}$ One of the eigen values of matrix $[A]$ is $4$ $8$ $15$ $16$
In matrix equation $[A] \{X\}=\{R\}$,$[A] = \begin{bmatrix} 4 & 8 & 4 \\ 8 & 16 & -4 \\ 4 & -4 & 15 \end{bmatrix} \{X\} = \begin{Bmatrix} 2 \\ 1 \\ 4 \end{Bmatrix} \text{...
Lakshman Bhaiya
21.8k
points
Lakshman Bhaiya
retagged
Mar 6, 2021
Linear Algebra
gateme-2019-set2
linear-algebra
matrices
eigen-values
+
–
To see more, click for all the
questions in this category
.
GO Mechanical
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register