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Recent questions and answers in Engineering Mathematics
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answer
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 $\sqrt{np},np\left ( 1-2p \right )$ $\sqrt{np},\sqrt{np\left ( 1-p \right )}$ $np,np$ $np, np\left ( 1-p \right )$
ShouvikSVK
answered
in
Probability and Statistics
Jan 22
by
ShouvikSVK
280
points
gateme-2021-set2
probability-and-statistics
probability
binomial-distribution
1
answer
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: $\alpha$ $\alpha ^{2}$ $\surd{\alpha }$ $\alpha ^{4}$
ShouvikSVK
answered
in
Linear Algebra
Jan 22
by
ShouvikSVK
280
points
gateme-2021-set2
linear-algebra
matrices
eigen-values
1
answer
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 $0$ $\frac{1}{2}$ $1$ $\frac{3}{2}$
Hashtag
answered
in
Differential Equations
Jun 20, 2021
by
Hashtag
140
points
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 $3$ $9$ $27$ $81$
go_editor
asked
in
Probability and Statistics
Mar 1, 2021
by
go_editor
5.0k
points
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 ... $u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}$
go_editor
asked
in
Calculus
Mar 1, 2021
by
go_editor
5.0k
points
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 $x^{2}y=1$ $xy^{2}=1$ $x^{2}y^{2}=1$ $x/y^{2}=1$
go_editor
asked
in
Calculus
Mar 1, 2021
by
go_editor
5.0k
points
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 $1.83$ $1.60$ $1.51$ $1.06$
go_editor
asked
in
Numerical Methods
Mar 1, 2021
by
go_editor
5.0k
points
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 $4$ $16$ $4i$ $16i$
go_editor
asked
in
Calculus
Mar 1, 2021
by
go_editor
5.0k
points
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 $0$ $\frac{1}{6}$ $\frac{4}{3}$ $\pi$
go_editor
asked
in
Calculus
Mar 1, 2021
by
go_editor
5.0k
points
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 $Q^{T}r$ $Q^{-1}r$ $\frac{r}{r^{T}r}$ $r$
go_editor
asked
in
Linear Algebra
Mar 1, 2021
by
go_editor
5.0k
points
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 $2ye^{y}=e^{x}+e$ $y^{2}e^{y}=e^{x}$ $ye^{y}=e^{x}$ $\left ( 1+y \right )e^{y}=2e^{x}$
go_editor
asked
in
Differential Equations
Mar 1, 2021
by
go_editor
5.0k
points
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 ______ ($\textit{round off to two decimal places}$).
go_editor
asked
in
Numerical Methods
Mar 1, 2021
by
go_editor
5.0k
points
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 $0$ $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\frac{\pi}{2}$
gatecse
asked
in
Differential Equations
Feb 22, 2021
by
gatecse
1.6k
points
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 $\frac{1}{4}$ $\frac{1}{3}$ $\frac{1}{2}$ $1$
gatecse
asked
in
Calculus
Feb 22, 2021
by
gatecse
1.6k
points
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 $\text{t}$, $t_{0} \in \mathbb{R}$ ... $0$ $\infty$ $e^{sa}$ $e^{-sa}$
gatecse
asked
in
Differential Equations
Feb 22, 2021
by
gatecse
1.6k
points
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 $h> 0$
gatecse
asked
in
Differential Equations
Feb 22, 2021
by
gatecse
1.6k
points
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
gatecse
asked
in
Probability and Statistics
Feb 22, 2021
by
gatecse
1.6k
points
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 $\text{A}$ ... ${p}'=\theta ,\left \| {p}' \right \|= \left \| p \right \|/\lambda$
gatecse
asked
in
Linear Algebra
Feb 22, 2021
by
gatecse
1.6k
points
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 $0$ $2$ $\pi i$ $2 \pi i$
gatecse
asked
in
Calculus
Feb 22, 2021
by
gatecse
1.6k
points
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 $0.39$ $0.86$ $0.50$ $0.61$
gatecse
asked
in
Probability and Statistics
Feb 22, 2021
by
gatecse
1.6k
points
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 $0$ $1$ $2$ $3$
gatecse
asked
in
Calculus
Feb 22, 2021
by
gatecse
1.6k
points
gateme-2021-set1
calculus
maxima-minima
1
answer
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)
haralk10
answered
in
Probability and Statistics
Dec 29, 2020
by
haralk10
180
points
gateme-2020-set2
numerical-answers
probability-and-statistics
probability
1
answer
0
votes
GATE2020-ME-2: 2
A matrix $P$ is decomposed into its symmetric part $S$ and skew symmetric part $V$ ... $\begin{pmatrix} -2 & 9/2 & -1 \\ -1 & 81/4 & 11 \\ -2 & 45/2 & 73/4 \end{pmatrix}$
haralk10
answered
in
Linear Algebra
Dec 2, 2020
by
haralk10
180
points
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
go_editor
asked
in
Probability and Statistics
Sep 18, 2020
by
go_editor
5.0k
points
gateme-2020-set2
probability-and-statistics
probability
normal-distribution
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 $\displaystyle \int_{y=0}^1 \int_{x=0}^{\sqrt{y}} xy^2 dx \: dy$ $\displaystyle \int_{y=0}^1 \int_{x=\sqrt{y}}^1 yx^2 dx \: dy$ $\displaystyle \int_{y=0}^1 \int_{x=\sqrt{y}}^1 xy^2 dx \: dy$ $\displaystyle \int_{y=0}^1 \int_{x=0}^{\sqrt{y}} yx^2 dx \: dy$
go_editor
asked
in
Calculus
Sep 18, 2020
by
go_editor
5.0k
points
gateme-2020-set2
calculus
definite-integrals
double-interals
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 $\dfrac{1}{s(s+1)(s-1)} \\$ $\dfrac{1}{s(s+1)} \\$ $\dfrac{1}{s(s-1)} \\$ $\dfrac{1}{s-1} \\$
go_editor
asked
in
Differential Equations
Sep 18, 2020
by
go_editor
5.0k
points
gateme-2020-set2
differential-equations
laplace-transforms
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 _________
go_editor
asked
in
Linear Algebra
Sep 18, 2020
by
go_editor
5.0k
points
gateme-2020-set2
numerical-answers
linear-algebra
eigen-values
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} \\ $ $7$
go_editor
asked
in
Calculus
Sep 18, 2020
by
go_editor
5.0k
points
gateme-2020-set2
calculus
vector-identities
directional-derivatives
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
go_editor
asked
in
Calculus
Sep 18, 2020
by
go_editor
5.0k
points
gateme-2020-set2
calculus
complex-variables
analytic-functions
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).
go_editor
asked
in
Numerical Methods
Sep 18, 2020
by
go_editor
5.0k
points
gateme-2020-set2
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
numerical-answers
0
answers
0
votes
#MADE EASY MOCK TEST GATE2021
The area common to both circles r=a$\sqrt{2}$ and r=2a cos$\theta$.
Gokulan K
asked
in
Calculus
Sep 3, 2020
by
Gokulan K
160
points
#made-easy
mock-gate
2021
0
answers
0
votes
GATE MOCK TEST(MADE EASY)
The area enclosed between the circles r=2a cos$\theta$ and r=a$\sqrt{2}$.
Gokulan K
asked
in
Calculus
Sep 3, 2020
by
Gokulan K
160
points
#gate-mock-test
1
answer
0
votes
GATE Mechanical 2014 Set 1 | Question: 28
In the following table, $x$ is a discrete random variable and $p(x)$ is the probability density. The standard deviation of $x$ is $\begin{array}{|c|c|c|c|} \hline x & 1 & 2 & 3 \\ \hline p(x) & 0.3 & 0.6 & 0.1 \\ \hline \end{array}$ $0.18$ $0.36$ $0.54$ $0.60$
Gyanu
answered
in
Probability and Statistics
Sep 3, 2020
by
Gyanu
140
points
gateme-2014-set1
probability-and-statistics
probability
random-variables
mode-and-standard-deviation
0
answers
0
votes
#GATE QUESTION BANK
The minimum number of equal length subintervals needed to approximate $\int_{1}^{2}xe^xdx$ to an accuracy of atleast (10^(-6))/3 using trapezoidal rule is __________.
Gokulan K
asked
in
Numerical Methods
Jul 15, 2020
by
Gokulan K
160
points
#gate-question-bank
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
go_editor
asked
in
Linear Algebra
Feb 19, 2020
by
go_editor
5.0k
points
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 $\text{c} \\$ $\text{c + 1} \\$ $\dfrac{c}{c+1} \\$ $\dfrac{c+1}{c}$
go_editor
asked
in
Calculus
Feb 19, 2020
by
go_editor
5.0k
points
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 $f\left ( t \right )=\dfrac{1}{\omega ^{2}}\left ( 1-\cos\:\omega t \right ) \\$ $f\left ( t \right )=\dfrac{1}{\omega}\cos\:\omega t \\$ $f\left ( t \right )=\dfrac{1}{\omega}\sin\:\omega t \\$ $f\left ( t \right )=\dfrac{1}{\omega^{2}}\left ( 1-\sin\:\omega t \right )$
go_editor
asked
in
Differential Equations
Feb 19, 2020
by
go_editor
5.0k
points
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? $f\left ( z \right )=z^{2}$ $f\left ( z \right )=e^{z}$ $f\left ( z \right )=\sin z$ $f\left ( z \right )=\log z$
go_editor
asked
in
Calculus
Feb 19, 2020
by
go_editor
5.0k
points
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 __________.
go_editor
asked
in
Engineering Mathematics
Feb 19, 2020
by
go_editor
5.0k
points
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 $0.914$ $1.248$ $0.581$ $0.592$
go_editor
asked
in
Numerical Methods
Feb 19, 2020
by
go_editor
5.0k
points
gateme-2020-set1
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
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