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Highest voted questions in Engineering Mathematics
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GATE CH 2021 | Question: 1
An ordinary differential equation $\text{(ODE)}, \: \dfrac{dy}{dx}=2y$, with an initial condition $y(0)=1$, has the analytical ... $0.06$ $0.8$ $4.0$ $8.0$
An ordinary differential equation $\text{(ODE)}, \: \dfrac{dy}{dx}=2y$, with an initial condition $y(0)=1$, has the analytical solution $y=e^{2x}$.Using Runge-Kutta secon...
go_editor
1.4k
points
go_editor
asked
Mar 1, 2021
Numerical Methods
gatech-2021
numerical-methods
runge-kutta-method
+
–
0
answers
0
votes
GATE CH 2021 | Question: 2
The function $\cos(x)$ is approximated using Taylor series around $x=0$ as $\cos(x) \approx 1 + ax + bx^2 + cx^3 + dx^4$. The values ... $a=-0.5, \: b=0,\: c=0.042, \: d=0$
The function $\cos(x)$ is approximated using Taylor series around $x=0$ as $\cos(x) \approx 1 + ax + bx^2 + cx^3 + dx^4$. The values of $a,b,c$ and $d$ are$a=1, \: b=-0....
go_editor
1.4k
points
go_editor
asked
Mar 1, 2021
Calculus
gatech-2021
calculus
taylor-series
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–
0
answers
0
votes
GATE CH 2021 | Question: 5
A three-dimensional velocity field is given by $V=5x^2y \: i + Cy \: j-10xyz \: k$, where $i,j,k$ are the unit vectors in ... fluid flow, the value of $C$ is $-1$ $0$ $1$ $5$
A three-dimensional velocity field is given by $V=5x^2y \: i + Cy \: j-10xyz \: k$, where $i,j,k$ are the unit vectors in $x,y,z$ directions, respectively, describing a c...
go_editor
1.4k
points
go_editor
asked
Mar 1, 2021
Calculus
gatech-2021
calculus
vector-calculus
vector-identities
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–
0
answers
0
votes
GATE CH 2021 | Question: 16
For the function $f(x) = \begin{cases} -x, & x<0 \\ x^2, & x \geq 0 \end{cases}$ ... $x=0$ $f(x)$ is differentiable at $x=0$
For the function $f(x) = \begin{cases} -x, & x<0 \\ x^2, & x \geq 0 \end{cases}$ the $\text{CORRECT}$ statement(s) is/are$f(x)$ is continuous at $x=1$$f(x) $ is different...
go_editor
1.4k
points
go_editor
asked
Mar 1, 2021
Calculus
gatech-2021
calculus
continuity-and-differentiability
multiple-selects
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–
0
answers
0
votes
GATE CH 2021 | Question: 20
$\textbf{A, B, C}$ and $\textbf{D}$ are vectors of length $4$ ... is __________
$\textbf{A, B, C}$ and $\textbf{D}$ are vectors of length $4$. $$\textbf{A} = \begin{bmatrix} a_1 & a_2 & a_3 & a_4 \end{bmatrix} \\ \textbf{B} = \begin{bmatrix}b_1 & b_2...
go_editor
1.4k
points
go_editor
asked
Mar 1, 2021
Linear Algebra
gatech-2021
numerical-answers
linear-algebra
matrices
rank-of-matrix
+
–
0
answers
0
votes
GATE CH 2021 | Question: 26
Let $A$ be a square matrix of size $n \times n (n>1)$. The elements of $A=\{a_{ij}\}$ ... $A$ is $0$ $1$ $n!$ $(n!)^2$
Let $A$ be a square matrix of size $n \times n (n>1)$. The elements of $A=\{a_{ij}\}$ are given by $$a_{ij} = \begin{cases} i \times j, & \text{if } i \geq j \\ 0, & \tex...
go_editor
1.4k
points
go_editor
asked
Mar 1, 2021
Linear Algebra
gatech-2021
linear-algebra
matrix-algebra
determinant
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–
0
answers
0
votes
GATE CH 2021 | Question: 34
To solve an algebraic equation $f(x)=0$, an iterative scehme of the type $x_{n+1} = g(x_n)$ ... order of convergence for this iterative scheme near the solution is ________
To solve an algebraic equation $f(x)=0$, an iterative scehme of the type $x_{n+1} = g(x_n)$ is proposed, where $g(x)=x-\dfrac{f(x)}{f’(x)}$.At the solution $x=s,\: g’...
go_editor
1.4k
points
go_editor
asked
Mar 1, 2021
Calculus
gatech-2021
numerical-answers
calculus
convergence
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–
0
answers
0
votes
GATE CH 2021 | Question: 35
The probability distribution function of a random variable $X$ is shown in the following figure. From this distribution, ... is _______ (round off to $3$ decimal places)
The probability distribution function of a random variable $X$ is shown in the following figure.From this distribution, random samples with sample size $n=68$ are taken. ...
go_editor
1.4k
points
go_editor
asked
Mar 1, 2021
Probability and Statistics
gatech-2021
numerical-answers
probability-and-statistics
probability
uniform-distribution
+
–
0
answers
0
votes
GATE CH 2021 | Question: 36
For the ordinary differential equation $\dfrac{d^3y}{dt^3}+6 \dfrac{d^2y}{dt^2}+11 \dfrac{dy}{dt}+6y=1$ with ... $3$ decimal places).
For the ordinary differential equation $$\dfrac{d^3y}{dt^3}+6 \dfrac{d^2y}{dt^2}+11 \dfrac{dy}{dt}+6y=1$$ with initial conditions $y(0)=y’(0) = y’’(0)=y’’’(0)...
go_editor
1.4k
points
go_editor
asked
Mar 1, 2021
Differential equations
gatech-2021
numerical-answers
differential-equations
+
–
0
answers
0
votes
GATE Chemical 2020 | Question: 25
Sum of the eigenvalues of the matrix $\begin{bmatrix} 2 & 4 & 6 \\ 3 & 5 & 9 \\ 12 & 1 & 7 \end{bmatrix}$ is ______ (round off to nearest integer).
soujanyareddy13
1.8k
points
soujanyareddy13
asked
Nov 16, 2020
Linear Algebra
gate2020
numerical-answers
linear-algebra
matrices
eigen-values
+
–
0
answers
0
votes
GATE Chemical 2020 | Question: 26
In a box, there are $5$ green balls and $10$ blue balls. A person picks $6$ balls randomly. The probability that the person has picked $4$ green balls and $2$ blue balls ...
soujanyareddy13
1.8k
points
soujanyareddy13
asked
Nov 16, 2020
Probability and Statistics
gate2020
probability-and-statistics
probability
conditional-probability
+
–
0
answers
0
votes
GATE Chemical 2020 | Question: 27
The maximum value of the function $f(x)=-\dfrac{5}{3} x^3 +10x^2-15x+16$ in the interval $(0.5,3.5)$ is$0$$8$$16$$48$
soujanyareddy13
1.8k
points
soujanyareddy13
asked
Nov 16, 2020
Calculus
gate2020
calculus
maxima-minima
+
–
0
answers
0
votes
GATE Chemical 2020 | Question: 54
Given $\dfrac{dy}{dx}=y-20$, and $y \mid_{x=0}=40$, the value of $y$ at $x=2$ is _________ (round off to nearest integer)
soujanyareddy13
1.8k
points
soujanyareddy13
asked
Nov 16, 2020
Differential equations
gate2020
numerical-answers
differential-equations
+
–
0
answers
0
votes
GATE Chemical 2020 | Question: 55
Consider the following dataset.$$\begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 3 & 5 & 15 & 25 \\ \hline f(x) & 6 & 8 & 10 & 12 & 5 \\ \hline \end{array}$$The value of the ...
soujanyareddy13
1.8k
points
soujanyareddy13
asked
Nov 16, 2020
Numerical Methods
gate2020
numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
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–
0
answers
0
votes
GATE Chemical 2020 | Question: 1
Which one of the following methods requires specifying an initial interval containing the root (i.e., bracketing) to obtain the solution of $f(x) =0$, where $f(x)$ is a c...
soujanyareddy13
1.8k
points
soujanyareddy13
asked
Nov 16, 2020
Numerical Methods
gate2020
numerical-methods
newton-raphson-method
+
–
0
answers
0
votes
GATE Chemical 2020 | Question: 3
Consider the following continuously differentiable function $$\textbf{v}(x,y,z)=3x^2y \textbf{ i} + 8y^2z \textbf{ j} + 5xyz \textbf{ k}$$ where $\textbf{i, j,}$ and $\te...
soujanyareddy13
1.8k
points
soujanyareddy13
asked
Nov 16, 2020
Calculus
gate2020
calculus
vector-calculus
vector-identities
+
–
0
answers
0
votes
GATE Chemical 2020 | Question: 4
Consider the following unit step function.The Laplace transform of this function is$\dfrac{e^{-3s}}{s} \\ $$\dfrac{e^{-3s}}{s^2} \\$$\dfrac{e^{-3s}}{3s} \\$$\dfrac{e^{-6s...
soujanyareddy13
1.8k
points
soujanyareddy13
asked
Nov 16, 2020
Differential equations
gate2020
differential-equations
laplace-transforms
+
–
0
answers
0
votes
GATE Chemical 2019 | Question: 1
A system of $n$ homogeneous linear equations containing $n$ unknowns will have non-trivial solutions if and only if the determinant of the coefficient matrix is$1$$-1$$0$...
Arjun
4.7k
points
Arjun
asked
Feb 24, 2019
Linear Algebra
gate2019
linear-algebra
matrices
system-of-equations
+
–
0
answers
0
votes
GATE Chemical 2019 | Question: 2
The value of the expression $\underset{x\rightarrow \frac{\pi }{2}}{\lim}\: \mid \frac{\tan\:x}{x} \mid $ is $\infty$$0$$1$$-1$
Arjun
4.7k
points
Arjun
asked
Feb 24, 2019
Calculus
gate2019
calculus
limits
+
–
0
answers
0
votes
GATE Chemical 2019 | Question: 22
The product of the eigenvalues of the matrix $\begin{pmatrix} 2 &3 \\ 0& 7 \end{pmatrix}$ is ____________ (rounded off to one decimal place).
Arjun
4.7k
points
Arjun
asked
Feb 24, 2019
Linear Algebra
gate2019
numerical-answers
linear-algebra
matrices
eigen-values
+
–
0
answers
0
votes
GATE Chemical 2019 | Question: 26
The solution of the ordinary differential equation$\frac{dy}{dx}+3y=1$, subjects to the initial condition $y=1$ at $x=0$, is$\frac{1}{3}\left ( 1+2e^{-x/3} \right )$$\fra...
Arjun
4.7k
points
Arjun
asked
Feb 24, 2019
Differential equations
gate2019
differential-equations
+
–
0
answers
0
votes
GATE Chemical 2019 | Question: 27
The value of the complex number $i^{-1/2}$ (where $i=\sqrt{-1}$) is $\frac{1}{\sqrt{2}}\left ( 1-i \right )$$-\frac{1}{\sqrt{2}}i$$\frac{1}{\sqrt{2}}i$$\frac{1}{\sqrt{2}}...
Arjun
4.7k
points
Arjun
asked
Feb 24, 2019
Complex variables
gate2019
complex-variables
complex-number
+
–
0
answers
0
votes
GATE Chemical 2019 | Question: 34
If $x,y$ and $z$ are directions in a Cartesian coordinate system and $i$, $j$ and $k$ are the respective unit vectors, the directional derivative of the function $u\left ...
Arjun
4.7k
points
Arjun
asked
Feb 24, 2019
Calculus
gate2019
numerical-answers
calculus
vector-calculus
directional-derivatives
+
–
0
answers
0
votes
GATE Chemical 2019 | Question: 35
Two unbiased dice are thrown. Each dice can show any number between $1$ and $6$. The probability that the sum of the outcomes of the two dice is divisible by $4$ is _____...
Arjun
4.7k
points
Arjun
asked
Feb 24, 2019
Probability and Statistics
gate2019
numerical-answers
probability-and-statistics
probability
conditional-probability
+
–
0
answers
0
votes
GATE Chemical 2019 | Question: 36
The Newton-Raphson method is used to determine the root of the equation $f(x)=e^{-x}-x$. If the initial guess for the root is 0, the estimate of the root after two iterat...
Arjun
4.7k
points
Arjun
asked
Feb 24, 2019
Numerical Methods
gate2019
numerical-answers
numerical-methods
newton-raphson-method
+
–
0
answers
0
votes
GATE Chemical 2017 | Question: 1
The value of $\underset{x\rightarrow 0}{\lim}\:\frac{\tan\left ( x \right )}{x}$ is ________________.
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2017
numerical-answers
calculus
limits
+
–
0
answers
0
votes
GATE Chemical 2017 | Question: 2
The real part of $6e^{i\pi /3}$ is _______________.
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Complex variables
gate2017
numerical-answers
complex-variables
complex-number
+
–
0
answers
0
votes
GATE Chemical 2017 | Question: 3
The number of positive roots of the function $f(x)$ shown below in the range $0<x<6$ is ___________________.
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2017
numerical-answers
calculus
maxima-minima
+
–
0
answers
0
votes
GATE Chemical 2017 | Question: 4
Let $i$ and $j$ be the unit vectors in the $x$ and $y$ directions, respectively. For the function $F\left ( x,y \right )=x^{3}+y^{2}$ the gradient of the function. i.e.. ...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2017
calculus
vector-calculus
unit-vectors
gradient
+
–
0
answers
0
votes
GATE Chemical 2017 | Question: 5
The marks obtained by a set of students are: $38,\:84,\:45,\:70,\:75,\:60,\;48$.The mean and median marks, respectively, are$45$ and $75$$55$ and $48$$60$ and $60$$60$ an...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2017
probability-and-statistics
statistics
mean-median-mode
+
–
0
answers
0
votes
GATE Chemical 2017 | Question: 26
For the initial value problem$$\frac{dx}{dt}=\sin\left ( t \right ),\:\:\:\:x\left ( 0 \right )=0$$the value of $x$ at $t=\pi /3$ , is _____________.
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Differential equations
gate2017
numerical-answers
differential-equations
initial-and-boundary-value-problems
+
–
0
answers
0
votes
GATE Chemical 2017 | Question: 27
The Laplace transform of a function is $\frac{s+1}{s\left ( s+2 \right )}$The initial and final values, respectively, of the function are $0$ and $1$$1$ and $\frac{1}{2}$...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Differential equations
gate2017
differential-equations
laplace-transforms
+
–
0
answers
0
votes
GATE Chemical 2017 | Question: 29
A box has $6$ red balls and $4$ white balls. A ball is picked at random and replaced in the box, after which a second ball is picked.The probability of both the balls bei...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2017
numerical-answers
probability-and-statistics
probability
conditional-probability
+
–
0
answers
0
votes
GATE Chemical 2016 | Question: 1
Which one of the following is an iterative technique for solving a system of simultaneous linear algebraic equations?Gauss eliminationGauss-JordanGauss-Seidel$LU$ decompo...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Numerical Methods
gate2016
numerical-methods
system-of-equations
+
–
0
answers
0
votes
GATE Chemical 2016 | Question: 2
The Laplace transform of $e^{at}\sin\left ( bt \right )$ is$\frac{b}{\left ( s-a \right )^{2}+b^{2}}$$\frac{s-a}{\left ( s-a \right )^{2}+b^{2}}$$\frac{s-a}{\left ( s-a \...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Differential equations
gate2016
differential-equations
laplace-transforms
+
–
0
answers
0
votes
GATE Chemical 2016 | Question: 3
What are the modulus $\left ( r \right )$ and argument $\left ( \theta \right )$ of the complex number $3+4i$ ?$r=\sqrt{7}, \theta =tan^{-1}\left ( \frac{4}{3} \right )$$...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Complex variables
gate2016
complex-variables
complex-number
+
–
0
answers
0
votes
GATE Chemical 2016 | Question: 26
A set of simultaneous linear algebraic equations is represented in a matrix form as shown below.$\begin{bmatrix} 0 &0 &0 &4 &13 \\ 2& 5& 5& 2& 10\\ 0&0 &2 &5 &3 \\ 0&0 &0...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Linear Algebra
gate2016
numerical-answers
linear-algebra
system-of-equations
+
–
0
answers
0
votes
GATE Chemical 2016 | Question: 27
What is the solution for the second order differential equation $\frac{\mathrm{d} ^{2}y}{\mathrm{d} x}^{2}+y=0$, with the initial conditions $y\left | _{x-0}=5\:and\:\fra...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Differential equations
gate2016
differential-equations
+
–
0
answers
0
votes
GATE Chemical 2016 | Question: 28
The model $y=mx^{2}$ is to be fit to the data given below.$$\begin{array}{|cl|cI|}\hline&{x} & {1} & {\sqrt{2}} & {\sqrt{3}} \\ \hline &{y} & {2} & {5} & {8} \\ \hline \e...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Numerical Methods
gate2016
numerical-answers
numerical-methods
linear-regression
+
–
0
answers
0
votes
GATE Chemical 2016 | Question: 29
The Lagrange mean-value theorem is satisfied for $f\left ( x \right )=x^{3}+5$, in the interval $\left ( 1,4 \right )$ at a value (rounded off to the second decimal place...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2016
numerical-answers
calculus
mean-value-theorems
+
–
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