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Recent questions in Engineering Mathematics
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GATE Chemical 2016 | Question: 30
Values of $f\left ( x \right )$ in the interval $\left [ 0,4 \right ]$ are given below.$\begin{array}{|cl|cI|cI|cI|cI|cI|}\hline&{x} & \text{0} & \text{1} & \text{2} & \t...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Numerical Methods
gate2016
numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
0
answers
0
votes
GATE Chemical 2015 | Question: 11
The following set of the three vectors$$\begin{pmatrix} 1\\2\\1 \end{pmatrix}, \begin{pmatrix} x\\6\\x \end{pmatrix}\:and \:\begin{pmatrix} 3\\4 \\2 \end{pmatrix},$$is li...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015
calculus
vector-calculus
vector-identities
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–
0
answers
0
votes
GATE Chemical 2015 | Question: 12
For the matrix $\begin{pmatrix} 4 & 3\\ 3& 4 \end{pmatrix}$, if $\begin{pmatrix} 1\\ 1 \end{pmatrix}$ is an eigenvector, the corresponding eigenvalue is __________ .
Milicevic3306
7.9k
points
Milicevic3306
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Mar 26, 2018
Linear Algebra
gate2015
numerical-answers
linear-algebra
matrices
eigen-values
eigen-vectors
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–
0
answers
0
votes
GATE Chemical 2015 | Question: 13
Consider a linear ordinary differential equation: $\frac{dy}{dx}+p\left ( x \right )y=r\left ( x \right )$. Functions $p\left ( x \right )$ and $r\left ( x \right )$ are...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Differential equations
gate2015
differential-equations
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–
0
answers
0
votes
GATE Chemical 2015 | Question: 14
A complex-valued function, $f(z)$, given below is analytic in domain $D$:$$f\left ( z \right )=u\left ( x,y\right )+i\nu \left ( x,y\right )\:\:\:\:\:\:\:z=x+iy$$Which of...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Complex variables
gate2015
complex-variables
complex-valued-function
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–
0
answers
0
votes
GATE Chemical 2015 | Question: 15
A scalar function in the $xy$-plane is given by $\phi \left ( x,y \right )=x^{2}+y^{2}$. If $\hat{i}$ and $\hat{j}$ are unit vectors in the $x$ and $y$ directions, the d...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015
calculus
vector-calculus
unit-vectors
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–
0
answers
0
votes
GATE Chemical 2015 | Question: 37
A vector $u=-2y\hat{i}+2x\hat{j}$, where $\hat{i}$ and $\hat{j}$ are unit vectors in $x$ and $y$ directions, respectively. Evaluate the line integral$$I=\oint _{C}u.dr$$w...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015
numerical-answers
calculus
line-integral
vector-identities
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–
0
answers
0
votes
GATE Chemical 2015 | Question: 38
The solution of the non-linear equation$$x^{3}-x=0$$is to be obtained using Newton-Raphson method. If the initial guess is $x=0.5$, the method converges to which one of t...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Numerical Methods
gate2015
numerical-methods
newton-raphson-method
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–
0
answers
0
votes
GATE Chemical 2015 | Question: 39
For complex variable $z$, the value of the contour integral $\frac{1}{2\pi i} \underset{C}{\int }\frac{e^{-2z}}{z(z-3)}dz$ along the clockwise contour $C:\left | z \right...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Complex variables
gate2015
numerical-answers
complex-variables
contour-integral
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–
0
answers
0
votes
GATE Chemical 2014 | Question: 30
In rolling of two fair dice, the outcome of an experiments is considered to be the sum of the numbers appearing on the dice. The probability is highest for the outcome of...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014
numerical-answers
probability-and-statistics
probability
conditional-probability
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–
0
answers
0
votes
GATE Chemical 2014 | Question: 29
Consider the following two normal distributions$f_{1}\left ( x \right )=exp\left ( -\pi x^{2} \right )$$f_{2}\left ( x \right )=\frac{1}{2 \pi}exp\left \{ -\frac{1}{4\pi ...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014
probability-and-statistics
probability
normal-distribution
mean-and-standard-deviation
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–
0
answers
0
votes
GATE Chemical 2014 | Question: 28
The differential equation $\frac{d^{2}y}{dx^{2}}+x^{2}\frac{dy}{dx}+x^{3}y=e^{x}$ is a non-linear differential equation of first degreelinear differential equation of fir...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2014
differential-equations
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–
0
answers
0
votes
GATE Chemical 2014 | Question: 27
The integrating factor for the differential equation$\frac{dy}{dx}-\frac{y}{1+x}=\left ( 1+x \right )$ is$\frac{1}{1+x}$$(1+x)$$x(1+x)$$\frac{x}{1+x}$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2014
differential-equations
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–
0
answers
0
votes
GATE Chemical 2014 | Question: 26
Consider the following differential equation$\frac{dy}{dx}=x+In\:\left ( y \right ); y=2 \: at \: x=0$The solution of this equation at $x=0.4$ using Euler method with a s...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2014
numerical-answers
differential-equations
euler-method
+
–
0
answers
0
votes
GATE Chemical 2014 | Question: 9
Integral of the time-weighted absolute error $(ITAE)$ is expressed as$\int _{0}^{\infty }\frac{\left | \varepsilon \left ( t \right ) \right |}{t^{2}}dt$$\int _{0}^{\inft...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2014
calculus
definite-integrals
+
–
0
answers
0
votes
GATE Chemical 2014 | Question: 3
If $f*(x)$ is the complex conjugate of $f(x)=\cos(x) + i\: \sin(x)$, then for real $a$ and $b$, $\int _{a}^{b}f*\left ( x \right )f\left ( x \right )$ is $ALWAYS$positive...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2014
calculus
definite-integrals
+
–
0
answers
0
votes
GATE Chemical 2014 | Question: 2
For the time domain function $f(t)=t^{2}$, which $ONE$ of the following is the Laplace transform of $\int _{0}^{t}f\left ( t \right )dt$?$\frac{3}{s^{4}}$$\frac{1}{4s^{2}...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2014
differential-equations
laplace-transforms
+
–
0
answers
0
votes
GATE Chemical 2014 | Question: 1
Gradient of a scalar variable is alwaysa vectora scalara dot productzero
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2014
calculus
vector-calculus
gradient
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–
0
answers
0
votes
GATE Chemical 2013 | Question: 28
The solution of the differential equation$\frac{d^2y}{dx^2}$ – $\frac{dy}{dx}$ + 0.25y = 0, given y = 0 at x = 0 and $\frac{dy}{dx}$ = 1 at x = 0 isxe$^{0.5x}$ – xe$...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2013
differential-equations
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–
0
answers
0
votes
GATE Chemical 2013 | Question: 26
For the functionf(z) = $\frac{1}{(2-z)(z+2)}$the residue at z = 2 is $\_\_\_\_\_$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Complex variables
gate2013
numerical-answers
complex-variables
cauchy-residue-theorems
+
–
0
answers
0
votes
GATE Chemical 2013 | Question: 27
The solution of the differential equation$\frac{dy}{dx}$ – y$^{2}$ = 0, given y=1 at x=0 is$\frac{1}{1+x}$$\frac{1}{1-x}$$\frac{1}{(1-x)^2}$$\frac{x^3}{3}$+1
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2013
differential-equations
+
–
0
answers
0
votes
GATE Chemical 2013 | Question: 29
The value of the integral${\scriptstyle \int^{0.5} _{0.1}}$ e$^{-x^3}$dxevaluated by Simpson’s rule using 4 subintervals (up to 3 digits after the decimal point) is $\_...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Numerical Methods
gate2013
numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
0
answers
0
votes
GATE Chemical 2013 | Question: 7
An equation of state is explicit in pressure $p$ and cubic in the specific volume $v$. At the critical point $‘c’$ , the isotherm passing through $‘c’$ satisfies$...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2013
calculus
partial-derivatives
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–
0
answers
0
votes
GATE Chemical 2013 | Question: 4
Evaluate ${\displaystyle \int \frac{dx}{e^x – 1}}$(Note: C is a constant of integration)$\frac{e^x}{e^x -1}$ + C$\frac {In(e^x -1)}{e^x}$ + CIn$(\frac {e^x}{e^x -1})$ ...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2013
calculus
integrals
+
–
0
answers
0
votes
GATE Chemical 2013 | Question: 3
Which of the following statements are TRUE?P.The eigenvalues of a symmetric matrix are realQ.The value of the determinant of an orthogonal matrix can only be +1R.The tr...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2013
linear-algebra
matrices
eigen-values
+
–
0
answers
0
votes
GATE Chemical 2013 | Question: 2
For two rolls of a fair die, the probability of getting a 4 in the first roll and a number less than 4 in the second roll, up to 3 digits after the decimal point, is ____...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2013
numerical-answers
probability-and-statistics
probability
conditional-probability
+
–
0
answers
0
votes
GATE Chemical 2013 | Question: 1
The number of emails received on six consecutive days is 11, 9, 18, 18, 4 and 15,respectively.what are the median and the mode for these data?18 and 11, respectively13 an...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2013
probability-and-statistics
statistics
mean-median-mode
+
–
0
answers
0
votes
GATE Chemical 2012 | Question: 27
If $a$ is a constant, then the value of the integral $a^{2}\int^\infty_0 xe^{-ax}dx$ is$1/a$$a$$1$$0$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2012
calculus
definite-integrals
+
–
0
answers
0
votes
GATE Chemical 2012 | Question: 28
The Newton – Raphson method is used to find the roots of the equation $f(x) = x- \cos\pi x$ $0\...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Numerical Methods
gate2012
numerical-methods
newton-raphson-method
+
–
0
answers
0
votes
GATE Chemical 2012 | Question: 29
If $i = \sqrt{-1}$, the value of the integral $$\oint_{c}\dfrac{7z + i}{z(z^2 + 1)}dz \quad\quad\quad\quad|z|<2$$,u...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Complex variables
gate2012
complex-variables
cauchy-residue-theorems
+
–
0
answers
0
votes
GATE Chemical 2012 | Question: 5
Consider the following $(2\times2)$ matrix $\left( \begin{array}{c} 4 & 0 \\ 0 & 4 \end{array} \right)$Whi...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2012
linear-algebra
matrices
eigen-values
eigen-vectors
+
–
0
answers
0
votes
GATE Chemical 2012 | Question: 3
For the function $f(t) = e^{-t}/\tau$,the Taylor series approximation for $t\ll$$\tau$ is$1+\frac{t}{\tau}$$1-\frac{t}{\tau}$$1-\frac{t^2}{2\tau^2}$$1+t$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2012
calculus
taylor-series
+
–
0
answers
0
votes
GATE Chemical 2012 | Question: 2
If $a$ and $b$ are arbitrary constants, then the solutions to the ordinary differential equation $\dfrac{d^...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2012
differential-equations
+
–
0
answers
0
votes
GATE Chemical 2012 | Question: 1
Consider the following set of linear algebraic equations $x{_1} + 2x{_2} + 3x{_3} = 2$ ...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2012
linear-algebra
matrices
system-of-equations
+
–
0
answers
0
votes
GATE Chemical 2018 | Question: 47
For the matrix $A=\begin{bmatrix} \cos\theta &-\sin\theta \\ \sin \theta & \cos\theta \end{bmatrix}$ if $\det$ stands for the determinant and $A^{T}$ is the transpose of ...
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Linear Algebra
gate2018
numerical-answers
linear-algebra
matrices
determinant
+
–
0
answers
0
votes
GATE Chemical 2018 | Question: 46
If $y=e^{-x^{2}}$ then the value of $\underset{x\rightarrow \infty }{\lim}\frac{1}{x}\frac{dy}{dx}$ is __________
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Calculus
gate2018
numerical-answers
calculus
limits
+
–
0
answers
0
votes
GATE Chemical 2018 | Question: 31
The decay ratio for a system having complex conjugate poles as $\left ( -\frac{1}{10}+j\frac{2}{15} \right )$ and $\left ( -\frac{1}{10}-j\frac{2}{15} \right )$ is $7\ti...
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Complex variables
gate2018
complex-variables
complex-conjugate-poles
+
–
0
answers
0
votes
GATE Chemical 2018 | Question: 1
Consider the following two equation:$\frac{dx}{dt}+x+y=0$$\frac{dy}{dt}-x=0$The above set of equations is represented by$\frac{d^{2}y}{dt^{2}}-\frac{dy}{dt}-y=0$$\frac{d^...
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Differential equations
gate2018
differential-equations
+
–
0
answers
0
votes
GATE Chemical 2018 | Question: 4
The figure which represents for $y=\frac{sin \:x}{x}$ for $x>0$ ($x$ in radians) is
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Calculus
gate2018
calculus
functions
graphs
+
–
0
answers
0
votes
GATE Chemical 2018 | Question: 2
The fourth order Runge-Kutta ($RK4$) method to solve an ordinary differential equation $\frac{dy}{dx}=f\left ( x,y \right )$ is given as $$y\left ( x+h \right )=y\left ( ...
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Numerical Methods
gate2018
numerical-methods
runge-kutta-method
+
–
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