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Hot questions in Engineering Mathematics
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0
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121
GATE2015-2-4
$\underset{x \to \infty}{\lim} \bigg( 1+ \dfrac{1}{x} \bigg)^{2x} $ is equal to $e^{-2}$ $e$ $1$ $e^2$
$\underset{x \to \infty}{\lim} \bigg( 1+ \dfrac{1}{x} \bigg)^{2x} $ is equal to$e^{-2}$$e$$1$$e^2$
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015-ce-2
calculus
limits
+
–
0
votes
0
answers
122
GATE2015-1-2
The integral $\int_{x_{1}}^{x_{2}}x^{2}\:dx$ with $x_{2}>x_{1}>0$ is evaluated analytically as well as numerically using a single application of the trapezoidal rule. If $I$ is the exact value of the integral obtained analytically and ... , which of the following statement is correct about their relationship? $J>I$ $J<I$ $J=I$ Insufficient data to determine the relationship
The integral $\int_{x_{1}}^{x_{2}}x^{2}\:dx$ with $x_{2}>x_{1}>0$ is evaluated analytically as well as numerically using a single application of the trapezoidal rule. If ...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 26, 2018
Numerical Methods
gate2015-ce-1
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
0
votes
0
answers
123
GATE2015-1-28
Consider the following differential equation: $x(y\:dx +x\:dy) \cos \dfrac{y}{x}=y(x\:dy-y\:dx) \sin \dfrac{y}{x}$ Which of the following is the solution of the above equation ($c$ is an arbitrary constant)? $\dfrac{x}{y} \cos \dfrac{y}{x} = c \\$ $\dfrac{x}{y} \sin \dfrac{y}{x} = c \\$ $xy \cos \dfrac{y}{x} = c \\$ $xy \sin \dfrac{y}{x} = c$
Consider the following differential equation:$$x(y\:dx +x\:dy) \cos \dfrac{y}{x}=y(x\:dy-y\:dx) \sin \dfrac{y}{x}$$Which of the following is the solution of the above equ...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 26, 2018
Ordinary Differential Equation (ODE)
gate2015-ce-1
ordinary-differential-equation
+
–
0
votes
0
answers
124
GATE Civil 2012 | Question: 1
The estimate of $\int_{0.5}^{1.5} \dfrac{dx}{x}$ obtained using Simpson’s rule with three-point function evaluation exceeds the exact value by $0.235$ $0.068$ $0.024$ $0.012$
The estimate of $$\int_{0.5}^{1.5} \dfrac{dx}{x}$$ obtained using Simpson’s rule with three-point function evaluation exceeds the exact value by$0.235$$0.068$$0.024$$0....
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Numerical Methods
gate2012-ce
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
0
votes
0
answers
125
GATE2015-2-1
While minimizing the function $f(x)$, necessary and sufficient conditions for a point, $x_0$ to be a minima are: $f’(x_0) > 0$ and $f’’(x_0)=0$ $f’(x_0) < 0$ and $f’’(x_0)=0$ $f’(x_0) = 0$ and $f’’(x_0)<0$ $f’(x_0) = 0$ and $f’’(x_0)>0$
While minimizing the function $f(x)$, necessary and sufficient conditions for a point, $x_0$ to be a minima are:$f’(x_0) 0$ and $f’’(x_0)=0$$f’(x_0) < 0$ and $f�...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015-ce-2
calculus
maxima-minima
+
–
0
votes
0
answers
126
GATE2015-1-27
The quadratic equation $x^2 – 4x +4 =0$ is to be solved numerically, starting with the initial guess $x_0=3$. The Newton-Raphson method is applied once to get a new estimate and then the Secant method is applied once using the initial guess and this new estimate. The estimated value of the root after the application of the Secant method is _________.
The quadratic equation $x^2 – 4x +4 =0$ is to be solved numerically, starting with the initial guess $x_0=3$. The Newton-Raphson method is applied once to get a new est...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 26, 2018
Numerical Methods
gate2015-ce-1
numerical-answers
numerical-methods
newton-raphson-method
+
–
0
votes
0
answers
127
GATE2015-1-1
For what value of $p$ the following set of equations will have no solution? $2x+3y=5$ $3x+py=10$
For what value of $p$ the following set of equations will have no solution?$2x+3y=5$$3x+py=10$
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 26, 2018
Linear Algebra
gate2015-ce-1
numerical-answers
linear-algebra
system-of-equations
+
–
0
votes
0
answers
128
GATE2014-2-1
A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes: (i) Head, (ii) Head, (iii) Head, (iv) Head. The probability of obtaining a ‘Tail’ when the coin is tossed again is $0$ $\dfrac{1}{2} \\$ $\dfrac{4}{5} \\$ $\dfrac{1}{5}$
A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes: (i) Head, (ii) Head, (iii) Head, (iv) Head. The probability of obtainin...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014-ce-2
probability-and-statistics
probability
conditional-probability
+
–
0
votes
0
answers
129
GATE Civil 2013 | Question: 2
What is the minimum number of multiplications involved in computing the matrix product $PQR?$ Matrix P has $4$ rows an $2$ columns, matrix $Q$ has $2$ rows and $4$ columns, and matrix R has $4$ rows and $1$ column. __________
What is the minimum number of multiplications involved in computing the matrix product $PQR?$ Matrix P has $4$ rows an $2$ columns, matrix $Q$ has $2$ rows and $4$ column...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2013-ce
numerical-answers
linear-algebra
matrices
+
–
0
votes
0
answers
130
GATE2014-2-4
The integrating factor for the differential equation $\dfrac{dP}{dt}+k_2P=k_1L_0e^{-k_1t}$ is $e^{-k_1t} \\$ $e^{-k_2t} \\$ $e^{k_1t} \\$ $e^{k_2t}$
The integrating factor for the differential equation $\dfrac{dP}{dt}+k_2P=k_1L_0e^{-k_1t}$ is$e^{-k_1t} \\$$e^{-k_2t} \\$$e^{k_1t} \\$$e^{k_2t}$
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Ordinary Differential Equation (ODE)
gate2014-ce-2
ordinary-differential-equation
+
–
0
votes
0
answers
131
GATE Civil 2013 | Question: 28
The solution for $\int_0^{\pi/6} \cos^4 3 \theta \sin^3 6 \theta \: d \theta$ is $0 \\$ $\dfrac{1}{15} \\$ $1 \\$ $\dfrac{8}{3}$
The solution for $\int_0^{\pi/6} \cos^4 3 \theta \sin^3 6 \theta \: d \theta$ is$0 \\$$\dfrac{1}{15} \\$$1 \\$$\dfrac{8}{3}$
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2013-ce
calculus
definite-integral
+
–
0
votes
0
answers
132
GATE2014-2-28
The rank of the matrix $\begin{bmatrix} 6 & 0 & 4 & 4 \\ -2 & 14 & 8 & 18 \\ 14 & -14 & 0 & -10 \end{bmatrix}$ is _________
The rank of the matrix $\begin{bmatrix} 6 & 0 & 4 & 4 \\ -2 & 14 & 8 & 18 \\ 14 & -14 & 0 & -10 \end{bmatrix}$ is _________
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2014-ce-2
numerical-answers
linear-algebra
matrices
rank-of-matrix
+
–
0
votes
0
answers
133
GATE2014-1-2
Given the matrices $J=\begin{bmatrix} 3 & 2 & 1 \\ 2 & 4 & 2 \\ 1 & 2 & 6 \end{bmatrix}$ and $K = \begin{bmatrix} 1 \\ 2 \\ -1 \end{bmatrix}$, the product of $K^TJK$ is _______
Given the matrices $J=\begin{bmatrix} 3 & 2 & 1 \\ 2 & 4 & 2 \\ 1 & 2 & 6 \end{bmatrix}$ and $K = \begin{bmatrix} 1 \\ 2 \\ -1 \end{bmatrix}$, the product of $K^TJK$ is _...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2014-ce-1
numerical-answers
linear-algebra
matrices
+
–
0
votes
0
answers
134
GATE2014-2-3
$z=\dfrac{2-3i}{-5+i}$ can be expressed as $-0.5-0.5i$ $-0.5+0.5i$ $0.5-0.5i$ $0.5+0.5i$
$z=\dfrac{2-3i}{-5+i}$ can be expressed as$-0.5-0.5i$$-0.5+0.5i$$0.5-0.5i$$0.5+0.5i$
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2014-ce-2
calculus
complex-number
+
–
0
votes
0
answers
135
GATE2014-2-26
The expression $\displaystyle{} \lim_{a \to 0} \dfrac{x^a-1}{a}$ is equal to $\log x$ $0$ $x \log x$ $\infty$
The expression $\displaystyle{} \lim_{a \to 0} \dfrac{x^a-1}{a}$ is equal to$\log x$$0$$x \log x$$\infty$
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2014-ce-2
calculus
limits
+
–
0
votes
0
answers
136
GATE Civil 2012 | Question: 30
The solution of the ordinary differential equation $\dfrac{dy}{dx}+2y=0$ for the boundary condition, $y=5$ at $x=1$ is $y=e^{-2x}$ $y=2e^{-2x}$ $y=10.95 e^{-2x}$ $y=36.95 e^{-2x}$
The solution of the ordinary differential equation $\dfrac{dy}{dx}+2y=0$ for the boundary condition, $y=5$ at $x=1$ is$y=e^{-2x}$$y=2e^{-2x}$$y=10.95 e^{-2x}$$y=36.95 e^{...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Ordinary Differential Equation (ODE)
gate2012-ce
ordinary-differential-equation
+
–
0
votes
0
answers
137
GATE2014-1-1
$\underset{x \to \infty}{\lim} \bigg( \dfrac{x+\sin x}{x} \bigg)$ equals to $- \infty$ $0$ $1$ $\infty$
$\underset{x \to \infty}{\lim} \bigg( \dfrac{x+\sin x}{x} \bigg)$ equals to$- \infty$$0$$1$$\infty$
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2014-ce-1
calculus
limits
+
–
0
votes
0
answers
138
GATE Civil 2012 | Question: 2
The annual precipitation data of a city is normally distributed with mean and standard deviation as $1000$ mm and $200$ mm, respectively. The probability that the annual precipitation will be more than $1200$ mm is $<50 \%$ $50 \%$ $75 \%$ $100\%$
The annual precipitation data of a city is normally distributed with mean and standard deviation as $1000$ mm and $200$ mm, respectively. The probability that the annual ...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2012-ce
probability-and-statistics
probability
normal-distribution
+
–
0
votes
0
answers
139
GATE Civil 2012 | Question: 3
The infinite series $1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\dfrac{x^4}{4!} + \dots $ corresponds to $\sec x$ $e^x$ $\cos x$ $1+\sin^2x$
The infinite series $1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\dfrac{x^4}{4!} + \dots $ corresponds to$\sec x$$e^x$$\cos x$$1+\sin^2x$
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2012-ce
calculus
taylor-series
+
–
0
votes
0
answers
140
GATE2018 CE-1: 2
For the given orthogonal matrix Q, $Q = \begin{bmatrix} 3/7 & 2/7 & 6/7 \\ -6/7 & 3/7 & 2/7 \\ 2/7 & 6/7 & -3/7 \end{bmatrix}$ ... $\begin{bmatrix} -3/7 & 6/7 & -2/7 \\ -2/7 & -3/7 & -6/7 \\ -6/7 & -2/7 & 3/7 \end{bmatrix}$
For the given orthogonal matrix Q, $Q = \begin{bmatrix} 3/7 & 2/7 & 6/7 \\ -6/7 & 3/7 & 2/7 \\ 2/7 & 6/7 & -3/7 \end{bmatrix}$ The inverse is$\begin{bmatrix} 3/7 & 2/7 &...
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Linear Algebra
gate2018-ce-1
linear-algebra
matrices
orthogonal-matrix
inverse-of-matrix
+
–
0
votes
0
answers
141
GATE2018 CE-1: 3
At the point $x= 0$, the function $f(x) = x^3$ has local maximum local minimum both local maximum and minimum neither local maximum nor local minimum
At the point $x= 0$, the function $f(x) = x^3$ haslocal maximumlocal minimumboth local maximum and minimumneither local maximum nor local minimum
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Calculus
gate2018-ce-1
calculus
maxima-minima
+
–
0
votes
1
answer
142
GATE2018 CE-1: 1
Which one of the following matrices is singular? $\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix} \\$ $\begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix} \\$ $\begin{bmatrix} 2 & 4\\ 3 & 6 \end{bmatrix} \\$ $\begin{bmatrix} 4 & 3\\ 6 & 2 \end{bmatrix}$
Which one of the following matrices is singular?$\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix} \\$$\begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix} \\$$\begin{bmatrix} 2 & 4\\...
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Linear Algebra
gate2018-ce-1
linear-algebra
matrices
determinant
+
–
0
votes
1
answer
143
GATE2018 CE-1: 37
The solution at $x=1$, $t=1$ of the partial differential equation $\dfrac{\partial ^2 u}{\partial x^2} = 25 \dfrac{\partial ^2 u}{\partial t^2}$ subject to initial conditions of $u(0) = 3x$ and $\dfrac{\partial u}{\partial t}(0) =3$ is _______ $1$ $2$ $4$ $6$
The solution at $x=1$, $t=1$ of the partial differential equation $\dfrac{\partial ^2 u}{\partial x^2} = 25 \dfrac{\partial ^2 u}{\partial t^2}$ subject to initial condit...
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Partial Differential Equation (PDE)
gate2018-ce-1
partial-differential-equation
+
–
0
votes
1
answer
144
GATE2018 CE-2: 26
The matrix $\begin{pmatrix} 2 & -4 \\ 4 & -2 \end{pmatrix}$ has real eigenvalues and eigenvectors real eigenvalues but complex eigenvectors complex eigenvalues but real eigenvectors complex eigenvalues and eigenvectors
The matrix $\begin{pmatrix} 2 & -4 \\ 4 & -2 \end{pmatrix}$ hasreal eigenvalues and eigenvectorsreal eigenvalues but complex eigenvectorscomplex eigenvalues but real eige...
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Linear Algebra
gate2018-ce-2
linear-algebra
matrices
eigen-values
eigen-vectors
+
–
0
votes
1
answer
145
GATE2018 CE-1: 38
The solution (up to three decimal places) at $x=1$ of the differential equation $\dfrac{d^2y}{dx^2} + 2 \dfrac{dy}{dx} + y =0$ subject to boundary conditions $y(0) = 1$ and $\dfrac{dy}{dx}(0) = -1$ is _____
The solution (up to three decimal places) at $x=1$ of the differential equation $\dfrac{d^2y}{dx^2} + 2 \dfrac{dy}{dx} + y =0$ subject to boundary conditions $y(0) = 1$ a...
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Ordinary Differential Equation (ODE)
gate2018-ce-1
ordinary-differential-equation
numerical-answers
+
–
0
votes
1
answer
146
GATE2018 CE-2: 20
The quadratic equation $2x^2 - 3x +3=0$ is to be solved numerically starting with an initial guess as $x_0=2$. The new estimate of $x$ after the first iteration using Newton-Raphson method is _________
The quadratic equation $2x^2 - 3x +3=0$ is to be solved numerically starting with an initial guess as $x_0=2$. The new estimate of $x$ after the first iteration using New...
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Numerical Methods
gate2018-ce-2
numerical-methods
newton-raphson-method
numerical-answers
+
–
0
votes
0
answers
147
GATE2018 CE-2: 3
A probability distribution with right skew is shown in the figure. The correct statement for the probability distribution is Mean is equal to mode Mean is greater than median but less than mode Mean is greater than median and mode Mode is greater than median
A probability distribution with right skew is shown in the figure.The correct statement for the probability distribution isMean is equal to modeMean is greater than media...
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Probability and Statistics
gate2018-ce-2
probability-and-statistics
statistics
probability-distribution
mean-median-mode
+
–
0
votes
0
answers
148
GATE2018 CE-2: 19
Probability (up to one decimal place) of consecutively picking $3$ red balls without replacement from a box containing $5$ red balls and $1$ white ball is ___________
Probability (up to one decimal place) of consecutively picking $3$ red balls without replacement from a box containing $5$ red balls and $1$ white ball is ___________
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Probability and Statistics
gate2018-ce-2
probability-and-statistics
probability
conditional-probability
numerical-answers
+
–
0
votes
0
answers
149
GATE2018 CE-2: 2
The graph of a function $f(x)$ is shown in the figure. For $f(x)$ to be a valid probability density function, the value of $h$ is $1/3$ $2/3$ $1$ $3$
The graph of a function $f(x)$ is shown in the figure.For $f(x)$ to be a valid probability density function, the value of $h$ is$1/3$$2/3$$1$$3$
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Probability and Statistics
gate2018-ce-2
probability-and-statistics
probability
probability-density-function
+
–
0
votes
0
answers
150
GATE2018 CE-2: 37
The value (up to two decimal places) of a line integral $\int_C \overrightarrow{F}(\overrightarrow{r}) . d\overrightarrow{r}$, for $ \overrightarrow{F}(\overrightarrow{r}) = x^2 \hat{i} + y^2 \hat{j} $ along $C$ which is a straight line joining $(0, 0)$ to $(1, 1)$ is _________
The value (up to two decimal places) of a line integral $\int_C \overrightarrow{F}(\overrightarrow{r}) . d\overrightarrow{r}$, for $ \overrightarrow{F}(\overrightarrow{r...
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Calculus
gate2018-ce-2
numerical-answers
calculus
vector-calculus
line-integral
+
–
0
votes
0
answers
151
GATE2018 CE-2: 28
The rank of the following matrix is $\\ \begin{pmatrix} 1 & 1 & 0 & -2 \\ 2 & 0 & 2 & 2 \\ 4 & 1 & 3 & 1 \end{pmatrix}$ $1$ $2$ $3$ $4$
The rank of the following matrix is $\\ \begin{pmatrix} 1 & 1 & 0 & -2 \\ 2 & 0 & 2 & 2 \\ 4 & 1 & 3 & 1 \end{pmatrix}$$1$$2$$3$$4$
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Linear Algebra
gate2018-ce-2
linear-algebra
matrices
rank-of-matrix
+
–
0
votes
0
answers
152
GATE2018 CE-2: 27
The Laplace transform $F(s)$ of the exponential function, $f(t) = e^{at}$ when $t \geq 0$, where $a$ is a constant and $(s-a) >0$, is $\dfrac{1}{s+a} \\$ $\dfrac{1}{s-a} \\$ $\dfrac{1}{a-s} \\$ $\infty$
The Laplace transform $F(s)$ of the exponential function, $f(t) = e^{at}$ when $t \geq 0$, where $a$ is a constant and $(s-a) >0$, is$\dfrac{1}{s+a} \\$$\dfrac{1}{s-a} \\...
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Ordinary Differential Equation (ODE)
gate2018-ce-2
ordinary-differential-equation
laplace-transform
+
–
0
votes
0
answers
153
GATE2018 CE-1: 26
The value of the integral $\int_0^{\pi} x \cos^2 x \: dx$ is $\pi^2/8$ $\pi^2/4$ $\pi^2/2$ $\pi^2$
The value of the integral $\int_0^{\pi} x \cos^2 x \: dx$ is$\pi^2/8$$\pi^2/4$$\pi^2/2$$\pi^2$
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Calculus
gate2018-ce-1
calculus
definite-integral
+
–
0
votes
0
answers
154
GATE2018 CE-2: 1
The solution of the equation $x \frac{dy}{dx} +y = 0$ passing through the point $(1,1)$ is $x$ $x^2$ $x^{-1}$ $x^{-2}$
The solution of the equation $x \frac{dy}{dx} +y = 0$ passing through the point $(1,1)$ is$x$$x^2$$x^{-1}$$x^{-2}$
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Ordinary Differential Equation (ODE)
gate2018-ce-2
ordinary-differential-equation
+
–
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