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Highest voted questions in Engineering Mathematics
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121
GATE2014-1-4
The sum of Eigen values of the matrix, $[M]$ is where $[M] = \begin{bmatrix} 215 & 650 & 795 \\ 655 & 150 & 835 \\ 485 & 355 & 550 \end{bmatrix}$ $915$ $1355$ $1640$ $2180$
The sum of Eigen values of the matrix, $[M]$ iswhere $[M] = \begin{bmatrix} 215 & 650 & 795 \\ 655 & 150 & 835 \\ 485 & 355 & 550 \end{bmatrix}$$915$$1355$$1640$$2180$
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2014-ce-1
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
122
GATE2014-1-5
With reference to the conventional Cartesian $(x,y)$ coordinate system, the vertices of a triangle have the following coordinates: $(x_1, y_1) = (1,0)$; $(x_2,y_2) = (2,2)$; and $(x_3,y_3)=(4,3)$. The area of the triangle is equal to $\dfrac{3}{2} \\$ $\dfrac{3}{4} \\$ $\dfrac{4}{5} \\$ $\dfrac{5}{2}$
With reference to the conventional Cartesian $(x,y)$ coordinate system, the vertices of a triangle have the following coordinates: $(x_1, y_1) = (1,0)$; $(x_2,y_2) = (2,2...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Numerical Methods
gate2014-ce-1
numerical-answers
numerical-ability
triangle
cartesian-coordinate-system
+
–
0
votes
0
answers
123
GATE Civil 2013 | Question: 51
For a portion of national highway where a descending gradient of $1$ in $25$ meets with an ascending gradient of $1$ in $20$, a valley curve needs to be designed for a vehicle travelling at $90$ kmph based on the following conditions. headlight sight ... ; and beam angle $1^{\circ}$. What is the length of valley curve (in m) based on the comfort condition? __________
For a portion of national highway where a descending gradient of $1$ in $25$ meets with an ascending gradient of $1$ in $20$, a valley curve needs to be designed for a ve...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2013-ce
numerical-answers
calculus
gradient
+
–
0
votes
0
answers
124
GATE Civil 2013 | Question: 50
For a portion of national highway where a descending gradient of $1$ in $25$ meets with an ascending gradient of $1$ in $20$, a valley curve needs to be designed for a vehicle travelling at $90$ kmph based on the following conditions. headlight ... $1^{\circ}$. What is the length of valley curve (in m) based on the head light sight distance condition? ___________
For a portion of national highway where a descending gradient of $1$ in $25$ meets with an ascending gradient of $1$ in $20$, a valley curve needs to be designed for a ve...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2013-ce
numerical-answers
calculus
gradient
+
–
0
votes
0
answers
125
GATE Civil 2013 | Question: 29
Find the value of $\lambda$ such that the function $f(x)$ is a valid probability density function _______ $f(x) = \begin{cases} \lambda (x-1)(2-x) & \text{for } 1 \leq x \leq 2 \\ 0 & \text{otherwise} \end{cases}$
Find the value of $\lambda$ such that the function $f(x)$ is a valid probability density function _______$f(x) = \begin{cases} \lambda (x-1)(2-x) & \text{for } 1 \leq x \...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2013-ce
numerical-answers
probability-and-statistics
probability
probability-density-function
+
–
0
votes
0
answers
126
GATE Civil 2013 | Question: 30
Laplace equation for water flow in soils is given below. $\dfrac{\partial ^2H}{\partial x^2} + \dfrac{\partial ^2H}{\partial y^2} + \dfrac{\partial ^2H}{\partial z^2} = 0$ Head $H$ does not vary in $y$ and $z$ directions. Boundary conditions are: at $x=0$, $H=5$; and $\dfrac{dH}{dx}=-1$. What is the value of $H$ at $x=1.2$? __________
Laplace equation for water flow in soils is given below. $$\dfrac{\partial ^2H}{\partial x^2} + \dfrac{\partial ^2H}{\partial y^2} + \dfrac{\partial ^2H}{\partial z^2} = ...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Partial Differential Equation (PDE)
gate2013-ce
numerical-answers
partial-differential-equation
laplace-equation
+
–
0
votes
0
answers
127
GATE Civil 2013 | Question: 27
Find the magnitude of the error (correct to two decimal places) in the estimation of following integral using Simpson’s $\dfrac{1}{3}$ Rule. Take the step length as $1$ _________ $\int_0^4 (x^4+10) dx$
Find the magnitude of the error (correct to two decimal places) in the estimation of following integral using Simpson’s $\dfrac{1}{3}$ Rule. Take the step length as $1$...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Numerical Methods
gate2013-ce
numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
0
votes
0
answers
128
GATE Civil 2013 | Question: 28
The solution for $\int_0^{\pi/6} \cos^4 3 \theta \sin^3 6 \theta \: d \theta$ is $0 \\$ $\dfrac{1}{15} \\$ $1 \\$ $\dfrac{8}{3}$
The solution for $\int_0^{\pi/6} \cos^4 3 \theta \sin^3 6 \theta \: d \theta$ is$0 \\$$\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
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
GATE Civil 2013 | Question: 3
A $1$-h rainfall of $10$ cm magnitude at a station has a return period of $50$ years. The probability that a $1$-h rainfall of magnitude $10$ cm or more will occur in each of two successive years is $0.04$ $0.2$ $0.02$ $0.0004$
A $1$-h rainfall of $10$ cm magnitude at a station has a return period of $50$ years. The probability that a $1$-h rainfall of magnitude $10$ cm or more will occur in eac...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2013-ce
probability-and-statistics
probability
+
–
0
votes
0
answers
131
GATE Civil 2013 | Question: 1
There is no value of $x$ that can simultaneously satisfy both the given equations. Therefore, find the ‘least squares error’ solution to the two equations, i.e., find the value of $x$ that minimizes the sum of squares of the errors in the two equations. _____ $2x=3$ $4x=1$
There is no value of $x$ that can simultaneously satisfy both the given equations. Therefore, find the ‘least squares error’ solution to the two equations, i.e., find...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Numerical Methods
gate2013-ce
numerical-answers
numerical-methods
+
–
0
votes
0
answers
132
GATE Civil 2012 | Question: 26
The error in $\dfrac{d}{dx} f(x) \mid_{x=x_0}$ for a continuous function estimated with $h=0.03$ using the central difference formula $\dfrac{d}{dx} f(x) \mid_{x=x_0} \approx \dfrac{f(x_0+h)-f(x_0-h)}{2h}$, is $2 \times 10^{-3}$. The values of $x_0$ ... $1.3 \times 10^{-4}$ $3.0 \times 10^{-4}$ $4.5 \times 10^{-4}$ $9.0 \times 10^{-4}$
The error in $\dfrac{d}{dx} f(x) \mid_{x=x_0}$ for a continuous function estimated with $h=0.03$ using the central difference formula $\dfrac{d}{dx} f(x) \mid_{x=x_0} \ap...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Numerical Methods
gate2012-ce
numerical-methods
+
–
0
votes
0
answers
133
GATE Civil 2012 | Question: 27
In an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is $\dfrac{1}{32} \\$ $\dfrac{2}{32} \\$ $\dfrac{3}{32} \\$ $\dfrac{6}{32}$
In an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is$\dfrac{1}{32} \\$$\d...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2012-ce
probability-and-statistics
probability
+
–
0
votes
0
answers
134
GATE Civil 2012 | Question: 28
The eigenvalues of matrix $\begin{bmatrix} 9 & 5 \\ 5 & 8 \end{bmatrix}$ are $-2.42$ and $6.86$ $3.48$ and $13.53$ $4.70$ and $6.86$ $6.86$ and $9.50$
The eigenvalues of matrix $\begin{bmatrix} 9 & 5 \\ 5 & 8 \end{bmatrix}$ are$-2.42$ and $6.86$$3.48$ and $13.53$$4.70$ and $6.86$$6.86$ and $9.50$
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2012-ce
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
135
GATE Civil 2012 | Question: 29
For the parallelogram OPQR shown in the sketch, $\overrightarrow{OP}=a \hat{i}+b \hat{j}$ and $\overrightarrow{OR}=c \hat{i} +d \hat{j}$. The area of the parallelogram is $ad-bc$ $ac+bd$ $ad+bc$ $ab-cd$
For the parallelogram OPQR shown in the sketch, $\overrightarrow{OP}=a \hat{i}+b \hat{j}$ and $\overrightarrow{OR}=c \hat{i} +d \hat{j}$. The area of the parallelogram is...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2012-ce
calculus
vector-identities
+
–
0
votes
0
answers
136
GATE Civil 2012 | Question: 30
The solution of the ordinary differential equation $\dfrac{dy}{dx}+2y=0$ for the boundary condition, $y=5$ at $x=1$ is $y=e^{-2x}$ $y=2e^{-2x}$ $y=10.95 e^{-2x}$ $y=36.95 e^{-2x}$
The solution of the ordinary differential equation $\dfrac{dy}{dx}+2y=0$ for the boundary condition, $y=5$ at $x=1$ is$y=e^{-2x}$$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
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
138
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$$1+\sin^2x$
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2012-ce
calculus
taylor-series
+
–
0
votes
0
answers
139
GATE Civil 2012 | Question: 1
The estimate of $\int_{0.5}^{1.5} \dfrac{dx}{x}$ obtained using Simpson’s rule with three-point function evaluation exceeds the exact value by $0.235$ $0.068$ $0.024$ $0.012$
The estimate of $$\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
140
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
141
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
142
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
1
answer
143
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
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
0
answers
145
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
146
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}$$x^{-2}$
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Ordinary Differential Equation (ODE)
gate2018-ce-2
ordinary-differential-equation
+
–
0
votes
0
answers
147
GATE2018 CE-2: 2
The graph of a function $f(x)$ is shown in the figure. For $f(x)$ to be a valid probability density function, the value of $h$ is $1/3$ $2/3$ $1$ $3$
The graph of a function $f(x)$ is shown in the figure.For $f(x)$ to be a valid probability density function, the value of $h$ is$1/3$$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
148
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
1
answer
149
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
150
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
0
answers
151
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$$\pi^2$
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Calculus
gate2018-ce-1
calculus
definite-integral
+
–
0
votes
1
answer
152
GATE2018 CE-1: 1
Which one of the following matrices is singular? $\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix} \\$ $\begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix} \\$ $\begin{bmatrix} 2 & 4\\ 3 & 6 \end{bmatrix} \\$ $\begin{bmatrix} 4 & 3\\ 6 & 2 \end{bmatrix}$
Which one of the following matrices is singular?$\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix} \\$$\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
0
answers
153
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
154
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
+
–
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