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Hot questions in Engineering Mathematics
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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 __________.
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},...
go_editor
5.0k
points
go_editor
asked
Feb 19, 2020
Engineering Mathematics
gateme-2020-set1
numerical-answers
engineering-mathematics
+
–
0
answers
0
votes
GATE2020-ME-1: 35
Consider two exponentially distributed random variables $\text{X and Y}$, both having a mean of $0.50$. Let $Z=X+Y$ and $r$ be the correlation between $\text{X and Y}$.If the variance of $Z$ equals $0$, then the value of $r$ is __________ (roundoff to $2$ decimal places).
Consider two exponentially distributed random variables $\text{X and Y}$, both having a mean of $0.50$. Let $Z=X+Y$ and $r$ be the correlation between $\text{X and Y}$.If...
go_editor
5.0k
points
go_editor
asked
Feb 19, 2020
Engineering Mathematics
gateme-2020-set1
numerical-answers
engineering-mathematics
differential-equation
random-variables
+
–
1
answers
0
votes
GATE2019 ME-2: 1
In matrix equation $[A] \{X\}=\{R\}$, $[A] = \begin{bmatrix} 4 & 8 & 4 \\ 8 & 16 & -4 \\ 4 & -4 & 15 \end{bmatrix} \{X\} = \begin{Bmatrix} 2 \\ 1 \\ 4 \end{Bmatrix} \text{ and} \{ R \} = \begin{Bmatrix} 32 \\ 16 \\ 64 \end{Bmatrix}$ One of the eigen values of matrix $[A]$ is $4$ $8$ $15$ $16$
In matrix equation $[A] \{X\}=\{R\}$,$[A] = \begin{bmatrix} 4 & 8 & 4 \\ 8 & 16 & -4 \\ 4 & -4 & 15 \end{bmatrix} \{X\} = \begin{Bmatrix} 2 \\ 1 \\ 4 \end{Bmatrix} \text{...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Linear Algebra
gateme-2019-set2
linear-algebra
matrices
eigen-values
+
–
1
answers
0
votes
GATE2019 ME-2: 4
An analytic function $f(z)$ of complex variable $z=x+iy$ may be written as $f(z)=u(x,y)+iv(x,y)$. Then $u(x,y)$ and $v(x,y)$ ...
An analytic function $f(z)$ of complex variable $z=x+iy$ may be written as $f(z)=u(x,y)+iv(x,y)$. Then $u(x,y)$ and $v(x,y)$ must satisfy$\dfrac{\partial u}{ \partial x} ...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Calculus
gateme-2019-set2
calculus
partial-derivatives
complex-variables
analytic-functions
+
–
1
answers
0
votes
GATE2019 ME-2: 3
The differential equation $\dfrac{dy}{dx}+4y=5$ is valid in the domain $0 \leq x \leq 1$ with $y(0)=2.25$. The solution of the differential equation is $y=e^{-4x}+5$ $y=e^{-4x}+1.25$ $y=e^{4x}+5$ $y=e^{4x}+1.25$
The differential equation $\dfrac{dy}{dx}+4y=5$ is valid in the domain $0 \leq x \leq 1$ with $y(0)=2.25$. The solution of the differential equation is$y=e^{-4x}+5$$y=e^{...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Differential Equations
gateme-2019-set2
differential-equations
+
–
1
answers
0
votes
GATE2019 ME-1: 51
The value of the following definite integral is __________ (round off to three decimal places) $\int_1^e (x \: \ln \: x) dx$
The value of the following definite integral is __________ (round off to three decimal places)$$\int_1^e (x \: \ln \: x) dx$$
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Calculus
gateme-2019-set1
numerical-answers
calculus
definite-integrals
+
–
1
answers
0
votes
GATE2019 ME-1: 3
For the equation $\dfrac{dy}{dx}+7x^2y=0$, if $y(0)=3/7$, then the value of $y(1)$ is $\dfrac{7}{3}e^{-7/3} \\$ $\dfrac{7}{3}e^{-3/7} \\$ $\dfrac{3}{7}e^{-7/3} \\$ $\dfrac{3}{7}e^{-3/7}$
For the equation $\dfrac{dy}{dx}+7x^2y=0$, if $y(0)=3/7$, then the value of $y(1)$ is$\dfrac{7}{3}e^{-7/3} \\$$\dfrac{7}{3}e^{-3/7} \\$$\dfrac{3}{7}e^{-7/3} \\$$\dfrac{3}...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Differential Equations
gateme-2019-set1
differential-equations
+
–
1
answers
0
votes
GATE2019 ME-2: 19
If $x$ is the mean of data $3, x, 2$ and $4$, then the mode is _____
If $x$ is the mean of data $3, x, 2$ and $4$, then the mode is _____
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Probability and Statistics
gateme-2019-set2
numerical-answers
probability-and-statistics
statistics
+
–
1
answers
1
votes
GATE2019 ME-1: 1
Consider the matrix $P=\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$ The number of distinct eigenvalues $0$ $1$ $2$ $3$
Consider the matrix$$P=\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$$The number of distinct eigenvalues$0$$1$$2$$3$
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Linear Algebra
gateme-2019-set1
linear-algebra
matrices
eigen-values
+
–
0
answers
0
votes
GATE2019 ME-1: 28
The variable $x$ takes a value between $0$ and $10$ with uniform probability distribution. The variable $y$ takes a value between $0$ and $20$ with uniform probability distribution. The probability of the sum of variables $(x+y)$ being greater then $20$ is $0$ $0.25$ $0.33$ $0.50$
The variable $x$ takes a value between $0$ and $10$ with uniform probability distribution. The variable $y$ takes a value between $0$ and $20$ with uniform probability di...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Probability and Statistics
gateme-2019-set1
probability-and-statistics
probability
uniform-distribution
+
–
0
answers
0
votes
GATE2019 ME-2: 18
The transformation matrix for mirroring a point in $x – y$ plane about the line $y=x$ is given by $\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \\$ $\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix} \\$ $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \\$ $\begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix}$
The transformation matrix for mirroring a point in $x – y$ plane about the line $y=x$ is given by$\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \\$$\begin{bmatrix} -1 &...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Linear Algebra
gateme-2019-set2
linear-algebra
matrix-algebra
+
–
0
answers
0
votes
GATE2019 ME-2: 40
The probability that a part manufactured by a company will be defective is $0.05$. If $15$ such parts are selected randomly and inspected, then the probability that at least two parts will be defective is _____ (round off to two decimal places).
The probability that a part manufactured by a company will be defective is $0.05$. If $15$ such parts are selected randomly and inspected, then the probability that at le...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Probability and Statistics
gateme-2019-set2
numerical-answers
probability-and-statistics
probability
+
–
0
answers
0
votes
GATE2019 ME-2: 28
The derivative of $f(x)= \cos x$ can be estimated using the approximation $f'(x)=\dfrac{f(x+h)-f(x-h)}{2h}$. The percentage error is calculated as $\bigg( \dfrac{\text{Exact value - Approximate value}}{\text{Exact value}} \bigg) \times 100$. The percentage error in the derivative of $f(x)$ ... $> 0.1 \% \text{ and } <1 \%$ $> 1 \% \text{ and } <5 \%$ $>5 \%$
The derivative of $f(x)= \cos x$ can be estimated using the approximation $f’(x)=\dfrac{f(x+h)-f(x-h)}{2h}$. The percentage error is calculated as $\bigg( \dfrac{\text{...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Calculus
gateme-2019-set2
calculus
derivatives
+
–
0
answers
0
votes
GATE2019 ME-2: 2
The directional derivative of the function $f(x,y)=x^2+y^2$ along a line directed from $(0,0)$ to $(1,1)$, evaluated at the point $x=1, y=1$ is $\sqrt{2}$ $2$ $2 \sqrt{2}$ $4 \sqrt{2}$
The directional derivative of the function $f(x,y)=x^2+y^2$ along a line directed from $(0,0)$ to $(1,1)$, evaluated at the point $x=1, y=1$ is$\sqrt{2}$$2$$2 \sqrt{2}$$4...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Calculus
gateme-2019-set2
calculus
directional-derivatives
+
–
0
answers
0
votes
GATE2019 ME-2: 27
A diffferential equation is given as $x^2 \frac{d^2y}{dx^2} – 2x \frac{dy}{dx} +2y =4$ The solution of the differential equation in terms of arbitrary constants $C_1$ and $C_2$ is $y=C_1x^2 +C_2 x+2 \\$ $y=\dfrac{C_1}{x^2} +C_2x+2 \\$ $y=C_1x^2+C_2x+4 \\$ $y=\dfrac{C_1}{x^2}+C_2x+4$
A diffferential equation is given as $$x^2 \frac{d^2y}{dx^2} – 2x \frac{dy}{dx} +2y =4$$ The solution of the differential equation in terms of arbitrary constants $C_1$...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Engineering Mathematics
gateme-2019-set2
engineering-mathematics
differential-equation
+
–
0
answers
0
votes
GATE2019 ME-1: 2
A parabola $x=y^2$ with $0 \leq x \leq 1$ is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by $360^{\circ}$ around x-axis is $\dfrac{\pi}{4} \\$ $\dfrac{\pi}{2} \\$ ${\pi} \\$ $2 \pi$
A parabola $x=y^2$ with $0 \leq x \leq 1$ is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by $360^{\circ}$ around x-axis ...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Calculus
gateme-2019-set1
calculus
area-under-curve
+
–
0
answers
0
votes
GATE2019 ME-1: 26
The set of equations $\begin{array}{l} x+y+z=1 \\ ax-ay+3z=5 \\ 5x-3y+az=6 \end{array}$ has infinite solutions, if $a=$ $-3$ $3$ $4$ $-4$
The set of equations $$\begin{array}{l} x+y+z=1 \\ ax-ay+3z=5 \\ 5x-3y+az=6 \end{array}$$has infinite solutions, if $a=$$-3$$3$$4$$-4$
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Linear Algebra
gateme-2019-set1
linear-algebra
system-of-equations
+
–
0
answers
0
votes
GATE2019 ME-2: 26
Given a vector $\overrightarrow{u} = \dfrac{1}{3} \big(-y^3 \hat{i} + x^3 \hat{j} + z^3 \hat{k} \big)$ and $\hat{n}$ as the unit normal vector to the surface of the hemipshere $(x^2+y^2+z^2=1; \: z \geq 0)$ ... $S$ is $- \dfrac{\pi}{2} \\$ $\dfrac{\pi}{3} \\$ $\dfrac{\pi}{2} \\$ $\pi$
Given a vector $\overrightarrow{u} = \dfrac{1}{3} \big(-y^3 \hat{i} + x^3 \hat{j} + z^3 \hat{k} \big)$ and $\hat{n}$ as the unit normal vector to the surface of the hemi...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Calculus
gateme-2019-set2
calculus
vector-identities
+
–
0
answers
0
votes
GATE2019 ME-1: 27
A harmonic function is analytic if it satisfies the Laplace equation. If $u(x,y)=2x^2-2y^2+4xy$ is a harmonic function, then its conjugate harmonic function $v(x,y)$ is $4xy-2x^2+2y^2+ \text{constant}$ $4y^2-4xy + \text{constant}$ $2x^2-2y^2+ xy + \text{constant}$ $-4xy+2y^2-2x^2+ \text{constant}$
A harmonic function is analytic if it satisfies the Laplace equation. If $u(x,y)=2x^2-2y^2+4xy$ is a harmonic function, then its conjugate harmonic function $v(x,y)$ is$4...
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Differential Equations
gateme-2019-set1
differential-equations
laplace-transforms
+
–
0
answers
0
votes
GATE2019 ME-1: 18
Evaluation of $\int_2^4 x^3 dx$ using a $2$-equal-segment trapezoidal rule gives a value of _______
Evaluation of $\int_2^4 x^3 dx$ using a $2$-equal-segment trapezoidal rule gives a value of _______
Arjun
28.5k
points
Arjun
asked
Feb 9, 2019
Numerical Methods
gateme-2019-set1
numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
1
answers
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$
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 &...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Probability and Statistics
gateme-2014-set1
probability-and-statistics
probability
random-variables
mode-and-standard-deviation
+
–
1
answers
0
votes
GATE2017 ME-2: 28
Consider the matrix $A=\begin{bmatrix} 50 &70 \\ 70 & 80 \end{bmatrix}$ whose eigenvectors corresponding to eigenvalues $\lambda _{1}$ and $\lambda _{2}$ are $x_{1}=\begin{bmatrix} 70 \\ \lambda_{1}-50 \end{bmatrix}$ and $x_{2}=\begin{bmatrix} \lambda _{2}-80\\ 70 \end{bmatrix}$, respectively. The value of $x^{T}_{1} x_{2}$ is _________.
Consider the matrix $A=\begin{bmatrix}50 &70 \\70 & 80\end{bmatrix}$ whose eigenvectors corresponding to eigenvalues $\lambda _{1}$ and $\lambda _{2}$ are $x_{1}=\begin{b...
Arjun
28.5k
points
Arjun
asked
Feb 26, 2017
Linear Algebra
gateme-2017-set2
numerical-answers
linear-algebra
eigen-values
eigen-vectors
+
–
1
answers
0
votes
GATE2017 ME-2: 29
If $f(z)=(x^{2}+ay^{2})+i bxy$ is a complex analytic function of $z=x+iy$, where $i=\sqrt{-1}$, then $a=-1, b=-1$ $a=-1, b=2$ $a=1, b= 2$ $a=2, b=2$
If $f(z)=(x^{2}+ay^{2})+i bxy$ is a complex analytic function of $z=x+iy$, where $i=\sqrt{-1}$, then$a=-1, b=-1$$a=-1, b=2$$a=1, b= 2$$a=2, b=2$
Arjun
28.5k
points
Arjun
asked
Feb 26, 2017
Calculus
gateme-2017-set2
calculus
complex-variables
+
–
0
answers
1
votes
GATE ME 2012 | Question: 54
For a particular project, eight activities are to be carried out. Their relationships with other activities and expected durations are mentioned in the table below. ... critical path for the project is $a-b-e-g-h$ $a-c-g-h$ $a-d-f-h$ $a-b-c-f-h$
For a particular project, eight activities are to be carried out. Their relationships with other activities and expected durations are mentioned in the table below.$\begi...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
+
–
0
answers
0
votes
GATE ME 2012 | Question: 55
For a particular project, eight activities are to be carried out. Their relationships with other activities and expected durations are mentioned in the table below. ... the project remain the same critical path changes but the total duration to complete the project changes to $17$ days
For a particular project, eight activities are to be carried out. Their relationships with other activities and expected durations are mentioned in the table below.$\begi...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
+
–
0
answers
0
votes
GATE ME 2012 | Question: 46
Consider the differential equation $x^2 \dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}-4y=0$ with the boundary conditions of $y(0)=0$ and $y(1)=1$. The complete solution of the differential equation is $x^2 \\$ $\sin \left (\dfrac{\pi x}{2} \right ) \\$ $e^x \sin \left (\dfrac{\pi x}{2} \right ) \\$ $e^{-x} \sin \left (\dfrac{\pi x}{2} \right) \\$
Consider the differential equation $x^2 \dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}-4y=0$ with the boundary conditions of $y(0)=0$ and $y(1)=1$. The complete solution of the diffe...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Differential Equations
gateme-2012
differential-equation
boundary-value-problems
+
–
0
answers
0
votes
GATE ME 2012 | Question: 45
A box contains $4$ red balls and $6$ black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is $1/20$ $1/12$ $3/10$ $1/2$
A box contains $4$ red balls and $6$ black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Probability and Statistics
gateme-2012
probability-and-statistics
probability
+
–
0
answers
0
votes
GATE ME 2012 | Question: 47
$x+2y+z=4$ $2x+y+2z=5$ $x-y+z=1$ The system of algebraic equations given above has a unique solution of $x=1$, $y=1$ and $z=1$ only the two solutions of $(x=1, y=1, z=1)$ and $(x=2, y=1, z=0)$ infinite number of solutions no feasible solution
$x+2y+z=4$$2x+y+2z=5$$x-y+z=1$The system of algebraic equations given above hasa unique solution of $x=1$, $y=1$ and $z=1$only the two solutions of $(x=1, y=1, z=1)$ and ...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Linear Algebra
gateme-2012
linear-algebra
system-of-equations
+
–
0
answers
0
votes
GATE ME 2012 | Question: 36
For the matrix $A = \begin{bmatrix} 5 & 3 \\ 1 & 3 \end{bmatrix}$, ONE of the normalized eigen vectors is given as $\begin{pmatrix} \dfrac{1}{2} \\ \dfrac{\sqrt{3}}{2} \end{pmatrix} \\$ ... $\begin{pmatrix} \dfrac{1}{\sqrt{5}} \\ \dfrac{2}{\sqrt{5}} \end{pmatrix}$
For the matrix $A = \begin{bmatrix} 5 & 3 \\ 1 & 3 \end{bmatrix}$, ONE of the normalized eigen vectors is given as$\begin{pmatrix} \dfrac{1}{2} \\ \dfrac{\sqrt{3}}{2} \en...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Linear Algebra
gateme-2012
linear-algebra
eigen-values
eigen-vectors
+
–
0
answers
0
votes
GATE ME 2012 | Question: 12
$\underset{x \rightarrow 0}{\lim} \bigg( \dfrac{1- \cos x}{x^2} \bigg)$ is $1/4$ $1/2$ $1$ $2$
$\underset{x \rightarrow 0}{\lim} \bigg( \dfrac{1- \cos x}{x^2} \bigg)$ is$1/4$$1/2$$1$$2$
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
limits
+
–
0
answers
0
votes
GATE ME 2012 | Question: 24
At $x=0$, the function $f(x)=x^3+1$ has a maximum value a minimum value a singularity a point of inflection
At $x=0$, the function $f(x)=x^3+1$ hasa maximum valuea minimum valuea singularitya point of inflection
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
functions-of-single-variable
maxima-minima
+
–
0
answers
0
votes
GATE ME 2012 | Question: 25
For the spherical surface $x^2+y^2+z^2=1$, the unit outward normal vector at th point $\left( \dfrac{1}{\sqrt{2}}, \dfrac{1}{\sqrt{2}}, 0\right)$ is given by $\dfrac{1}{\sqrt{2}} \hat{i} +\dfrac{1}{\sqrt{2}} \hat{j} \\$ ... $\hat{k} \\$ $\dfrac{1}{\sqrt{3}} \hat{i} +\dfrac{1}{\sqrt{3}} \hat{j} +\dfrac{1}{\sqrt{3}} \hat{k}$
For the spherical surface $x^2+y^2+z^2=1$, the unit outward normal vector at th point $\left( \dfrac{1}{\sqrt{2}}, \dfrac{1}{\sqrt{2}}, 0\right)$ is given by$\dfrac{1}{\s...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
vector-identities
+
–
0
answers
0
votes
GATE ME 2012 | Question: 12
Consider the function $f(x) = \mid x \mid $ in the interval $-1 \leq x \leq 1$. At the point $x=0, \: f(x)$ is continuous and differentiable non-continuous and differentiable continuous and non-differentiable neither continuous nor differentiable
Consider the function $f(x) = \mid x \mid $ in the interval $-1 \leq x \leq 1$. At the point $x=0, \: f(x)$ iscontinuous and differentiablenon-continuous and differentiab...
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
continuity-and-differentiability
+
–
0
answers
0
votes
GATE ME 2012 | Question: 11
The area enclosed between the straight line $y=x$ and the parabola $y=x^2$ in the $x-y$ plane is $1/6$ $1/4$ $1/3$ $1/2$
The area enclosed between the straight line $y=x$ and the parabola $y=x^2$ in the $x-y$ plane is$1/6$$1/4$$1/3$$1/2$
Andrijana3306
1.5k
points
Andrijana3306
asked
Mar 19, 2018
Calculus
gateme-2012
calculus
definite-integrals
area-under-curve
+
–
1
answers
0
votes
GATE2018-2-27
Let $X_1$ and $X_2$ be two independent exponentially distributed random variables with means $0.5$ and $0.25$, respectively. Then $Y=\text{min}(X_1, X_2)$ is exponentially distributed with mean $1/6$ exponentially distributed with mean $2$ normally distributed with mean $3/4$ normally distributed with mean $1/6$
Let $X_1$ and $X_2$ be two independent exponentially distributed random variables with means $0.5$ and $0.25$, respectively. Then $Y=\text{min}(X_1, X_2)$ isexponentially...
Arjun
28.5k
points
Arjun
asked
Feb 17, 2018
Probability and Statistics
gateme-2018-set2
probability-and-statistics
probability
random-variables
exponential-distributions
+
–
1
answers
0
votes
GATE2018-2-24
The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of $30$ customers/hour. The probability that the time between successive customer arrival is between $1$ and $3$ minutes is _____ (correct to two decimal places)
The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of $30$ customers/hour. The probability that the time between s...
Arjun
28.5k
points
Arjun
asked
Feb 17, 2018
Probability and Statistics
gateme-2018-set2
numerical-answers
probability-and-statistics
probability
poisson-distribution
+
–
1
answers
0
votes
GATE2018-2-19
If $A=\begin{bmatrix}1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 1 \end{bmatrix}$ then $\text{det}(A^{-1})$ is _______ (correct to two decimal palces).
If $A=\begin{bmatrix}1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 1 \end{bmatrix}$ then $\text{det}(A^{-1})$ is _______ (correct to two decimal palces).
Arjun
28.5k
points
Arjun
asked
Feb 17, 2018
Linear Algebra
gateme-2018-set2
numerical-answers
linear-algebra
matrices
rank-of-matrix
+
–
0
answers
0
votes
GATE2018-2-28
For a position vector $\overrightarrow{r} = x \hat{i}+y \hat{j} + z\hat{k}$ the norm of the vector can be defined as $\mid \overrightarrow{r} \mid = \sqrt{x^2+y^2+z^2}$. Given a function $\phi =\text{ln} \mid \overrightarrow{r} \mid$, its ... $\dfrac{\overrightarrow{r}}{\overrightarrow{r} \cdot \overrightarrow{r} } \\ $ $\dfrac{\overrightarrow{r}}{\mid \overrightarrow{r} \mid^3} $
For a position vector $\overrightarrow{r} = x \hat{i}+y \hat{j} + z\hat{k}$ the norm of the vector can be defined as $\mid \overrightarrow{r} \mid = \sqrt{x^2+y^2+z^2}$. ...
Arjun
28.5k
points
Arjun
asked
Feb 17, 2018
Calculus
gateme-2018-set2
calculus
vector-identities
+
–
0
answers
0
votes
GATE2018-1-3
According to the Mean Value Theorem, for a continuous function $f(x)$ in the interval $[a,b]$, there exists a value $\xi$ in this interval such that $\int_a^b f(x) dx = $ $f(\xi)(b-a)$ $f(b)(\xi-a)$ $f(a)(b-\xi)$ $0$
According to the Mean Value Theorem, for a continuous function $f(x)$ in the interval $[a,b]$, there exists a value $\xi$ in this interval such that $\int_a^b f(x) dx = $...
Arjun
28.5k
points
Arjun
asked
Feb 17, 2018
Calculus
gateme-2018-set1
calculus
mean-value-theorems
definite-integrals
+
–
0
answers
0
votes
GATE2018-1-18
A six-faced fair dice is rolled five times. The probability (in $\%$) of obtaining "ONE" at least four times is $33.3$ $3.33$ $0.33$ $0.0033$
A six-faced fair dice is rolled five times. The probability (in $\%$) of obtaining "ONE" at least four times is$33.3$$3.33$$0.33$$0.0033$
Arjun
28.5k
points
Arjun
asked
Feb 17, 2018
Probability and Statistics
gateme-2018-set1
probability-and-statistics
probability
+
–
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