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Most answered questions in Engineering Mathematics
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GATE Mechanical 2014 Set 1 | Question: 50
Jobs arrive at a facility at an average rate of $5$ in an $8$ hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the facility is $40$ minutes. The service time follows exponential distribution. Idle time (in hours) at the ... be $\dfrac{5}{7} \\$ $\dfrac{14}{3} \\$ $\dfrac{7}{5} \\$ $\dfrac{10}{3}$
Jobs arrive at a facility at an average rate of $5$ in an $8$ hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the f...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Probability and Statistics
gateme-2014-set1
probability-and-statistics
probability
poisson-distribution
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–
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 27
If $y = f(x)$ is the solution of $\dfrac{d^2y}{dx^2}=0$ with the boundary conditions y = $5$ at $x = 0$ and $\dfrac{dy}{dx}=2$ at $x = 10$, $f(15) =$ _____________ .
If $y = f(x)$ is the solution of $\dfrac{d^2y}{dx^2}=0$ with the boundary conditions y = $5$ at $x = 0$ and $\dfrac{dy}{dx}=2$ at $x = 10$, $f(15) =$ _____________ .
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Calculus
gateme-2014-set1
numerical-answers
calculus
initial-and-boundary-value-problems
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–
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 29
Using the trapezoidal rule, and dividing the interval of integration into three equal subintervals, the definite integral $\int_{-1}^{+1} \mid x \mid dx$ is _____
Using the trapezoidal rule, and dividing the interval of integration into three equal subintervals, the definite integral $\int_{-1}^{+1} \mid x \mid dx$ is _____
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Numerical Methods
gateme-2014-set1
numerical-answers
numerical-methods
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–
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 18
The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jobs in a fixed time interval is Normal Poisson Erlang Beta
The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jobs in a fixed time interval isNormalPoissonErlangB...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Probability and Statistics
gateme-2014-set1
probability-and-statistics
probability
poisson-distribution
+
–
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 26
The integral $\oint_{c}^{ } (ydx-xdy)$ is evaluated along the circle $x^2+y^2=\frac{1}{4}$ traversed in counter clockwise direction. The integral is equal to $0$ $\frac{-\pi }{4}$ $\frac{-\pi }{2}$ $\frac{\pi }{4}$
The integral $\oint_{c}^{ } (ydx-xdy)$ is evaluated along the circle $x^2+y^2=\frac{1}{4}$ traversed in counter clockwise direction. The integral is equal to$0$$\frac{-\p...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Calculus
gateme-2014-set1
calculus
definite-integrals
area-under-curve
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–
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 1
Given that the determinant of the matrix $\begin{bmatrix} 1 & 3 & 0\\ 2 & 6 & 4\\ -1 & 0 & 2 \end{bmatrix}$ is $-12$, the determinant of the matrix $\begin{bmatrix} 2 & 6 & 0\\ 4 & 12 & 18\\ -2 & 0 & 4 \end{bmatrix}$ is $-96$ $-24$ $24$ $96$
Given that the determinant of the matrix $\begin{bmatrix} 1 & 3 & 0\\ 2 & 6 & 4\\ -1 & 0 & 2 \end{bmatrix}$ is $-12$, the determinant of the matrix $\begin{bmatrix} 2 & 6...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Linear Algebra
gateme-2014-set1
linear-algebra
matrices
determinant
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–
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 2
$\displaystyle{} \lim_{x\rightarrow 0}\dfrac{x- \sin x}{1- \cos x}$ is $0$ $1$ $3$ not defined
$\displaystyle{} \lim_{x\rightarrow 0}\dfrac{x- \sin x}{1- \cos x}$ is$0$$1$$3$not defined
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Calculus
gateme-2014-set1
calculus
limits
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–
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 3
The argument of the complex number $\dfrac{1+\imath }{1-\imath }$ where $\imath =\sqrt{-1}$ ,is $-\pi \\$ $\dfrac{-\pi }{2} \\$ $\dfrac{\pi }{2} \\$ $\pi$
The argument of the complex number $\dfrac{1+\imath }{1-\imath }$ where $\imath =\sqrt{-1}$ ,is$-\pi \\$$\dfrac{-\pi }{2} \\$$\dfrac{\pi }{2} \\$ $\pi$
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Calculus
gateme-2014-set1
calculus
complex-variables
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–
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 4
The matrix form of the linear syatem $\dfrac{dx}{dt}=3x-5y$ and $\dfrac{dy}{dt}=4x+8y$ is $\dfrac{d}{dt}\begin{Bmatrix} x\\y \end{Bmatrix}=\begin{bmatrix} 3 & -5\\ 4& 8 \end{bmatrix}\begin{Bmatrix} x\\y \end{Bmatrix} \\$ ...
The matrix form of the linear syatem $\dfrac{dx}{dt}=3x-5y$ and $\dfrac{dy}{dt}=4x+8y$ is$\dfrac{d}{dt}\begin{Bmatrix} x\\y \end{Bmatrix}=\begin{bmatrix} 3 & -5\\ 4& 8 \e...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Linear Algebra
gateme-2014-set1
linear-algebra
matrices
matrix-algebra
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–
0
answers
0
votes
GATE Mechanical 2014 Set 1 | Question: 5
Which one of the following describes the relationship among the three vectors, $\hat{i}+\hat{j}+\hat{k}$ , $2\hat{i}+3\hat{j}+\hat{k}$ and $5\hat{i}+6\hat{j}+4\hat{k}$ ? The vectors are mutually perpendicular The vectors are linearly dependent The vectors are linearly independent The vectors are unit vectors
Which one of the following describes the relationship among the three vectors, $\hat{i}+\hat{j}+\hat{k}$ , $2\hat{i}+3\hat{j}+\hat{k}$ and $5\hat{i}+6\hat{j}+4\hat{k}$ ?T...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Calculus
gateme-2014-set1calculus
vector-identities
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–
0
answers
0
votes
GATE ME 2013 | Question: 45
The probability that a student knows the correct answer to a multiple choice question is $\dfrac{2}{3}$ . If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is $\dfrac{1}{4}$. Given that the student has ... answer is $\dfrac{2}{3} \\$ $\dfrac{3}{4} \\$ $\dfrac{5}{6} \\$ $\dfrac{8}{9}$
The probability that a student knows the correct answer to a multiple choice question is $\dfrac{2}{3}$ . If the student does not know the answer, then the student guesse...
piyag476
1.4k
points
piyag476
asked
Feb 19, 2017
Probability and Statistics
gateme-2013
probability-and-statistics
probability
conditional-probability
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–
0
answers
0
votes
GATE ME 2013 | Question: 46
The solution to the differential equation $\dfrac{d^2u}{dx^2}-k\dfrac{du}{dx}=0$ where $k$ is a constant, subjected to the boundary conditions $u(0)$ = $0$ and $u(L)$ = $U$, is $u=U\dfrac{x}{L} $ $u=U\left(\dfrac{1-e^{kx}}{1-e^{kL}}\right) $ $u=U\left(\dfrac{1-e^{-kx}}{1-e^{-kL}}\right)$ $u=U\left(\dfrac{1+e^{kx}}{1+e^{kL}}\right)$
The solution to the differential equation $\dfrac{d^2u}{dx^2}-k\dfrac{du}{dx}=0$ where $k$ is a constant, subjected to theboundary conditions $u(0)$ = $0$ and $u(L)$ = $...
piyag476
1.4k
points
piyag476
asked
Feb 19, 2017
Differential Equations
gateme-2013
differential-equations
initial-and-boundary-value-problems
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–
0
answers
0
votes
GATE ME 2013 | Question: 47
The value of the definite integral $\int_{1}^{e}\sqrt{x}\ln(x)dx$ is $\dfrac{4}{9}\sqrt{e^3}+\dfrac{2}{9} \\$ $\dfrac{2}{9}\sqrt{e^3}-\dfrac{4}{9} \\$ $\dfrac{2}{9}\sqrt{e^3}+\dfrac{4}{9}\\$ $\dfrac{4}{9}\sqrt{e^3}-\dfrac{2}{9}$
The value of the definite integral $\int_{1}^{e}\sqrt{x}\ln(x)dx$ is$\dfrac{4}{9}\sqrt{e^3}+\dfrac{2}{9} \\$$\dfrac{2}{9}\sqrt{e^3}-\dfrac{4}{9} \\$$\dfrac{2}{9}\sqrt{e^3...
piyag476
1.4k
points
piyag476
asked
Feb 19, 2017
Calculus
gateme-2013
calculus
definite-integrals
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–
0
answers
0
votes
GATE ME 2013 | Question: 36
A linear programming problem is shown below. $\begin{array}{ll} \text{Maximize} & 3x + 7y \\ \text{Subject to} & 3x + 7y \leq 10 \\ & 4x + 6y \leq 8 \\ & x, y \geq 0 \end{array}$ It has an unbounded objective function. exactly one optimal solution. exactly two optimal solutions. infinitely many optimal solutions.
A linear programming problem is shown below.$\begin{array}{ll} \text{Maximize} & 3x + 7y \\ \text{Subject to} & 3x + 7y \leq 10 \\ & 4x + 6y \leq 8 \\ & x, y \geq 0 \end{...
piyag476
1.4k
points
piyag476
asked
Feb 19, 2017
Numerical Methods
gateme-2013
numerical-methods
linear-programming
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–
0
answers
0
votes
GATE ME 2013 | Question: 24
Let $X$ be a normal random variable with mean $1$ and variance $4$. The probability $P \left \{ X \right.<\left. 0 \right \}$ is $0.5$ greater than zero and less than $0.5$ greater than $0.5$ and less than $1.0$ $1.0$
Let $X$ be a normal random variable with mean $1$ and variance $4$. The probability $P \left \{ X \right.<\left. 0 \right \}$ is$0.5$greater than zero and less than $0.5...
piyag476
1.4k
points
piyag476
asked
Feb 19, 2017
Probability and Statistics
gateme-2013
probability-and-statistics
probability
random-variables
variance
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–
0
answers
0
votes
GATE ME 2013 | Question: 25
Choose the CORRECT set of functions, which are linearly dependent. $\sin x , \sin^2 x$ and $\cos^2 x$ $\cos x , \sin x$ and $\tan x$ $\cos 2x, \sin^2 x$ and $\cos^2 x$ $\cos 2x , \sin x$ and $cos x$
Choose the CORRECT set of functions, which are linearly dependent.$\sin x , \sin^2 x$ and $\cos^2 x$$\cos x , \sin x$ and $\tan x$$\cos 2x, \sin^2 x$ and $\cos^2 x$$\cos ...
piyag476
1.4k
points
piyag476
asked
Feb 19, 2017
Calculus
gateme-2013
calculus
functions
+
–
0
answers
0
votes
GATE ME 2013 | Question: 26
The following surface integral is to be evaluated over a sphere for the given steady velocity vector field $F$ = $xi$ + $yj$+ $zk$ defined with respect to a Cartesian coordinate system having $i$, $j$ and $k$ ... is the outward unit normal vector to the sphere. The value of the surface integral is $\pi$ $2\pi$ $3\pi/4$ $4\pi$
The following surface integral is to be evaluated over a sphere for the given steady velocity vector field $F$ = $xi$ + $yj$+ $zk$ defined with respect to a Cartesian coo...
piyag476
1.4k
points
piyag476
asked
Feb 19, 2017
Calculus
gateme-2013
calculus
integrals
area-under-curve
+
–
0
answers
0
votes
GATE ME 2013 | Question: 27
The function $f(t)$ satisfies the differential equation $\dfrac{d^2f}{dt^2}+f=0$ and the auxiliary conditions, $f(0)=0$, $\dfrac{d(f)}{d(t)}(0)=4$. The Laplace transform of $f(t)$is given by $\dfrac{2}{s+1} \\$ $\dfrac{4}{s+1} \\$ $\dfrac{4}{s^2+1} \\$ $\dfrac{2}{s^4+1}$
The function $f(t)$ satisfies the differential equation $\dfrac{d^2f}{dt^2}+f=0$ and the auxiliary conditions, $f(0)=0$, $\dfrac{d(f)}{d(t)}(0)=4$. The Laplace transform ...
piyag476
1.4k
points
piyag476
asked
Feb 19, 2017
Differential Equations
gateme-2013
differential-equation
laplace-transforms
+
–
0
answers
0
votes
GATE ME 2013 | Question: 1
The partial differential equation $\dfrac{\partial u }{\partial t}+u\dfrac{\partial u}{\partial x}=\dfrac{\partial^2 u}{\partial x^2}$ is a linear equation of order $2$ non-linear equation of order $1$ linear equation of order $1$ non-linear equation of order $2$
The partial differential equation $\dfrac{\partial u }{\partial t}+u\dfrac{\partial u}{\partial x}=\dfrac{\partial^2 u}{\partial x^2}$ is alinear equation of order $2$no...
piyag476
1.4k
points
piyag476
asked
Feb 19, 2017
Differential Equations
gateme-2013
differential-equation
partial-differential-equation
+
–
0
answers
0
votes
GATE ME 2013 | Question: 2
The eigen values of a symmetric matrix are all complex with non-zero positive imaginary part. complex with non-zero negative imaginary part. real. pure imaginary.
The eigen values of a symmetric matrix are allcomplex with non-zero positive imaginary part.complex with non-zero negative imaginary part.real.pure imaginary.
piyag476
1.4k
points
piyag476
asked
Feb 19, 2017
Linear Algebra
gateme-2013
linear-algebra
matrices
eigen-values
+
–
0
answers
0
votes
GATE ME 2013 | Question: 3
Match the CORRECT pairs: ... $P-2; Q-1; R-3$ $P-3; Q-2; R-1$ $P-1; Q-2; R-3$ $P-3; Q-1; R-2$
Match the CORRECT pairs:$\begin{array}{llll} & \text{Numerical Integration Scheme} & & \text{Order of Fitting Polynomial} \\ P. & \text{Simpson's 3/8 Rule} & 1. & \text{F...
piyag476
1.4k
points
piyag476
asked
Feb 19, 2017
Numerical Methods
gateme-2013
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
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