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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 $x = 10$, $f(15) =$ _____________ .
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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 &...
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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 _____
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GATE Mechanical 2014 Set 1 | Question: 30
The state of stress at a point is given by $\sigma _x=-6 MPa$ ,$\sigma _y=4 MPa$ and $\tau _{xy}=-8 MPa$.The maximum tensile stress in (MPa) at the point is _____
The state of stress at a point is given by $\sigma _x=-6 MPa$ ,$\sigma _y=4 MPa$ and $\tau _{xy}=-8 MPa$.The maximum tensile stress in (MPa) at the point is _____
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GATE Mechanical 2014 Set 1 | Question: 37
An offset slider-crank mechanism is shown in the figure at an instant. Conventionally, the Quick Return Ratio (QRR) is considered to be greater than one. The value of QRR is _______
An offset slider-crank mechanism is shown in the figure at an instant. Conventionally, the Quick Return Ratio (QRR) is considered to be greater than one. The value of QRR...
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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...
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GATE Mechanical 2014 Set 1 | Question: 24
The process of reheating the martensitic steel to reduce its brittleness without any significant loss in its hardness is normalising annealing quenching tempering
The process of reheating the martensitic steel to reduce its brittleness without any significant loss in its hardness isnormalisingannealingquenchingtempering
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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...
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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
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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} \\$ $\pi$
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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...
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