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GATE Mechanical 2021 Set 2 | Question: 35
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Find the positive real root of $x^3-x-3=0$ using Newton-Raphson method. lf the starting guess $(x_{0})$ is $2,$ the numerical value of the root after two iterations $(x_{2})$ is ______ ($\textit{round off to two decimal places}$).
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GATE Mechanical 2021 Set 2 | Question: 18
Value of $\int_{4}^{5.2} \ln x\: dx$ using Simpson’s one-third rule with interval size $0.3$ is $1.83$ $1.60$ $1.51$ $1.06$
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Solve the equation $x=10\cos(x)$ using the Newton-Raphson method. The initial guess is $x=\pi /4$. The value of the predicted root after the first iteration, up to second decimal, is ________
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Newton-Raphson method is used to find the roots of the equation, $x^3+3x^2+3x-1=0$. If the initial guess is $x_0=1$, then the value of $x$ after $2^{nd}$ iteration is ________
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GATE Mechanical 2021 Set 2 | Question: 20
Consider adiabatic flow of air through a duct. At a given point in the duct, velocity of air is $\text{300 m/s}$, temperature is $\text{330 K}$ and pressure is $\text{180 kPa}$. Assume that the air behaves as a perfect gas with constant ... $\text{K} (\textit{round off to two decimal places}$).
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GATE Mechanical 2021 Set 2 | Question: 21
Consider an ideal vapour compression refrigeration cycle working on $\text{R-134a}$ refrigerant. The $\text{COP}$ of the cycle is $10$ and the refrigeration capacity is $\text{150 kJ/kg}$. The heat rejected by the refrigerant in the condenser is __________ $\text{kJ/kg} (\textit{round off to the nearest integer}$).
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