Mechanical Engineering
GATE ME format:nat PYQs
Build your understanding with focused practice from past exam papers.
Questions 211–220 of 418. Imported answers require independent review unless marked reviewed.
Question 25
Open questionMENAT1 markNeeds review
If a reversed Carnot cycle operates between the temperature limits of 27°C and −3°C, then the ratio of the COP of a refrigerator to that of a heat pump (COP of refrigerator / COP of heat pump) based on the cycle is __________ (round off to 2 decimal places).
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Open questionMENAT2 marksNeeds review
Consider two exponentially distributed random variables X and Y, both having a mean of 0.50. Let Z = X + Y and r be the correlation coefficient between X and Y. If the variance of Z equals 0, then the value of r is ______ (round off to 2 decimal places).
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Open questionMENAT2 marksNeeds review
For the integral
, the absolute percentage error in numerical evaluation with the Trapezoid rule, using only the end points, is ______ (round off to one decimal place).Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 36
Open questionMENAT2 marksNeeds review
An analytic function of a complex variable z = x + iy (i = √−1) is defined as
where ψ(x,y) is a real function. The value of the imaginary part of f(z) at z = (1 + i) is ______ (round off to 2 decimal places).
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 36
Open questionMENAT2 marksNeeds review
A fair coin is tossed 20 times. The probability that ‘head’ will appear exactly 4 times in the first ten tosses, and ‘tail’ will appear exactly 4 times in the next ten tosses is ______ (round off to 3 decimal places).
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 37
Open questionMENAT2 marksNeeds review
In a disc-type axial clutch, the frictional contact takes place within an annular region with outer and inner diameters 250 mm and 50 mm, respectively. An axial force F₁ is needed to transmit a torque by a new clutch. However, to transmit the same torque, one needs an axial force F₂ when the clutch wears out. If contact pressure remains uniform during operation of a new clutch while the wear is assumed to be uniform for an old clutch, and the coefficient of friction does not change, then the ratio F₁/F₂ is ______ (round off to 2 decimal places).
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 37
Open questionMENAT2 marksNeeds review
A hollow spherical ball of radius 20 cm floats in still water, with half of its volume submerged. Taking the density of water as 1000 kg/m
, and the acceleration due to gravity as 10 m/s
, the natural frequency of small oscillations of the ball, normal to the water surface is ______ radians (round off to 2 decimal places).Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 38
Open questionMENAT2 marksNeeds review
A cam with a translation flat-face follower is desired to have the follower motion
Contact stress considerations dictate that the radius of curvature of the cam profile should not be less than 40 mm anywhere. The minimum permissible base circle radius is ______ mm (round off to one decimal place).
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Open questionMENAT2 marksNeeds review
Uniaxial compression test data for a solid metal bar of length 1 m is shown in the figure.
The bar material has a linear elastic response from O to P followed by a nonlinear response. The point P represents the yield point of the material. The rod is pinned at both the ends. The minimum diameter of the bar so that it does not buckle under axial loading before reaching the yield point is ______ mm (round off to one decimal place).
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Open questionMENAT2 marksNeeds review
A rectangular steel bar of length 500 mm, width 100 mm, and thickness 15 mm is cantilevered to a 200 mm steel channel using 4 bolts, as shown.
For an external load of 10 kN applied at the tip of the steel bar, the resultant shear load on the bolt at B, is ______ kN (round off to one decimal place).
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