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GATE-ME-Section-Test-1
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Question 1
In the Taylor series expansion of ex about x = 2, the coefficient of (x – 2)4 is
Question 2
A straight rod of length L(t), hinged at one end and freely extensible at the other end, rotates through an angle θ(t) about the hinge. At time t, L(t) = 1 m, (t) = 1 m/s, 
rad and θ(t) = 1 rad/s. The magnitude of the velocity at the other end of the rod is
rad and θ(t) = 1 rad/s. The magnitude of the velocity at the other end of the rod is Question 3
A cantilever type gate hinged at Q is shown in the figure. P and R are the centers of gravity of the cantilever part and the counterweight respectively. The mass of the cantilever part is 75 kg. The mass of the counterweight, for static balance, is
Question 4
The effective number of lattice points in the unit cell of simple cubic, body centered cubic, and face centered cubic space lattices, respectively, are
Question 5
2 moles of oxygen are mixed adiabatically with another 2 moles of oxygen in a mixing chamber, so that the final total pressure and temperature of the mixture become same as those of the individual constituents at their initial states. The universal gas constant is given as R. The change in entropy due to mixing, per mole of oxygen, is given by __________.
Question 6
A journal bearing has a shaft diameter of 40 mm and a length of 40 mm. The shaft is rotating at 20 rad/s and the viscosity of the lubricant is 20mPa.s. The clearance is 0.020 mm. The loss of torque due to the viscosity of the lubricant is approximately
Question 7
A moving average system is used for forecasting weekly demand. F1(t) and F2(t) are sequences of forecasts with parameters m1 and m2, respectively, where m1 and m2 (m1 > m2) denote the numbers of weeks over which the moving averages are taken. The actual demand shows a step increase from d1 to d2 at a certain time. Subsequently,
Question 8
In arc welding of a butt joint, the welding speed is to be selected such that highest cooling rate is achieved. Melting efficiency and heat transfer efficiency are 0.5 and 0.7, respectively. The area of the weld cross section is 5 mm2 and the unit energy required to melt the metal is 10 J/mm3. If the welding power is 2 kW, the welding speed in mm/s is closest to
Question 9
Consider steady, incompressible and irrotational flow through a reducer in a horizontal pipe where the diameter is reduced from 20 cm to 10 cm. The pressure in the 20 cm pipe just upstream of the reducer is 150 kPa. The fluid has a vapour pressure of 50 kPa and a specific weight of 5 kN/m3. Neglecting frictional effects, the maximum discharge (in m3/s) that can pass through the reducer without causing cavitation is
Question 10
Consider the following two equations.
I. x4 - 227 = 398
II. y2 + 321 = 346
I. x4 - 227 = 398
II. y2 + 321 = 346
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