List of top Questions asked in GATE ME- 2021

The controlling force curves P, Q and R for a spring controlled governor are shown in the figure, where \( r_1 \) and \( r_2 \) are any two radii of rotation. 

The characteristics shown by the curves are

If the Laplace transform of a function \( f(t) \) is given by \( \dfrac{s + 3}{(s + 1)(s + 2)}, \) then \( f(0) \) is 
 

The ratio of the area of the inscribed circle to the area of the circumscribed circle of an equilateral triangle is

The torque provided by an engine is given by \( T(\theta) = 12000 + 2500 \sin(2\theta) \, \text{N.m}, \) where \( \theta \) is the angle turned by the crank from inner dead center. The mean speed of the engine is 200 rpm and it drives a machine that provides a constant resisting torque varying as \( 200 + 200 \cos(\theta) \). If variation of the speed from the mean speed is not to exceed \( \pm 0.5% \), the minimum mass moment of inertia of the flywheel should be \(\underline{\hspace{1cm}}\) kg.m² (round off to nearest integer).

Consider the system shown in the figure. A rope goes over a pulley. A mass, \( m \), is hanging from the rope. A spring of stiffness, \( k \), is attached at one end of the rope. Assume rope is inextensible, massless and there is no slip between pulley and rope. 

The pulley radius is \( r \) and its mass moment of inertia is \( J \). Assume that the mass is vibrating harmonically about its static equilibrium position. The natural frequency of the system is 
 

Consider the open feed water heater (FWH) shown in the figure given below: Specific enthalpy of steam at location 2 is 2624 kJ/kg, specific enthalpy of water at location 5 is 226.7 kJ/kg and specific enthalpy of saturated water at location 6 is 708.6 kJ/kg. If the mass flow rate of water entering the open feed water heater at location 5 is 100 kg/s then the mass flow rate of steam at location 2 will be \(\underline{\hspace{2cm}}\) kg/s (round off to one decimal place).

The demand and forecast of an item for five months are given in the table. 

\[ \begin{array}{|c|c|c|} \hline \text{Month} & \text{Demand} & \text{Forecast} \\ \hline \text{April} & 225 & 200 \\ \text{May} & 220 & 240 \\ \text{June} & 285 & 300 \\ \text{July} & 290 & 270 \\ \text{August} & 250 & 230 \\ \hline \end{array} \] 

The Mean Absolute Percent Error (MAPE) in the forecast is \(\underline{\hspace{1cm}}\) % (round off to two decimal places).

A plane frame PQR (fixed at P and free at R) is shown in the figure. Both members (PQ and QR) have length \( L \), and flexural rigidity \( EI \). Neglecting the effect of axial stress and transverse shear, the horizontal deflection at free end, \( R \), is

Value of \( (1 + i)^8\), where \(i = \sqrt{-1}\), is equal to

Value of \( \int_4^{5.2} \ln x \, dx \) using Simpson's one-third rule with interval size 0.3 is

Consider the mechanism shown in the figure. There is rolling contact without slip between the disc and ground. 

Select the correct statement about instantaneous centers in the mechanism. 
 

A plane truss PQRS (PQ = RS, and \( \angle PQR = 90^\circ \)) is shown in the figure. The forces in the members PR and RS, respectively, are \(\underline{\hspace{2cm}}\)