Past Year Paper - Mechanical Engineering GATE : 2021 (Session - 2) - Mechanical Engineering MCQ

Consider a square sheet of side 1 unit. The sheet is first folded along the main diagonal. This is followed by a fold along its line of symmetry. The resulting folded shape is again folded along its line of symmetry. The area of each face of the final folded shape, in square units, equal to _______  

The front door of Mr. X’s house faces East. Mr. X leaves the house walking 50 m straight from the back door that is situated directly opposite to the front door. He then turns to his right walks for another 50 m and stops. The direction of the point Mr. X is now located at with respect to the starting point is ___________   

Five person P, Q, R, S and T are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and T cannot be seated at either end of the row. P should not be seated adjacent to S. R is to be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is :  

The world is going through the worst pandemic in the past hundred years. The air travel industry is facing a crisis, as the resulting quarantine requirement for travelers led to weak demand.
In relation to the first sentence above, what does the second sentence do?  

If ⊕÷ Θ = 2, ⊕ ÷Δ = 3,Θ + Δ = 5, Δ × ⊗ = 10 then the value of (⊗ - ⊕)² is 

A digital watch X beeps every 30 secs while watch Y beeps 32 seconds. They beeped together at 10 AM. The immediate next time that they will beep together is _______.  

A box contains 15 blue balls and 45 black balls. If 2 balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball, is ___________.  

The wheels and axle system lying on a rough surface is shown in the figure. Each wheel has diameter 0.8 m and mass 1 kg. Assume that the mass of the wheel is concentrated at rim and neglect the mass of spokes. The diameter of axle is  0.2 m and its mass is 1.5 kg. Neglect the moment of Inertia of axle and assume g = 9.81 m/s² . An effort of 10 N is applied on the axle in the horizontal direction shown at mid span of the axle. Assume that the wheels move on a horizontal surface without slip. The acceleration of the wheel the axle system in horizontal direction is _______ m/s² (round off to one decimal place). 

Consider the following differential equation . The solution of the equation that satisfies the 
condition y (1) = 1 is 

A rigid tank of volume 50 m³ contains a pure substance as a saturated liquid vapour mixture at 400 kPa. Of the total mass of the mixture, 20% mass is liquid and 80% mass is vapour. Properties at 400 kPa are : Saturation temperature, T_sat = 143.61^oC; Specific volume of Saturated liquid, v_f = 0.001084 m³ /kg; Specific volume of saturated vapour, v_g = 0.46242m³/kg . The total mass of liquid vapour mixture in the tank is _______ kg (round off to the nearest integer).

A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness ( K) and damper (damping factor, ξ ) in parallel. The designer has the following four isolators:
1. K = 640 kN/m, ξ = 0.70
2. K = 640 kN/m, ξ = 0.07
3. K = 22.5 kN/m, ξ = 0.70
4. K = 22.5 kN/m, ξ = 0.07
Arrange the isolators in the ascending order of the force transmitted to the foundation. 

In a pure orthogonal turning by a zero rake angle single point carbide cutting tool the shear force has been computed to be 400 N. If the cutting velocity 100 m/min V_c = , depth of cut t = 2.0 mm , feed S₀ = 0.1 mm/revolution and chip flow velocity V_f = 20 m/min , then the shear strength τ_s of the material will be _______ MPa.(round off to two decimal places). 

A shell and tube heat exchange is used as a steam condenser. Coolant water inters the tube at 300 K and at a rate of 100 kg/s. The overall heat transfer coefficient is 1500 W/m²K and total heat transfer area is 400 m² . Steam condenses at a saturation temperature of 350 K. Assume that the specific heat of coolant water is 4000 J/kgK. The temperature of the coolant water coming out of the condenser is _______ K (round off to the nearest integer)

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

Select the correct statement about instantaneous centers in the mechanism.

An adiabatic vortex tube, shown in the figure given below is supplied with 5 kg/s of air (inlet 1) at 500 kPa and 300 K. Two separate streams of air are leaving the device from outlets 2 and 3. Hot air leaves the device at a rate of 3 kg/s from outlet 2 at 100 kPa and 340 K, while 2 kg/s of cold air stream is leaving the device from outlet 3 at 100 kPa and 240 K. 

Consider constant specific heat of air is 1005J/kgK and gas constant is 287J/kgK. There is no work transfer across the boundary of this device. The rate of entropy generation is _____ kW/K (round off to one decimal place). 

A column with one end fixed and one end free has a critical buckling load of 100 N. For the same column if free end is replaced with a pinned end then critical buckling load will be ______ N (round off to the nearest integer). 

Value of  using Simpson’s one third rule with interval size 0.3 is  

Consider the system shown in figure A rope goes over a pulley. A mass, m is hanging from rope. A spring of stiffness, k is attached at one end of 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 

A plane frame PQR (fixed at P and free at R) is shown in the figure. Both member (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

An object is moving with a mach number of 0.6 in an ideal gas environment, which is at a temperature of 350 K. The gas constant is 320 J/kgK and ratio of specific heats is 1.3. The speed of object is _______ m/s. (Round off to the nearest integer).

Let the superscript T represents the transpose operation. Consider the function ,  where x & r are n × 1 vectors and Q is a symmetric n × n Metrix. The stationary point of  f (x) is

A PERT network has 9 activities on its critical path. The standard deviation of each activity on critical path is 3. The standard deviation of critical path is_________.

In forced convective heat transfer Stanton number (St), Nusselt number (Nu), Reynolds number (Re) and Prandtl number (Pr) are related as

The thickness, width and length of a metals slab are 50 mm., 250 mm. and 3600 mm. respectively. A rolling operation on this slab reduces the thickness by 10% and increases the width by 3%. The length of the rolled slab is ______ mm (round off to one decimal place). 

The figure shows the relationship between fatigue strength  (S) and fatigue life (N) of a material. The fatigue strength of the material for a life of 1000 cycles is 450 MPa, while its fatigue strength for a life of 10⁶ cycles is 150 MPa. 

The life of a cylinder shaft made of this material subjected to an alternating stress of 200 MPa will then be _______ cycles (round off to the nearest integer). 

The size distribution of powder particles used in Powder Metallurgy process can be determined by  

Consider adiabatic flow of air through a duct. At a given point in the duct, velocity of air is 300 m/s, temperature is 330K and pressure is 180 kPa. Assume that the air behaves as a perfect gas with constant C_p = 1.005 kJ/kgK . The stagnation temperature at this point is ________ K (round off to two decimal places).