Past Year Paper - Mechanical Engineering GATE : 2021 (Session - 1) - Mechanical Engineering MCQ

Ms. X came out of a building through its front door to find her shadow due to the morning sun falling to her right side with the building to her back. From this, it can be inferred that building is facing_____

If 
Then the value of the expression  Δ2⊕3Δ (( 4⊗2)∇4) =

Oxpeckers and rhinos manifest a symbiotic relationship in the wild. The oxpeckers warn the rhinos about approaching poachers, thus possibly saving the lives of the rhinos. Oxpeckers also feed on the parasitic ticks found on rhinos.  In the symbiotic relationship described above, the primary benefits for oxpeckers and rhinos respectively are.

Consider the following statements:  
(i) After his surgery, Raja hardly could walk. 
(ii)  After his surgery, Raja could barely walk.  
(iii) After his surgery, Raja barely could walk.  
(iv) After his surgery, Raja could hardly walk.

The distribution of employees at the rank of executives, across different companies C₁, C₂, ….., C₆ is presented in the chart given below . The ratio of executives with a management degree to those without a management degree in each of these companies is provided in the table above. The total number of executives across all companies is 10,000.  

The total number of management degree holders among the executives in companies C₂ and C₅ together is _________ . 

The number of hens, ducks and goats in farm P are 65, 91 and 169, respectively. The total number of hens, ducks and goats in a nearby farm Q is 416. The ratio of hens:ducks:goats in farm Q is 5:14:13. All the hens, ducks and goats are sent from farm Q to farm P.  
The new ratio of hens:ducks:goats in farm P is ________  

In the below figure, O is the center of the circle and, M and N lie on the circle. The area of the right triangle MON is 50 cm² .

What is the area of the circle in cm² ?

Robot Ltd. wishes to maintain enough safety stock during the lead time period between starting a new production run and its completion such that the probability of satisfying the customer demand during the lead time period is 95%. The lead time period is 5 days and daily customer demand can be assumed to follow the Gaussian (normal) distribution with mean 50 units and a standard deviation of 10 units.
Using φ⁻¹ (0.95)= 1.64 where φ represents the cumulative distribution function of the standard normal random variable, the amount of safety stock that must be maintained by Robot Ltd. to achieve this demand fulfillment probability for the lead time period is units (round off to two decimal places).

The loading and unloading response of a metal is shown in figure. The elastic and plastic strains corresponding to 200 MPa stress, respectively, are 

The figure shows an arrangement of a heavy propeller shaft in a ship. The combined polar mass moment of inertia of the propeller and the shaft is 100 kg.m² . The propeller rotates at ω= 12 rad/s . The waves acting on the ship hull induces a rolling motion as shown in the figure with an angular velocity of 5 rad/s. The gyroscopic moment generated on the shaft due to the motion described is ________N.m (round off to the nearest integer). 

Shear stress distribution on the cross-section of the coil wire in a helical compression spring is shown in the figure. This shear stress distribution represents  

In the vicinity of the triple point, the equation of liquid-vapour boundary in the P – T phase diagram for ammonia is ln P = 24.38− 3063 /T , where P is pressure (in Pa) and T is temperature (in K). Similarly, the solid-vapour boundary is given by ln P = 27.92− 3754 /T . The temperature at the triple point is _______K (round off to one decimal place). 

A cantilever beam of length, L, and flexural rigidity, EI, is subjected to an end moment, M, as shown in the figure. The deflection of the beam at x = L/2 is

Consider a two degree of freedom system as shown in the figure, where PQ is a rigid uniform rod of length, b and mass, m .

Assume that the spring deflects only horizontally and force F is applied horizontally at Q . For this system, the Lagrangian, L is

A cantilever beam of rectangular cross-section is welded to a support by means of two fillet welds as shown in figure. A vertical load of 2 kN acts at free end of the beam  

Considering that  the allowable shear stress in weld is 60 N/mm² , the minimum size (leg) of the weld required is ________mm (round off to one decimal place).

The relative humidity of ambient air at 300 K is 50% with a partial pressure of water vapour equal to p_v . The saturation pressure of water at 300 K is p_sat. The correct relation for the air-water mixture is 

A cylindrical jet of water (density = 1000 kg/m³) impinges at the center of a flat, circular plate and spreads radially outward, as shown in figure. The plate is resting on a linear spring with a spring constant k = l kN/m. The incoming jet diameter is D = 1cm. 

If the spring shows a steady deflection of 1 cm upon impingement of jet, then the velocity of the incoming jet is _________ m/s. (round off to one decimal place ) 

A machine part in the form of cantilever beam is subjected to fluctuating load as shown in the figure. The load varies from 800 N to 1600 N. The modified endurance, yield and ultimate strengths of the material are 200 MPa. 500 MPa and 600 MPa, respectively. 

The factor of safety of the beam using modified Goodman criterion is_________ (round off to one decimal place). 

Consider a single degree of freedom system comprising a mass M, supported on a spring and a dashpot as shown in the figure 

If the amplitude of free vibration response reduces from 8 mm to 1.5 mm in 3 cycles, that damping ratio of the system is _________. (round off to three decimal places). 

Customers arrive at a shop according to the Poisson distribution with a mean of 10 customers/hour. The manager notes that no customer arrives for the first 3 minutes after the shop opens. The probability that a customer arrives within the next 3 minutes is 

An infinitely long pin fin, attached to an isothermal hot surface, transfers heat at a steady rate of  to the ambient air. If the thermal conductivity of the fin material is doubled, while keeping everything else constant, the rate of steady-state heat transfer from the fin becomes . The ratio is   

Two smooth identical spheres each of radius 125 mm and weight 100 N rest in a horizontal channel having vertical walls. The distance between vertical walls of the channel is 400 mm.  

The reaction at the point of contact between two spheres is _____ N (round off to one decimal place). 

The correct sequence of machining operations to be performed to finish a large diameter through hole is  

The Dirac-delta function (δ(t − t₀ )) for t ,t₀ ∈ R, has the following property 

The Laplace transform of the Dirac-delta function δ (t−a) for  a > 0;  
L{δ(t− a )} = F(s) is

A short shoe drum (radius 260 mm) brake is shown in the figure. A force of 1 kN is applied to the lever. The coefficient of friction is 0.4. 

The magnitude of the torque applied by the brake is _______ N.m (round off to one decimal place). 

A right solid circular cone standing on its base on a horizontal surface is of height H and base radius R. The cone is made of a material with specific weight w and elastic modulus E. The vertical deflection at the mid-height of the cone due to self-weight is given by 

A resistance spot welding of two 1.55 mm thick metal sheets is performed using welding current of 10000 A for 0.25 second. The contact resistance at the interface of the metal sheets is 0.0001Ω. The volume of weld nugget formed after welding is 70 mm3. Considering the heat required to melt unit volume of metal is 12 J/mm3, the thermal efficiency of the welding process is_________ %  (round off to one decimal place).