Mechanical Engineering GATE 2024 Questions with Answer

Ques 27 Industrial Engineering

A company orders gears in conditions identical to those considered in the economic order quantity (EOQ) model in inventory control. The annual demand is 8000 gears, the cost per order is 300 rupees, and the holding cost is 12 rupees per month per gear. The company uses an order size that is 25% more than the optimal order quantity determined by the EOQ model. The percentage change in the total cost of ordering and holding inventory from that associated with the optimal order quantity is

Ques 28 Industrial Engineering

At the current basic feasible solution (bfs) v₀ (v₀ ∈ ℝ⁵), the simplex method yields the following form of a linear programming problem in standard form.
minimize z = −x₁ − 2x₂
s.t. x₃ = 2 + 2x₁ − x₂
x₄ = 7 + x₁ − 2x₂
x₅ = 3 − x₁
x₁, x₂, x₃, x₄, x₅ ≥ 0
Here the objective function is written as a function of the non-basic variables. If the simplex method moves to the adjacent bfs v₁ (v₁ ∈ ℝ⁵) that best improves the objective function, which of the following represents the objective function at v₁, assuming that the objective function is written in the same manner as above?

Ques 29 Industrial Engineering

In a supplier-retailer supply chain, the demand 4 supplier, and the unit cost in rupees of material supply from each supplier to each retailer are tabulated below. The supply chain manager wishes to minimize the total cost of transportation across the supply chain.

Ques 30 Machine Design

For a ball bearing, the fatigue life in millions of revolutions is given by L = (C/P)ⁿ where P is the constant applied load and C is the basic dynamic load rating. Which one of the following statements is TRUE?

Ques 31 Machine Design

The change in kinetic energy ΔE of an engine is 300 J, and minimum and maximum shaft speeds are ω_min = 220 rad/s and, respectively. Assume that the torque-time function is purely harmonic. To achieve a coefficient of fluctuation of 0.05, the moment of inertia (in kg.m²) of the flywheel to be mounted on the engine shaft is

Ques 32 Machine Design

Which one of the following failure theories is the most conservative design approach against fatigue failure?

Ques 33 Machine Design

A solid massless cylindrical member of 50 mm diameter is rigidly attached at one end, and is subjected to an axial force P = 100 kN and a torque T = 600 N.m at the other end as shown. Assume that the axis of the cylinder is normal to the support. Considering distortion energy theory with allowable yield stress as 300 MPa, the factor of safety in the design is _______________ (rounded off to 1 decimal place).

Ques 34 Machine Design

The figure shows a thin cylindrical pressure vessel constructed by welding plates together along a line that makes an angle α = 60° with the horizontal. 1 The closed vessel has a wall thickness of 10 mm and a diameter of 2 m. When subjected to an internal pressure of 200 kPa, the magnitude of the normal stress acting on the weld is _______________ MPa (rounded off to 1 decimal place).

Ques 35 Manufacturing Processes-I

The "Earing" phenomenon in metal forming is associated with

Ques 36 Manufacturing Processes-I

The allowance provided to a pattern for easy withdrawal from a sand mold is

Ques 37 Manufacturing Processes-I

Aluminium is casted in a cube-shaped mold having dimensions as 20 m m × 20 m m × 20 mm. Another mold of the same mold material is used to cast a sphere of aluminium having a diameter of 20 mm. The pouring temperature for both cases is the same. The ratio of the solidification times of the cube-shaped mold to the spherical mold is (answer in integer).

Ques 38 Manufacturing Processes-I

A blanking operation is performed on C20 steel sheet to obtain a circular disc having a diameter of 20 mm and a thickness of 2 mm. An allowance of 0.04 is provided. The punch size used for the operation is _________ mm (rounded off to 2 decimal places).

Ques 39 Manufacturing Processes-II

The grinding wheel used to provide the best surface finish is