Mechanical Engineering Gate Yearwise

Mechanical Engineering GATE 2024 Questions with Answer

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Ques 40 Manufacturing Processes-II

The most suitable electrode material used for joining low alloy steels using Gas Metal Arc Welding (GMAW) process is

copper

low alloy steel

stainless steel

tungsten

Ques 41 Manufacturing Processes-II

The preparatory functions in Computer Numerical Controlled (CNC) machine programing are denoted by the alphabet

Ques 42 Manufacturing Processes-II

In an arc welding process, the voltage and current are 30 V and 200 A, respectively. The cross-sectional area of the joint is 20 m m 2 and the welding speed is 5 m m / s. The heat required to melt the material is 20 J / s. The percentage of heat lost to the surrounding during the welding process is _________.(rounded off to 2 decimal places).

40.00 is the correct answer.

Ques 43 Manufacturing Processes-II

A flat surface of a C60 steel having dimensions of 100 mm (length) × 200 mm (width) is produced by a HSS slab mill cutter. The 8-toothed cutter has 100 mm diameter and 200 mm width. The feed per tooth is 0.1 mm, cutting velocity is 20 m/min and depth of cut is 2 mm. The machining time required to remove the entire stock is _______.

1.60 is the correct answer.

Ques 44 Mathematics

How many combinations of non-null sets A, B, C are possible from the subsets of {2, 3, 5} satisfying the conditions: (i) A is a subset of B, and (ii) B is a subset of C?

Ques 45 Mathematics

The bar chart gives the batting averages of VK and RS for 11 calendar years from 2012 to 2022. Considering that 2015 and 2019 are world cup years, which one of the following options is true?

RS has a higher yearly batting average than that of VK in every world cup year.

VK has a higher yearly batting average than that of RS in every world cup year.

VK’s yearly batting average is consistently higher than that of RS between the two world cup years.

RS’s yearly batting average is consistently higher than that of VK in the last three years.

Ques 46 Mathematics

Four equilateral triangles are used to form a regular closed three-dimensional object by joining along the edges. The angle between any two faces is

30°

60°

45°

90°

Ques 47 Mathematics

In order to numerically solve the ordinary differential equation 𝑑𝑦/𝑑𝑡 = −𝑦 for 𝑡 > 0, with an initial condition 𝑦(0) = 1, the following scheme is employed

Here, Δ𝑡 is the time step and 𝑦𝑛 = 𝑦(𝑛Δ𝑡) for 𝑛 = 0, 1, 2, …. This numerical scheme will yield a solution with non-physical oscillations for Δ𝑡 > ℎ. The value of ℎ is

1/2

3/2

Ques 48 Mathematics

The value of the surface integral

where 𝑆 is the external surface of the sphere 𝑥² + 𝑦² + 𝑧² = 𝑅² is

4𝜋𝑅³

(4𝜋/3) 𝑅³

𝜋𝑅³

Ques 49 Mathematics

Let 𝑓(𝑧) be an analytic function, where 𝑧 = 𝑥 + 𝑖𝑦. If the real part of 𝑓(𝑧) is cosh 𝑥 cos 𝑦, and the imaginary part of 𝑓(𝑧) is zero for 𝑦 = 0, then 𝑓(𝑧) is

cosh 𝑥 exp (−𝑖𝑦)

cosh 𝑧 exp 𝑧

cosh 𝑧 cos 𝑦

cosh z

Ques 50 Mathematics

Consider the system of linear equations
𝑥 + 2𝑦 + 𝑧 = 5
2𝑥 + 𝑎𝑦 + 4𝑧 = 12
2𝑥 + 4𝑦 + 6𝑧 = 𝑏
The values of 𝑎 and 𝑏 such that there exists a non-trivial null space and the system admits infinite solutions are

𝑎 = 8, 𝑏 = 14

𝑎 = 4, 𝑏 = 12

𝑎 = 8, 𝑏 = 12

𝑎 = 4, 𝑏 = 14

Ques 51 Mathematics

Let f(⋅) be a twice differentiable function from ℝ² → ℝ. If p, x₀ ∈ ℝ² where ‖ p ‖ is sufficiently small (here ‖ ⋅ ‖ is the Euclidean norm or distance function), then:

f(x₀ + p) = f(x₀) + ∇f(x₀)^T p + (1/2) p^T ∇² f(ψ) p

where ψ ∈ ℝ² is a point on the line segment joining x₀ and x₀ + p. If x₀ is a strict local minimum of f(x), then which one of the following statements is TRUE?

∇f(x₀)^T p > 0 and p^T ∇² f(ψ) p = 0

∇f(x₀)^T p = 0 and p^T ∇² f(ψ) p > 0

∇f(x₀)^T p = 0 and p^T ∇² f(ψ) p = 0

∇f(x₀)^T p = 0 and p^T ∇² f(ψ) p < 0

Ques 52 Mathematics

In the following series, identify the number that needs to be changed to form the Fibonacci series
1, 1, 2, 3, 6, 8, 13, 21,…

1 2 3 4 5

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