# GATE Mechanical Engineering 2023

 Question 1
A machine produces a defective component with a probability of 0.015. The number of defective components in a packed box containing 200 components produced by the machine follows a Poisson distribution. The mean and the variance of the distribution are
 A 3 and 3, respectively B $\sqrt{3}$ and $\sqrt{3}$ , respectively C 0.015 and 0.015, respectively D 3 and 9, respectively
Industrial Engineering   Production Planning and Control
Question 1 Explanation:
P = 0.015
n = 200
mean $=\lambda =np= 200 \times 0.015 = 3$
variance $=\sigma ^2=\lambda =3$
 Question 2
The figure shows the plot of a function over the interval [-4, 4]. Which one of the options given CORRECTLY identifies the function?

 A $|2-x|$ B $|2-|x||$ C $|2+|x||$ D $2-|x|$
Engineering Mathematics   Calculus
Question 2 Explanation:
(a) Graph of y = 2 - x

(b) Graph of y = |2 - x|

(c) Graph of y = |2 - |x||

 Question 3
With reference to the Economic Order Quantity (EOQ) model, which one of the options given is correct?

 A Curve P1: Total cost, Curve P2: Holding cost, Curve P3: Setup cost, and Curve P4: Production cost. B Curve P1: Holding cost, Curve P2: Setup cost, Curve P3: Production cost, and Curve P4: Total cost. C Curve P1: Production cost, Curve P2: Holding cost, Curve P3: Total cost, and Curve P4: Setup cost. D Curve P1: Total cost, Curve P2: Production cost, Curve P3: Holding cost, and Curve P4: Setup cost.
Industrial Engineering   Inventory Control
Question 3 Explanation:

 Question 4
Which one of the options given represents the feasible region of the linear programming model:
\begin{aligned} Maximize\;\; 45X_1&+60X_2 \\ X_1&\leq 45 \\ X_2&\leq 50 \\ 10X_1+10X_2& \geq 600 \\ 25X_1+5X_2&\leq 750 \end{aligned}

 A Region P B Region Q C Region R D Region S
Industrial Engineering   Linear Programming
Question 4 Explanation:
\begin{aligned} x_1&=45 &...(i)\\ x_2&= 50&...(ii)\\ 10x_1+10x_2&=600 \\ or\; x_1+x_2&=60&...(iii) \\ 25x_1+5x_2&=750 \\ or\; 5x_1+x_2&=150&...(iv) \\ \end{aligned}
By drawing the curve we get 3 values of $x_1$ and $x_2$ as (10, 50), (20, 50), (22.5, 37.5)
So, $Z_{max}=45x_1+60x_2$ for (10,50)
$Z_{max}=450+3000=4450$
for (20,50)
$Z_{max}=45\times 20+50 \times 60=3900$
for (22.5, 37.5)
$Z_{max}=45\times 22.5+60 \times 37.5=3262.5$
So, $Z_{max}=3900\; for \; (x_1,x_2)=(20,50)$
 Question 5
A cuboidal part has to be accurately positioned first, arresting six degrees of freedom and then clamped in a fixture, to be used for machining. Locating pins in the form of cylinders with hemi-spherical tips are to be placed on the fixture for positioning. Four different configurations of locating pins are proposed as shown. Which one of the options given is correct?

 A Configuration P1 arrests 6 degrees of freedom, while Configurations P2 and P4 are over-constrained and Configuration P3 is under-constrained. B Configuration P2 arrests 6 degrees of freedom, while Configurations P1 and P3 are over-constrained and Configuration P4 is under-constrained. C Configuration P3 arrests 6 degrees of freedom, while Configurations P2 and P4 are over-constrained and Configuration P1 is under-constrained. D Configuration P4 arrests 6 degrees of freedom, while Configurations P1 and P3 are over-constrained and Configuration P2 is under-constrained.
Manufacturing Engineering   Machining and Machine Tool Operation
Question 5 Explanation:
3-2-1 principle of location
The 3-2-1 principle of location (six point location principle) is used to constrain the movement of workpiece along the three axes XX, YY and ZZ.
This is achieved by providing six locating points, 3-pins in base plate, 2-pins in vertical plane and 1-pin in a plane which is perpendicular to first two planes.

There are 5 questions to complete.