List of top Questions asked in GATE PI- 2024

In an air-standard Otto cycle, the pressure and temperature of air just before the compression stroke are 200 kPa and 26.85 °C, respectively. The combustion process is assumed to be a constant volume process, where 1.02 MJ/kg heat is added. The cycle efficiency is 50%. The adiabatic index \(γ\) and specific heat at constant volume \(C_v\) can be considered to be constant during the process (corresponding values taken at the mean cycle temperature).
Assuming that the ideal gas law is applicable, \(γ = \frac 43\) and \(c_v= 0.85\ kJ/kg-K\), the maximum pressure (in MPa) reached during the cycle is _____ . (Rounded off to 1 decimal place)

The values of function \(y(x)\) at discrete values of \(x\) are given in the table. The value of \(∫_0^4y(x)dx\), using Trapezoidal rule is _____ . (Rounded off to 1 decimal place)

x	0	1	2	3	4
y(x)	1	3	6	9	12

In a forming operation, the plastic deformation of a steel specimen starts under plane stress condition, where the principal stresses are \(σ_1=200\ Mpa\) and \(σ_2 = 100\ Mpa\). If the steel specimen follows von-Mises yield criterion, then the uniaxial tensile yield strength (in Mpa) of this steel material is ____ . (Rounded off to 1 decimal place)

Match the configurations of the listed 3 degrees-of-freedom industrial robots with the type of joints.

Configuration		Type of joints
P	Cartesian	1	One prismatic and two rotary
Q	Cylindrical	2	Three rotary
R	Spherical	3	Two prismatic and one rotary
S	Articulated	4	Three prismatic

Consider the following linear programming problem with two decision variables \(x_1\) and \(x_2\). There are three constraints involving resources \(R_1, R_2\) and \(R_3\) as indicated.
Maximize \(Z = 6x_1+5x_2\)
Subject to
\(2x_1+5x_2\leq 40\)       \(R_1\)
\(2x_1 + x_2 \leq 22\)         \(R_2\)
\(x_1 + x_2 \leq 13 \)           \(R_3\)
\(X_1 \geq0, \ X_2 \geq 0\)
The optimal solution of the problem is: \(x_1 =9\)  and \(x_2=4\)
For which one of the following options, the shadow price of the resource(s) will have non-zero value(s)?

Choose the item(s) which is/are required to make an eccentric hole on a disc, as shown, using a lathe.

Which of the following statement(s) is/are TRUE for a given acceptance sampling plan?

Seven cards numbered 1 to 7 are placed in a box. After thoroughly mixing all the cards, one card is drawn at random.
If it is known that the number on the card drawn is odd, then the probability that the number on the card drawn is greater than 4 is _____ %. (Answer in integer)

In the truss shown in the figure, member AC is an inextensible string, other members are rigid, and ABCD is a square with each side of length a. The maximum value of force F (in kN) for which the truss will remain in static equilibrium is _____ . (Rounded off to 2 decimal places)

If \(A=\begin{bmatrix} a & b\\[0.3em] c & -a \\[0.3em] \end{bmatrix}\)is a matrix such that \(A^2=I\), where \(I\) is an identity matrix, then which of the following is TRUE?

In the iron-carbon equilibrium phase diagram, the temperature and composition of the eutectoid point are 727 °C and 0.77 weight % carbon, respectively. If a steel specimen with 1.2 weight % carbon is cooled from 1000 °C to the room temperature, then the fraction of pro-eutectoid cementite phase in the steel is _____ . (Rounded off to 2 decimal places)

For polymers, match each process with the most suitable application listed.

Process		Application
P	Extrusion	1	Producing complex parts with close tolerance
Q	Injection molding	2	Producing thermosetting plastic components
R	Blow molding	3	Producing long uniform sections
S	Compression molding	4	Producing hollow shapes

In a complex function
\(f(x, y) = u(x, y) + i v(x, y),\)
\(i\) is the imaginary unit, and \(x, y, u(x, y)\) and \(v(x, y)\) are real.
If \(f(x, y)\) is analytic then which of the following equations is/are TRUE?

For a mild steel specimen subjected to uniaxial tensile load, which of the following is/are TRUE?

Which among the following is/are TRUE for friction stir welding (FSW) process?

Which of the following areas is/are supply chain decision(s)?

If \(X\) is a continuous random variable with the probability density function
\(f(x) =   \begin{cases}     \frac K4      & ; 0\leq x \leq 1\\     0 & ; \text{otherwise}    \end{cases}\)
Then the value of \(K\) is _____ . (Answer in integer)

Which one of the following methods requires the least amount of data for forecasting?

Which one of the following is not true about Total Productive Maintenance (TPM)?

The following layout of four departments P, Q, R and S is provided as input to CRAFT (Computerized Relative Allocation of Facilities Technique). Which one of the following department pairs cannot be considered for exchange in CRAFT?

Which of the following concepts is not closely inter-related with INTERCHANGEABILITY in the context of product design?

Which one of the following THERBLIGS does not advance the progress of the work and can be eliminated by applying the principles of motion economy?

If work sampling is carried out using a large number of observations, then the required sample size is estimated using

Which of the following is NOT an assumption of a linear programming problem?

In a single server Markovian queuing system, if the customers arrive following the Poisson distribution, then the inter-arrival time follows