List of top Questions asked in GATE PI

An assembly line consists of three work stations (\(S_1, S_2\) and \(S_3\)) in series to assemble a toy. The times required to perform tasks at these stations are 6, 4 and T minutes, respectively. If the efficiency of the assembly line in the steady state is 75%, then the maximum value of T (in minutes) is _____ . (Answer in integer)

The pitch of a metric screw thread is calculated from pitch circle diameter measurement through two-wire method. If the thread is single-start with calculated pitch of 1.4 mm then the diameter (in mm) of the best-wire is ______ . (Rounded off to 2 decimal places)

During orthogonal turning, the cutting speed, feed and depth of cut are set as 2 m/s, 0.2 mm/rev and 2 mm, respectively. The specific cutting energy (neglecting the effect of feed force on the total cutting power) is 2 J/mm³. The main cutting force (in N) is _____ . (Answer in integer)

Mild steel plates are welded to make butt joints by arc welding with 85% heat transfer efficiency ignoring other losses. The first weld joint is made by selecting arc voltage of 30 V and current of 180 A with a welding speed of 6 mm/s. Using identical plates, a second weld joint is made with the same arc voltage and a welding speed of 8 mm/s. If both the welds have the same heat input, then the welding current (in A) for the second weld joint is _____. (Answer in integer)

Electro-chemical machining is performed on a flat copper workpiece. If the material removal rate is \(2\ cm^3/min\) throughout the process, then the required current (in A) is ______ . (Rounded off to 1 decimal place)
Copper properties: Melting point = \(1085 °C\), density = \(9\ g/cm^3\), gram atomic weight = \(63\), and valency of dissolution = \(2\)
Faraday's constant = \(96500 C\)
Stefan-Boltzmann constant = \(5.67 \times 10^{-8} W/m^2-K^4\)

The following data are given in relation to turning operation of a cylindrical workpiece.
Diameter of the workpiece = 160 mm, length of the workpiece = 190 mm, cutting velocity = 80 m/min, and tool feed = 0.2 mm/rev.
Assuming the approach and the overrun of the tool to be 5 mm each, the machining time (in minutes) is _____ . (Answer in integer)

A flat belt drive with pulley of r = 20 cm radius is designed to transmit 6.283 kW power at 600 RPM. In the figure, τ is the corresponding torque. If the coefficient of static friction between the belt and the pulley is 0.3, then the minimum value of the tightening force F (in kN) required to prevent the belt slip is _____ . (Rounded off 2 decimal places)

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

A project has six activities and the precedence relationship among them is shown in the table.

Activity	Precedent activities
A	None
B	None
C	None
D	A, B
E	B,C
F	A, B

The minimum number of dummy activities needed to draw an activity-on-arrow (AOA) representation of the project network is ___ .

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)

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

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)?

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

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)

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

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)

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)

A blank of 100 mm diameter is to be cut out of a 2 mm thick sheet through blanking operation. If the radial clearance between the punch and die is 6% of the sheet thickness then the diameter (in mm) of the punch 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

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 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?

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

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

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