List of top Questions asked in GATE PI

There are four locations (P, Q, R, S) and four factors to be considered for setting up a facility. The scores (on a scale of 0 to 10, with 10 being the maximum) for the given locations and the weight assigned to each factor are given as 

The best location for setting up the facility is

The dual of a LPP is
Minimize $w = 4w_1 + 6w_2 + 5w_3 - w_4$

Match the products to be manufactured with the given metal working processes. 

Match the recording techniques used in method study with the most appropriate application areas.

Match the engineering materials at room temperature with the given crystal structures. 

Six jobs (1, 2, 3, 4, 5, 6) undergo drilling, followed by reaming operation. The time required for each operation is given as \[ \begin{array}{|c|c|c|} \hline \text{Job} & \text{Drilling (min)} & \text{Reaming (min)} \\ \hline 1 & 30 & 40 \\ 2 & 30 & 15 \\ 3 & 60 & 40 \\ 4 & 20 & 25 \\ 5 & 35 & 28 \\ 6 & 45 & 70 \\ \hline \end{array} \] The sequence of processing the jobs, using the Johnson’s rule, is

A massless beam is fixed at one end and supported on a roller at other end. A point force \(P\) is applied at the midpoint of the beam as shown in figure. The reaction at the roller support is 

Match the machine elements with their functions. 

Given, \(z(x, y) = e^{x - 2y}\), where \(x(t) = e^t\) and \(y(t) = e^{-t}\). All the variables are real. The total differential \(\frac{dz}{dt}\) is
Two metal sheets are joined using resistance spot welding. A welding current of 4500 A is applied for 0.2 s. The effective contact resistance at the sheet interface is \(400 \times 10^{-6} \, \Omega\). The thermal efficiency of the welding process is 50%. The amount of heat, in J, used for producing a spot weld is ................. (in integer).

A wooden cubical block of side 0.1 m has specific gravity (SG) of 0.75. It is held submerged in a pool of oil and water by a massless rigid wire as shown in the figure. The density of water is 1000 kg/m$^3$ and acceleration due to gravity is 9.8 m/s$^2$. The tension, in N, in the wire is ................. (round off to 2 decimal places).

Travel details of two persons P and Q travelling from city X to city Y are given as: \[ \begin{array}{|c|c|c|c|} \hline \text{Person} & \text{Mode of travel} & \text{Monetary worth of functions} & \text{Ticket cost} \\ & & \text{(travel time and comfort), in Rupees} & \text{in Rupees} \\ \hline P & \text{Aircraft} & 8000 & 4000 \\ Q & \text{Train} & 2000 & 2000 \\ \hline \end{array} \] The positive difference in value of travel between the two modes is ................. (in integer).
Transformation matrix to translate a point P from (10, 15) to (15, 25) is

A symbol for surface texture parameters is shown in the figure. The difference between maximum and minimum values of surface roughness ($R_a$) is 

The combination of Directrix and Generatrix in a machining operation is shown in the figure. The surface produced is

Given matrices \[ A = \begin{bmatrix} 1 & -1 & 4 \\ 3 & 2 & -1 \\ 2 & 1 & -1 \end{bmatrix} \quad\text{and}\quad B = \begin{bmatrix} B_{11} & B_{12} & B_{13} \\ B_{21} & B_{22} & B_{23} \\ B_{31} & B_{32} & B_{33} \end{bmatrix} \] \(B\) is skew-symmetric matrix of \(A\). \(B_{13}\) is?

A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line. The given figure consists of 16 unit squares arranged as shown. In addition to the three black squares, what is the minimum number of squares that must be coloured black, such that both PQ and MN form lines of symmetry? (The figure is representative)

In the given figure, PQRS is a parallelogram with $PS = 7~\text{cm}$, $PT = 4~\text{cm}$ and $PV = 5~\text{cm}$. What is the length of $RS$ in cm? (The diagram is representative.)

A key of width and height of 6 mm each is used to fix a gear on a shaft of 20 mm diameter. The shaft is used to transmit 10 kW power at 600 rpm to the gear. Permissible shear stress in the key is 80 N/mm\(^2\), while compressive stress in the key is neglected. The minimum length of the key, in mm, is .................
A cylindrical casting has 10 cm diameter and a mass of 12.56 kg. The material density is \( 7.85 \times 10^{-3} \, \text{kg/cm}^3 \). The value of exponent \(n\) is 2 and solidification time is 12 min. The Chvorinov's constant, in min/cm\(^2\), is ................. (round off to 2 decimal places).
A pair of spur gears is designed to transmit 20 kW power at a pitch line velocity of 10 m/s. Diameter of the driving gear is 0.5 m. The tangential force, in N, between the driver and the driven gear is ................. (in integer).
Two products, P and Q, are sold in the ratio of 10:1. The fixed cost is Rs. 1,40,000. The selling price of P is Rs. 10/unit and Q is Rs. 40/unit. The variable costs of P and Q are Rs. 5/unit and Rs. 20/unit, respectively. The break-even point in terms of revenue, in Rs., is ................. (in integer).
A CNC water jet cutting machine is used to cut a straight slot between the points (2, 1) and (10, 10) on the XY plane (dimensions are in mm). If the feed rate is 1.5 mm/s, the time, in s, required to machine the slot following the shortest path, is ................. (round off to 2 decimal places).
In an orthogonal cutting with a tool of rake angle \(0^\circ\), the value of the cutting force is two times of the thrust force. The coefficient of friction is ................. (round off to 1 decimal place).
The solidification of a cubical casting of side 100 mm takes place with volumetric solidification shrinkage and solid contraction of 10% each. The shape of the casting is retained on cooling to room temperature. The side of the cubical cast, in mm, at room temperature is ................. (round off to 2 decimal places).