List of top Questions asked in GATE PI- 2024

A CNC milling operation is carried out by moving the tool from the point A to point B in anti-clockwise direction to cut a slot of quarter circle with center at C, as shown. The coordinates of the points A and B are (0,0) and (10,10), respectively. All dimensions are in mm. If the feed rate at point P along x-axis is 6 mm/min, then the feed rate (in mm/min) at point P along y-axis is ______ . (Rounded off to 1 decimal place)

A vector field is given as \(F(x, y) = (100x + 100y) i + (−50x + 200y) j\), where \(i\) and \(j\) are the unit vectors along the \(x\) and \(y\) axes in the Cartesian frame, respectively. Then the value of
\(∮F(x, y). dl\)
where \(dl = dx i + dy j\) is an elemental path taken over an anticlockwise circular contour \(C\) of radius \(r = 2\) is

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)

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 sand mold, a sprue of height \(h_2=200\ mm\) is to be provided for maintaining the molten metal flow rate of \(10^6\ mm^3/s\). The height of liquid column above the point 2 is kept constant at \(h_c=25\ mm\). The cross-sectional areas of the sprue at points 2 and 3 are \(A_2\) and \(A_3\), respectively. The points 1 and 3 are at the atmospheric pressure. Assuming the gauge pressure at point 2 to be zero as the limiting case to prevent aspiration effect, the ratio \(\frac {A_3}{A_2}\) _____ . (Rounded off to 2 decimal places)

In a time study, the average time taken for packaging a product in a warehouse by a worker with 120% performance rating is observed as 9 minutes. Assuming an allowance of 10% of the standard time, the standard time (in minutes) for packaging is ______ . (Answer in integer)

A company purchased two machines, Machine A and Machine B, at the same time. The purchase price, estimated useful life and the estimated salvage value of the two machines are given in the table.

	Machine A	Machine B
Purchase price	INR 20,000	INR 15,000
Estimated useful life	10 years	20 years
Estimated salvage value	INR 5,000	INR 5,000

Using the straight-line depreciation method for both the machines, the difference (in INR) between the value of Machine A and the value of Machine B at the end of five years is _____ . (Answer in integer)

The following differential equation governs the evolution of variable \(x(t)\) with time \(t, t \geq 0\).
\(\frac {d^2x}{dt^2} + 4x = e^{-t}\)
Given the initial conditions \(x = 0\) and \(\frac {dx}{dt} = 0\) at \(t = 0\), the value of \(x\) at \(t =\frac {\pi}{8}\) is _____  . (Rounded off to 3 decimal places)

An irrigation pump is used to draw water from a pond. One end of a 5.05 cm diameter hose pipe is connected to the outlet of the pump at 1.02 m below the surface level, and just after the pump, the static gauge pressure and flow rate of the water are 50 kPa and 8 kg/s, respectively. The pumped water is discharged at the ground level through a nozzle. Assume that the flow through the hose pipe and nozzle is steady and laminar, and frictional and viscous losses are negligible. The density of water is 1000 kg/m3 and the acceleration due to gravity is 9.81 m/s2. If the static pressure at the nose/exit of the nozzle just reduces to atmospheric pressure then the nose diameter (in cm) of the nozzle is _____ . (Rounded off to 2 decimal places)

In the Taylor series expansion of sin z around \(z = 0\), the coefficient of the term \(z^3\) is

In a single pass cold rolling operation, a flat plate is reduced to a thickness of 3 mm. In this operation, two rolls of diameter 400 mm each are rotating in opposite direction at 300 RPM, and the elastic deflection of these rolls is negligible. The angle of bite is 10°. If the neutral point is present at an angle of 7° from the exit side, then the thickness of the plate (in mm) at the neutral point is _____ . (Rounded off to 1 decimal place)

An offset slider-crank mechanism is shown in the figure. If the length l = 10 cm, then the stroke length (in cm) of the slider is _____ . (Rounded off to 1 decimal place)

If \(\lim\limits_{x \to1}(\frac {x^2-2ax+b}{x-1})=8\)
then \((a-b)\) is _____ . (Answer in integer)

The solidification time of a cube and a cylinder of the same material, produced through the same sand casting process, is found to be equal. Each side of the cube is \(a\), and the radius and the length of the cylinder are \(r\) and \(4r\), respectively. If the solidification time is governed by Chvorinov's equation, then the ratio \(\frac ra\) is

A metallic cylindrical pressure vessel, used to store compressed air in a plant, has 1 m mean radius and 4 mm wall thickness. The maximum allowable normal and shear stresses in the cylindrical portion of the vessel are 100 MPa and 40 MPa, respectively. Considering only these data in the design, the maximum allowable internal gauge pressure (in MPa) of the compressed air is ______ . (Rounded off to 2 decimal places)

A repairable machine operated for 2400 hours in a year and for that year the machine broke down 8 times. The mean time to repair including waiting time is found to be 20 hours for that year.
If the mean time to repair including waiting time could have been reduced to 10 hours for that year, then the improvement in the availability of that machine would be _____ %. (Rounded off to 2 decimal places)

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)

A company orders an item using the classical economic order quantity formula. If the ordering cost per order is increased by 20% and the demand per unit time is also increased by 20%, then the time between orders increases (in %) by ____ . (Answer in integer)

Five jobs A, B, C, D and E are available at time t = 0 for processing at a machine, and their processing times are listed.

Job	A	B	C	D	E
Processing time (in days)	9	6	4	5	8

If the jobs are processed using the shortest processing time (SPT) rule, the average flow time (in days) is _____ . (Rounded off to 1 decimal place)

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)

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)

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)

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)

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 = \(5.67 \times 10^{-8} W/m^2-K^4\)