List of top Questions asked in GATE PI

A through hole of 10 mm diameter is to be drilled in a mild steel plate of 30 mm thickness. The selected spindle speed and feed for drilling hole are 600 revolutions per minute (RPM) and 0.3 mm/rev, respectively. Take initial approach and breakthrough distances as 3 mm each. The total time (in minute) for drilling one hole is ______. (Rounded off to two decimal places) 
 

In a cold rolling process without front and back tensions, the required minimum coefficient of friction is 0.04. Assume large rolls. If the draft is doubled and roll diameters are halved, then the required minimum coefficient of friction is ___________. (Rounded off to two decimal places) 
 

Which one of the following casting defects is caused due to the supply of the molten metal through two gates?
The relationship between the hoop stress \(\sigma_1\) and the longitudinal stress \(\sigma_2\) of a closed cylindrical thin-walled pressure vessel is
Three principal stresses at a point in a material are 300 MPa, 250 MPa, and 100 MPa. If the yielding just starts at that point, the yield strength (in MPa) of the material as per Tresca criterion is ............
Answer: The yield strength lies between 199 to 201 MPa.
In an orthogonal straight turning process, the feed is 0.1 mm/rev and the depth of cut is 0.5 mm. In ASA system, the side cutting edge angle of the cutting tool is 0°. The width (in mm) of the chip is ............ (Rounded off to one decimal place)
The pitch of the single-start lead screw of a lathe is 6 mm. It is used to cut double start thread of 3 mm pitch on a cylindrical work piece. During the thread cutting, the spindle rotates at 400 revolutions per minute (RPM). The speed (in RPM) of the lead screw is ............ (Answer in integer)
Two options are available to meet the annual demand of batteries in a toy company. In option 1, batteries are manufactured in the plant having fixed cost of Rupees 2,00,000 and a variable cost of Rupees 70 per unit. Option 2 consists of buying batteries from the market at a price of Rupees 90 per unit. The annual demand (in number of batteries) at which the company should switch from buying to making the batteries in the plant is .......... (Answer in integer)
A company estimates the demand of 2000 bulbs for the next year. The ordering cost is Rupees 300 per order and the annual carrying cost per bulb is Rupees 30. The economic order quantity (number of bulbs) is .......... (Answer in integer)
While inspecting final assembly of automobile-gear-boxes, 15 features were considered critical-to-quality (CTQ). During last quarter, 40000 gear boxes were produced among which 1500 defects were found of the CTQ features. The defects per million opportunities (DPMO) is .......... (Answer in integer)

The hole and the shaft dimensions (in mm) are given as
Hole dimension = \(30 \pm 0.04\) and Shaft dimension = \(30 \pm 0.06\). 
The maximum possible clearance (in mm) is .......... (Rounded off to two decimal places)
 

The value of the integral \[ \int_1^3 \left( x^2 - 2x \right) \, dx \] obtained by using Simpson’s 1/3 rule with 4 subintervals is equal to \( \frac{n}{3} \). The value of \( n \) is .............
If \( i \), \( j \), and \( k \) are the orthogonal unit vectors in Cartesian x-y-z coordinate system, the rate of change of the function \( f(x, y, z) = x^2 + 2y^2 + z \) at point \( (1, 1, 1) \) in the direction of \( 3i + 4k \) is .............
In a wire drawing of a perfectly-plastic material with flow stress of 300 MPa, the back tension is zero and front tension is 200 MPa. Assuming ideal deformation with zero friction, the percentage reduction of the cross-sectional area of the wire is .............
In a cold rolling process without front and back tensions, the required minimum coefficient of friction is 0.04. Assume large rolls. If the draft is doubled and roll diameters are halved, then the required minimum coefficient of friction is .............
In a direct current arc welding, the voltage \( V \) (in volt) is related to the arc length \( l \) (in cm) as \[ V = 30 + 30l. \] The open circuit voltage is 80 volts. The maximum possible arc length is ............. (Rounded off to two decimal places)
A worker is allowed half an hour personal time in a normal 8-hour shift. If the normal time for manufacturing a product is 5 minutes, the standard time (in seconds) is .............
A product has to be manufactured in a single-line layout by carrying out the six tasks in a sequence. The time (in minutes) of the six sequential tasks are 37, 8, 19, 34, 36, and 17. These tasks cannot be further sub-divided. For minimizing the cycle time, the number of stations to be used is .............
A through hole of 10 mm diameter is to be drilled in a mild steel plate of 30 mm thickness. The selected spindle speed and feed for drilling hole are 600 revolutions per minute (RPM) and 0.3 mm/rev, respectively. Take initial approach and breakthrough distances as 3 mm each. The total time (in minute) for drilling one hole is ............. (Rounded off to two decimal places)
In the iron-carbon equilibrium phase diagram, the eutectoid reaction occurs at 723°C with the eutectoid composition of 0.83 weight % carbon. Ferrite and cementite phases are considered to contain 0.022 weight % carbon and 6.67 weight % carbon, respectively. If a steel specimen with 0.7 weight % carbon is cooled from 950°C to below 723°C, the fraction of eutectoid ferrite is .............
During orthogonal cutting with a tool of 10° rake angle, the cutting and thrust forces are 900 N and 275 N, respectively. The coefficient of friction on the rake surface of the tool is .............
In casting a cube of 80 mm side, the volumetric shrinkages due to solidification and solid contraction are 4.5% and 2%, respectively. Assume uniform cooling in all directions. The side (in mm) of the cubical pattern for getting the required size casting is .............
The solidification of a casting starts at 10 AM. However, the solidification of the molten metal at the center-line of the mold starts at 10:03 AM and ends at 10:10 AM. The casting is considered solidified completely when the solidification is completed at the center-line of the mold. The center-line feeding resistance (CFR) in percentage is .............

A link \( OA \) of length 200 mm is rotating counterclockwise about \( O \) in the \( x \)-\( y \) plane with a constant angular velocity of 100 rad/s, as shown in the figure. The absolute value of the \( x \)-component of the linear velocity (in m/s) of point \( A \) at the instant shown in the figure is .............. 

A force of 1000 N is acting at point \( A \) on a bracket fixed at point \( B \) as shown in the figure. The magnitude of the moment of the force about \( B \) (in N·m) is ..............