List of top Questions asked in GATE PI

A CNC vertical milling is used for cutting a straight line slot in the x-y plane. The cutter is located at point P. The slope \( \frac{dy}{dx} \) of the straight line created by the cutter is 1.25. The feed rate of x-axis is 120 mm/min. The new position of the cutter after 20 seconds is: 

Match the operation/phenomenon in a grinding process with the corresponding definition listed in the table. 

Match the following with reference to the machining process and its feature. 

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)
 

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)
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)
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)

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 ............ 

For an ideal Diesel cycle, the heat addition is an:

The starting simplex table of a linear programming problem is given below, where \( S_1, S_2, S_3, S_4 \) are the slack variables. The objective of the problem is
Maximize \( z = 6x_1 + 4x_2 \)
The leaving variable among the basic variables is:

A simply supported beam \( AB \) of span \( L \) is shown in the figure. A moment \( M \) is applied at point \( C \). The magnitude of the reaction force at point A is:

Match the following with reference to the CNC machine and its minimum number of axes available in the machine.

Atomic packing factor of a body centered cubic structure is closest to:
An aircraft has two engines, each having a reliability \( R \). The aircraft will crash only when both engines stop working. The reliability of the aircraft flying without crash is:
A bag contains 5 red, 7 green, and 3 blue balls. Two balls are drawn at random from the bag one-by-one. The probability of the second drawn ball being red is:
The eigenvalues of the matrix \( A = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix} \) are:
A broaching machine makes key slots with a mean dimension of 10.56 mm and a standard deviation of 0.05 mm. The upper control limit for mean of sample size 5 calculated using X-bar (\( \bar{X} \)) chart is .............. (Rounded off to two decimal places)
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)
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 .............
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 .............