List of top Questions asked in GATE PI

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)
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 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 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 .............
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 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 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 .............
Which one of the following functions is analytic, given \( i = \sqrt{-1} \)?
The solution of the linear differential equation \[ \frac{dy}{dx} + y = e^x, \] when \( y(0) = 0 \), is:
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)
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)
Which one of the following statements is FALSE with respect to the injection molding of polymer composite?
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:
A through hole of 8 mm diameter is to be drilled in a 30 mm thick mild steel plate. Which one of the following processes is the most appropriate to achieve high dimensional accuracy with less processing time?
In a work sampling, out of \( n \) observations, a worker was sitting idle in \( x \) observations. The standard deviation of the mean proportion of idle time is given by: