List of top Questions asked in GATE PI

The least number of squares that must be added so that the line P-Q becomes the line of symmetry is 

The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago? 
 

A 3.5 mm thick sheet is rolled using a two high rolling mill to reduce the thickness under plane strain condition. Both rolls have a diameter of 500 mm and are rotating at 200 RPM. The coefficient of friction at the sheet and roll interface is 0.08, and the elastic deflection of the rolls is negligible. If the mean flow strength of the sheet material is 400 MPa, then the minimum possible thickness (in mm) of sheet that can be produced in a single pass is _________. 
[round off to 2 decimal places]

Temperature field inside a sphere of radius \( R = 1 \, \text{m} \) with origin at its center is \[ T(x, y, z) = 100 - 70x + 51y - 80z - 10x^2 - 20y^2 - 20z^2. \] If thermal conductivity of the sphere material is \( K = 50 \, \text{W/m.K} \) and Fourier law of heat conduction is valid, net heat leaving the sphere per unit time in W is _________. 
[round off to one decimal place]

Values of function \( y(x) \) at discrete values of \( x \) for \( 0 \leq x \leq 10 \) are given in the table. Using trapezoidal rule, 
= _________. 

Consider the truss shown in the figure. The members AB, BC, and CA are all rigid and form an equilateral triangle. The contact between roller and ground at C is frictionless. If the self-weight of members is neglected, the force in member BC in N is (negative sign should be used if the force is compressive and positive if the force in the member is tensile) _________. 

A 30 kg smooth, solid sphere rests on two frictionless inclines as shown in the figure. The magnitude of contact force in N acting at the point A is (take acceleration due to gravity \( g = 9.81 \, \text{m/s}^2 \) and consider both sphere and inclines to be rigid) _________. 
[round off to 2 decimal places]

In a point-to-point open-loop NC drive, a stepper motor with 1.8° step angle is coupled to a leadscrew through a gear reduction of 4:1 (4 rotations of the motor enables 1 rotation of leadscrew). The single-start leadscrew has a pitch of 4 mm. The worktable of the system is driven by the leadscrew. If the table moves at a uniform speed of 10 mm/s, the pulse frequency (in Hz) required to drive the stepper motor is _________. 

A project consists of eight activities. The time required for each activity and its immediate predecessor(s) are given in the table below. 

If the project completion time using critical path method (CPM) is 15 days, then the value of X (in days) is _________.

A machine shop has received four jobs A, B, C, and D for processing on a single CNC machine. All jobs are available for processing on the first day of the production schedule calendar, and processing times and due dates as applicable on the first day are given below. Using earliest due date rule, the average tardiness (in days) is _________. 

A company manufactures two products P and Q with unit profit of 4 and 5, respectively. The production requires manpower and two kinds of raw materials R1 and R2. The following table summarizes the requirement and availability of resources. 

The maximum profit the company can make is 
 

The eigenvalues of matrix 

are 5 and 10. For matrix \( B = A + \alpha I \), where \( \alpha \) is a constant and \( I \) is the \( 2 \times 2 \) identity matrix, its eigenvalues are 
 

A retail chain company has identified four sites A, B, C and D to open a new retail store. The company has selected four factors as the basis for evaluation of these sites. The factors, their weights, and the score for each site are given in the following table. 

The site that should be selected to open the new retail store is 
 

Two cylindrical parts of equal length \( l \), as shown in the figure, made of steel having Young's modulus \( E = 200 \, \text{GPa} \) and Poisson's ratio \( \nu = 0.33 \) are press fitted upon one another. If radial interference \( \delta = 0.05 \, \text{mm} \) and radii \( R = 25 \, \text{mm} \) and \( R_0 = 40 \, \text{mm} \), then the contact pressure \( P \) in MPa at the interface upon press fit is 

A circular rod of length \( l = 2 \, \text{m} \) is subjected to a compressive load \( P \), as shown in the figure. The bending (flexural) rigidity of the rod is \( 2000 \, \text{Nm}^2 \). If both ends are pinned, then the critical load \( P_{cr} \) in N (rounded to the nearest integer) at which the rod buckles elastically is 

A cantilever beam of length 0.3 m is subjected to a uniformly distributed load \( C = 10 \, \text{kN/m} \), as shown in the figure. The bending (flexural) rigidity of the beam is 5000 Nm\(^2\). Neglecting the self-weight of the beam, the magnitude of beam curvature in m\(^{-1}\) at the fixed end is 

Match the measuring feature with the corresponding measuring instrument in the table below. 

Match the component with the corresponding manufacturing process in the table below.