List of top Questions asked in GATE PI- 2026

Iron powder produced by gas atomization has a tap density and an apparent density of 3.26 g/cm\(^3\) and 2.66 g/cm\(^3\), respectively. The density of solid iron is 7.85 g/cm\(^3\).
Which ONE of the following options is the closest approximation to the degree of densification (in percentage) of this iron powder?

Which ONE of the following options CORRECTLY matches the machining process and associated predominant material removal mechanism?

Advanced machining process		Predominant material removal mechanism
P	Laser beam machining	1	Impact based erosion
Q	Abrasive waterjet machining	2	Sputtering
R	Ion beam machining	3	Melting and vaporization
S	Mechanical milling	4	Shearing

A student is trying to determine the flatness and parallelism of the top surface of a part whose cross-section, assumed uniform in the Z direction, is shown in the figure.
Which ONE of the following options is CORRECT?

A sheet metal drawing is considered feasible if the following conditions are met:

Reduction ratio < 0.5
Thickness to diameter ratio > 1%

A sheet metal drawing process is being planned on a sheet metal with a thickness of 2 mm with a punch of diameter 100 mm with various blanks of diameter \( D_b \).
Which ONE of the following blank diameters \( D_b \) (in mm) will result in feasible drawing?

Consider the aggregate planning problem for a toy car manufacturing organization whose demand at a plant is as follows:

Month	September	October	November	December
Demand (in units)	8000	6500	10500	9500

The organization has ONLY the following options available for aggregate planning to meet the demand: (1) in-house production, (2) subcontracting, and (3) inventory holding. Assume that the quantity subcontracted in a given month is available in the same month.

A part of their optimal solution is as follows:
Inventory at the end of October = 1500 units
Units produced in-house in November = 8000 units
Units subcontracted in November = 1000 units

The inventory at the end of November is ______ units (in integer).

Consider the line integral
\[ \int_C (2x\, dx + 2y\, dy + 2z\, dz) \]
where \( C \) is a semi-circle in the \( z = 0 \) plane with start point at \( (0, 0, 0) \) and end point at \( (1, 0, 0) \).

The value of the line integral is ______ (in integer).

A modified Taylor tool life equation is given as follows:
\[ V T^n f^m = constant \]
where \( V \) is the cutting speed (m/s), \( T \) is the tool life in minutes and \( f \) is the feed in mm/rev, \( n = 0.25 \) and \( m = 0.5 \). Under two different cutting conditions \( (V_1, f_1) \) and \( (V_2, f_2) \) the tool life \( (T_1, T_2) \) was found to be the same.

If the ratio of the cutting speeds \( (V_1/V_2) \) used is 2/3, then the ratio of corresponding feeds \( (f_1/f_2) \) must be ______ (rounded off to two decimal places).

In a polymer extrusion process, some cross-sectional shapes of the extruded polymers are shown. Cross-sections of available dies are also shown.
Which ONE of the following options CORRECTLY matches the extruded cross section with the die opening that most likely generated it?
Note: The cross-sections are in a plane orthogonal to the extrusion direction. Figures are not to scale.

A square of side length 50 mm is to be blanked from a strip of 2 mm thickness. The sheet metal has a shear strength of 200 MPa.

To enable a single step blanking operation, the theoretical minimum blanking force required is ______ \( \times 10^3 \) N (in integer).

Note: Neglect the effect of clearances and friction.

A box in a machine shop consists of 5 coated and 10 uncoated cutting inserts which are of otherwise similar characteristics. The inserts got mixed up randomly in the box. An operator has taken 4 of them at once without noticing the differences to mount on a 4-tooth face milling cutter that uses inserts.

The probability of the milling cutter having all uncoated inserts is ______ (rounded off to two decimal places).

A customer has made a lumpsum investment of INR 2,00,000 with a bank. The discount rate is 15% per year. The investment enables the customer to receive a payout of INR 1,00,000 yearly for next three consecutive years.

The net present value (NPV) of his/her investment is INR ______ (rounded off to the nearest integer).

Which ONE or MORE among the following processes of the Carnot cycle is/are isentropic?

Note: Figure is not to scale

Which ONE or MORE among the options given is/are well established format(s) of data transfer used in geometrical modelling related to computer aided design (CAD)?

Which ONE or MORE among the following options CORRECTLY match(es) the type of defects with the corresponding metal working processes in which they are likely to occur?