GATE PI format:nat PYQs & Answers

Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.

Questions 1–10 of 264. Imported answers require independent review unless marked reviewed.

Topic practice 264 questionsPage 1 of 27

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 _____ × 10³ N (in integer).

Note: Neglect the effect of clearances and friction.

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A box in a machine shop consists of 5 coated and 10 uncoated cutting inserts which are of otherwise similar characters. 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).

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A customer has made a lump sum 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).

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A modified Taylor tool life equation is given as follows:

where

is the cutting speed (m/s),

is the tool life in minutes and

is the feed in mm/rev,

and

. Under two different cutting conditions

and

the tool life

was found to be the same.

If the ratio of the cutting speeds

used is 2/3, then the ratio of corresponding feeds

must be _____ (rounded off to two decimal places).

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Consider the line integral

where

is a semi-circle in the

plane with start point at

and end point at

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

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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	950

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).

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A linear slot is to be milled in a single pass from the point

on XY plane by a CNC machine. The actual velocity along the Y-axis is 5% less than the intended value. The programmed feed rate along the intended slot is 150 mm/min.

The magnitude of the positional error along the Y-axis when the X-coordinate reaches 180 mm is _____ mm (in integer).

Note: All coordinates are in mm.

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In laser beam machining, the time (

) required for the material to attain the melting temperature from a room temperature (

) of 32 °C is expressed by the following expression,

where

is thermal diffusivity,

is melting temperature,

is thermal conductivity,

is heat flux.

If a uniformly distributed 1 kW power laser beam with a beam diameter of 0.1 mm is used for machining tungsten carbide, and 10% of beam absorption is assumed, the time

is _____ μs (rounded off to one decimal place).

Note: Thermal properties of tungsten carbide: melting temperature = 3400 °C; thermal conductivity = 2.15 Wcm⁻¹°C⁻¹; diffusivity = 0.79 cm²s⁻¹; assume

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In the measurement of surface roughness using a 2D stylus profilometer, a surface profile measured over a length of 0.8 mm was recorded on a graph paper. During recording, vertical magnification of 10,000 and horizontal magnification of 100 were used. The areas in the as-recorded graph above and below the datum line are as follows:

Above (mm²): 140, 60, 150, 50 Below (mm²): 70, 50, 120, 160

The average surface roughness (

) of the surface is _____ μm (rounded off to two decimal places).

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A cylindrical metal component of 10 mm diameter is subjected to uniform uniaxial tension during operation. It was observed that a force of 14 kN produces a uniform reduction of

mm in diameter. Assume that material behaviour is homogeneous, isotropic, and linear elastic.

If its Young’s modulus is 150 GPa, the Poisson’s ratio of the material is _____ (rounded off to two decimal places).

Note: Assume

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GATE PI format:nat PYQs

How to practice format:nat

Question 30

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Question 55