Production and Industrial Engineering
GATE PI kind:question PYQs
Build your understanding with focused practice from past exam papers.
Questions 491–500 of 650. Imported answers require independent review unless marked reviewed.
Question 26
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If the Laplace transform of
is
, the Laplace transform of
isYour answerChoose one option.
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General solution of the Cauchy-Euler equation
isYour answerChoose one option.
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A uniform cantilever beam
of length
is subjected to a point load
at point B and a concentrated moment
at point C (as shown in figure). Let
be the Young’s modulus of the beam material and
be the area moment of inertia of the beam’s cross-section. Assuming the validity of the Euler-Bernoulli theory of slender beams, the downward deflection at point C is 
Your answerChoose one option.
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Three Carnot engines
,
,
operate as shown in the figure (
). 
The efficiency of the engine
in terms of the efficiencies
and
of the engines
and
, respectively, isYour answerChoose one option.
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True centrifugal casting process in horizontal configuration is to be used for casting a metallic cylinder with outside diameter 0.275 m and inside diameter 0.250 m. If G-factor (ratio of centrifugal force experienced by the rotating cast metal to its weight) is 65 and acceleration due to gravity is 9.8 m/s², the minimum rotational speed (in rpm) required is closest to
Your answerChoose one option.
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In a sine bar, let
denote height of slip gauge and
be the distance between the rollers. The relationship between error in angular measurement (
) and errors in the slip gauge combination (
) and in the spacing of the rollers (
) isYour answerChoose one option.
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A 100 mm long cylindrical workpiece of diameter 50 mm is reduced to 25 mm diameter using extrusion process. The flow curve for the metal has strength coefficient as
MPa and the strain hardening co-efficient is 0.15. Assuming no friction and no redundant work, the required ram pressure (in MPa) is closest toYour answerChoose one option.
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An LPP is defined as
Minimize
subject to,
The objective function of the dual of this LPP is
Your answerChoose one option.
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A 20 mm HS drill with a point angle of 118° is used for drilling a through hole on a metallic plate of thickness 100 mm with a cutting speed of 333.33 mm/s and feed of 0.22 mm/rev. Assuming that the drill is touching the surface of the plate at the start, the drilling time (in s) is closest to
Your answerChoose one option.
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An acceptance sampling plan is selected with sample size
, acceptance number
for a lot size of 10,000 units. The probability of accepting the lot is based on Poisson distribution. Assuming rectification inspection, if incoming lot quality
is 0.03 and mean (
) is 2.4, the average outgoing quality (AOQ) is closest toYour answerChoose one option.
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