Mechanical Engineering
GATE ME area:engineering-mathematics PYQs
Build your understanding with focused practice from past exam papers.
Questions 61–70 of 148. Imported answers require independent review unless marked reviewed.
Question 3
Open questionMEMCQ1 markNeeds review
The Dirac-delta function
for
, has the following property
The Laplace transform of the Dirac-delta function
for
;
isYour answerChoose one option.
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Open questionMEMCQ1 markNeeds review
The mean and variance, respectively, of a binomial distribution for
independent trials with the probability of success as
, areYour answerChoose one option.
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Open questionMEMCQ1 markNeeds review
The ordinary differential equation
subject to an initial condition
is solved numerically using the following scheme:
where
is the time step,
, and
. This numerical scheme is stable for all values of
in the interval ________.Your answerChoose one option.
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Open questionMEMCQ1 markNeeds review
Consider a binomial random variable
. If
are independent and identically distributed samples from the distribution of
with sum
, then the distribution of
as
can be approximated asYour answerChoose one option.
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Open questionMEMCQ1 markNeeds review
Value of
using Simpson’s one-third rule with interval size 0.3 isYour answerChoose one option.
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Open questionMEMCQ1 markNeeds review
Value of
, where
, is equal toYour answerChoose one option.
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Open questionMEMCQ2 marksNeeds review
Consider a vector
in 2-dimensional space. Let its direction (counter-clockwise angle with the positive
-axis) be
. Let
be an eigenvector of a
matrix
with corresponding eigenvalue
,
. If we denote the magnitude of a vector
by
, identify the VALID statement regarding
, where
.Your answerChoose one option.
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Open questionMEMCQ2 marksNeeds review
The value of
isYour answerChoose one option.
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Open questionMEMCQ2 marksNeeds review
Let
represent the unit circle centered at origin in the complex plane, and complex variable,
. The value of the contour integral
(where integration is taken counter clockwise) isYour answerChoose one option.
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Open questionMEMCQ2 marksNeeds review
Let the superscript
represent the transpose operation. Consider the function
, where
and
are
vectors and
is a symmetric
matrix. The stationary point of
isYour answerChoose one option.
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