Electronics and Communication Engineering
GATE ECE area:engineering-mathematics PYQs
Build your understanding with focused practice from past exam papers.
Questions 61–70 of 100. Imported answers require independent review unless marked reviewed.
Question 54
Open questionECNAT2 marksNeeds review
is a random variable with uniform probability density function in the interval
. For
, the conditional probability
(rounded off to three decimal places) is __________ .Log in to check the answer
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Which one of the following functions is analytic over the entire complex plane?
Your answerChoose one option.
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The families of curves represented by the solution of the equation
for
and
, respectively, areYour answerChoose one option.
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The value of the contour integral
evaluated over the unit circle
is ______.Log in to check the answer
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The number of distinct eigenvalues of the matrix
is equal to ______.Log in to check the answer
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If
and
are random variables such that
and
, then
_____.Log in to check the answer
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Open questionECNAT1 markNeeds review
The value of the integral
, is equal to _____.Log in to check the answer
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Open questionECNAT1 markNeeds review
Let
be an exponential random variable with mean 1. That is, the cumulative distribution function of
is given by
. Then
, rounded off to two decimal places, is equal to _____.Log in to check the answer
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Open questionECMCQ2 marksNeeds review
Consider a differentiable function
on the set of real numbers such that
and
. Given these conditions, which one of the following inequalities is necessarily true for all
?Your answerChoose one option.
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Open questionECMCQ2 marksNeeds review
Consider the line integral
, the integral being taken in a counterclockwise direction over the closed curve
that forms the boundary of the region
shown in the figure below. The region
is the area enclosed by the union of a
rectangle and a semi-circle of radius 1. The line integral evaluates to 
Your answerChoose one option.
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