GATE CSE 2021 Set 1 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2021 Set 1

MCQ (Single Correct Answer)

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Consider the two statements.

S₁ : There exist random variables X and Y such that

(E[X - E(X)) (Y - E(Y))])² > Var[X] Var[Y]

S₂ : For all random variables X and Y,

Cov[X, Y] = E [|X - E[X]| |Y - E[Y]|]

Which one of the following choices is correct?

S₁ is false, but S₂ is true.

S₁ is true, but S₂ is false.

Both S₁ and S₂ are true.

Both S₁ and S₂ are false.

GATE CSE 2021 Set 1

MCQ (More than One Correct Answer)

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An articulation point in a connected graph is a vertex such that removing the vertex and its incident edges disconnects the graph into two or more connected components.

Let T be a DFS tree obtained by doing DFS in a connected undirected graph G. Which of the following option is/are correct?

If u is an articulation point in G such that x is an ancestor of u in T and y is a descendent of u in T, then all paths from x to y in G must pass through u.

Root of T is an articulation point in G if and only if it has 2 or more children.

Root of T can never be an articulation point in G.

A leaf of T can be an articulation point in G.

GATE CSE 2021 Set 1

MCQ (More than One Correct Answer)

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A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?

If a relation S is transitive and circular, then S is an equivalence relation.

If a relation S is reflexive and symmetric, then S is an equivalence relation.

if a relation S is reflexive and circular, then S is an equivalence relation.

if a relation S is circular and symmetric, then S is an equivalence relation.

GATE CSE 2021 Set 1

Numerical

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The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter 2. For a randomly picked component of this type, the probability that, its lifetime exceeds the expected lifetime (rounded to 2 decimal places) is ______.

Your input ____

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2023