GATE CSE 2019 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2019

MCQ (Single Correct Answer)

-0.33

Let G be an arbitrary group. Consider the following relations on G :

R₁: ∀a,b ∈ G, aR₁b if and only if ∃g ∈ G such that a = g^-1bg

R₂: ∀a,b ∈ G, aR₂b if and only if a = b^-1

Which of the above is/are equivalence relation/relations?

R₁ only

Neither R₁ nor R₂

R₁ and R₂

R₂ only

GATE CSE 2019

MCQ (Single Correct Answer)

-0.33

Compute $$\mathop {\lim }\limits_{x \to 3} {{{x^4} - 81} \over {2{x^2} - 5x - 3}}$$

Limit does not exits

$${{53} \over {12}}$$

$${{108} \over {7}}$$

GATE CSE 2019

MCQ (Single Correct Answer)

-0.67

Let G be any connected, weighted, undirected graph.

I. G has a unique minimum spanning tree, if no two edges of G have the same weight.

II. G has a unique minimum spanning tree, if, for every cut of G, there is a unique minimum-weight edge crossing the cut.

Which of the above two statements is/are TRUE?

I only

II only

Both I and II

Neither I nor II

GATE CSE 2019

Numerical

-0

Consider the following matrix :

$$ R=\left[\begin{array}{cccc} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{array}\right] $$

The absolute value of the product of Eigen values of $R$ is ___________.

Your input ____

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