GATE CSE 2019 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2019

MCQ (Single Correct Answer)

-0.33

Let U = {1, 2 ,..., n}. Let A = {(x, X) | x ∈ X, X ⊆ U}. Consider the following two statements on |A|.

I. |A| = n2^n–1

II. |A| = $$\sum\limits_{k = 1}^n {k\left( {\matrix{ n \cr k \cr } } \right)} $$

Which of the above statements is/are TRUE?

Neither I nor II

Only II

Both I and II

Only I

GATE CSE 2019

Numerical

-0

Two numbers are chosen independently and uniformly at random from the set {1, 2, ...., 13}. The probability (rounded off to 3 decimal places) that their 4-bit (unsigned) binary representations have the same most significant bit is ______.

Your input ____

GATE CSE 2019

MCQ (Single Correct Answer)

-0.33

Let X be a square matrix. Consider the following two statements on X.

I. X is invertible.

II. Determinant of X is non-zero.

Which one of the following is TRUE?

I implies II; II does not imply I

II implies I; I does not imply II

I does not imply II; II does not imply I

I and II are equivalent statements

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

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