GATE CSE 2024 Set 1 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2024 Set 1

MCQ (More than One Correct Answer)

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Let A be any n x m matrix, where m > n. Which of the following statements is/are TRUE about the system of linear equations Ax = 0?

There exist at least m - n linearly independent solutions to this system

There exist m - n linearly independent vectors such that every solution is a linear combination of these vectors

There exists a non-zero solution in which at least m - n variables are 0

There exists a solution in which at least n variables are non-zero

GATE CSE 2024 Set 1

MCQ (More than One Correct Answer)

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The chromatic number of a graph is the minimum number of colours used in a proper colouring of the graph. Let $G$ be any graph with $n$ vertices and chromatic number $k$. Which of the following statements is/are always TRUE?

$G$ contains a complete subgraph with $k$ vertices

$G$ contains an independent set of size at least $n/k$

$G$ contains at least $k(k-1)/2$ edges

$G$ contains a vertex of degree at least $k$

GATE CSE 2024 Set 1

MCQ (More than One Correct Answer)

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Consider the operators $\diamond$ and $\square$ defined by $a \diamond b=a+2 b, a \square b=a b$, for positive integers. Which of the following statements is/are TRUE?

Operator $\diamond$ obeys the associative law

Operator $\square$ obeys the associative law

Operator $\diamond$ over the operator $\square$ obeys the distributive law

Operator $\square$ over the operator $\diamond$ obeys the distributive law

GATE CSE 2024 Set 1

Numerical

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The number of edges present in the forest generated by the DFS traversal of an undirected graph G with 100 vertices is 40. The number of connected components in G is ________

Your input ____

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2024