GATE DA 2024 Paper 1 — page 5

Questions 13–15 of 65. Imported answers require review unless explicitly marked reviewed.

Consider the matrix

Which ONE of the following statements is TRUE?

Your answerChoose one option.

The eigenvalues of

are non-negative and real.

The eigenvalues of

are complex conjugate pairs.

One eigenvalue of

is positive and real, and another eigenvalue of

is zero.

One eigenvalue of

is non-negative and real, and another eigenvalue of

is negative and real.

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Consider performing depth-first search (DFS) on an undirected and unweighted graph

starting at vertex

. For any vertex

is the length of the shortest path from

. Let

be an edge in

such that

. If the edge

is explored first in the direction from

during the above DFS, then

becomes a ______ edge.

Your answerChoose one option.

tree

cross

back

gray

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For any twice differentiable function

, if at some

and

, then the function

necessarily has a _____ at

. Note:

denotes the set of real numbers.

Your answerChoose one option.

local minimum

global minimum

local maximum

global maximum

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2024 · Paper 1

Question 13

Question 14

Question 15