GATE DA 2025 Paper 1 — page 17

Questions 49–51 of 65. Imported answers require review unless explicitly marked reviewed.

Paper practice 65 questionsPage 17 of 22

Consider the function

. Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

The maximum value of

is attained at

The minimum value of

is attained at

The maximum value of

The minimum value of the derivative of

is attained at

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Let

be a system of orthonormal vectors in

. Consider the matrix

. Which of the following statements is/are correct?

Your answerSelect all correct options. You can choose more than one.

Singular values of

are also its eigenvalues

Singular values of

are either 0 or 1

Determinant of

is 1

is invertible

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Let

be a twice-differentiable function and suppose its second derivative satisfies

for all

. Which of the following statements is/are ALWAYS correct?

Your answerSelect all correct options. You can choose more than one.

has a local minima

There does not exist

and

, such that

has at most one global minimum

has at most one local minimum

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2025 · Paper 1