GATE MA 2025 Paper 1 — page 6

Questions 16–18 of 65. Imported answers require review unless explicitly marked reviewed.

Consider the system of ordinary differential equations

where

is a

skew-symmetric matrix with entries in

. Then, for this system, the origin is a stable critical point for

Your answerChoose one option.

any such matrix

only such matrices

whose rank is 2

only such matrices

whose rank is 4

only such matrices

whose rank is 6

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Let

with the norm

, where

is the space of all real-valued continuous functions on

. Let

with the norm

. Let

and

be the closed unit balls in

and

centred at the origin, respectively. Consider

and

given by

Consider the following statements:

S1:

is attained at a point of

S2:

is attained at a point of

Then, which one of the following is correct?

Your answerChoose one option.

S1 is TRUE and S2 is FALSE

S2 is TRUE and S1 is FALSE

both S1 and S2 are TRUE

neither S1 nor S2 is TRUE

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Let

be defined in

, where

is a continuously differentiable non-zero homogeneous function of degree 4. Then,

holds for

Your answerChoose one option.

all points

on the line given by

all points

in the region of

except on the line given by

all points

on the line given by

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2025 · Paper 1

Question 16

Question 17

Question 18