2023 · Paper 1

Complete GATE MA 2023 Paper 1 overview, original pages and practice · Timed previous-paper practice

Questions 10–12 of 65. Imported answers require review unless explicitly marked reviewed.

Question 10

Open question

GAMCQ2 marksNeeds review

An opaque cylinder (shown below) is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The cylinder can be reoriented in any direction within the light beam. Under these conditions, which one of the shadows P, Q, R, and S is NOT possible?



Your answerChoose one option.

A.

P

B.

Q

C.

R

D.

S

Log in to check the answer

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Question 11

Open question

MAMCQ1 markNeeds review

Let



be defined by



and



for all



. Consider the following statements: P:



has a saddle point at



. Q:



has a saddle point at



. Then

Your answerChoose one option.

A.

both P and Q are TRUE

B.

P is FALSE but Q is TRUE

C.

P is TRUE but Q is FALSE

D.

both P and Q are FALSE

Log in to check the answer

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Question 12

Open question

MAMCQ1 markNeeds review

Let



be a topological space with the usual topology and



denote the set of rational numbers. Define the subspaces



and



of



as follows:



;



;



;



. Which of the following statements is correct?

Your answerChoose one option.

A.



is homeomorphic to



B.



is homeomorphic to



C.



is homeomorphic to



D.



is NOT homeomorphic to



Log in to check the answer

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer