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1
GATE ECE 2026
MCQ (Single Correct Answer)
+1
-0.33

The following observation is made about the scores obtained by 100 students in an exam: 'For each student, there exists another student in the class such that their scores are at most ten marks away.'

If the above statement is false, which one of the following statements is necessarily true?

A

For each student, the scores of all the other students are more than 10 marks away.

B

There exists at least one student in the class for whom the scores of all the other students are more than 10 marks away.

C

There is exactly one student in the class for whom the scores of some students are more than 10 marks away.

D

For each student, the score of exactly one other student is more than 10 marks away.

2
GATE ECE 2024
MCQ (Single Correct Answer)
+1
-0.33

P, Q, R, S, and T have launched a new startup. Two of them are siblings. The office of the startup has just three rooms. All of them agree that the siblings should not share the same room.

If S and Q are single children, and the room allocations shown below are acceptable to all,

PR | TS | Q

PQ | RT | S

Then, which one of the given options is the siblings?

A

P and T

B

P and S

C

T and Q

D

T and R

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