GATE ECE 2026 Paper 1 — page 2

Questions 4–6 of 65. Imported answers require review unless explicitly marked reviewed.

Real numbers

, and

(all greater than 1) satisfy

where the logarithms are taken to the bases

and

The value of

is ________

Your answerChoose one option.

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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?

Your answerChoose one option.

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

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

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

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

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Each one of the following clues contains a keyword that is partially filled.

Clue 1: Synonym of recognize (8 letters): _ D _ NT_ FY

Clue 2: A story long enough to fill a book (5 letters): _ _ EL

Clue 3: Two of something (6 letters): _ _ _ PLE

Clue 4: A fraction of something, split equally into two parts (4 letters): _ _ _ F

The first letter of each of the keywords can be rearranged to form a four-letter word.

Which one of the options below is a possible choice for the four-letter word?

Your answerChoose one option.

CHIN

COIN

ITCH

NOSE

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2026 · Paper 1