JEE Main 2021 — Mathematical Reasoning Question with Solution
From: JEE Main 2021 (Online) 27th July Evening Shift
Question
Which of the following is the negation of the statement "for all M > 0, there exists xS such that x M" ?
Choose an option
Show full solutionCorrect option: A
Correct answer
Athere exists M > 0, such that x < M for all xS
Step-by-step explanation
P : for all M > 0, there exists xS such that x M.
P : there exists M > 0, for all xS
Such that x < M
Negation of 'there exists' is 'for all'.
P : there exists M > 0, for all xS
Such that x < M
Negation of 'there exists' is 'for all'.
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This is a previous-year question from JEE Main 2021, covering the Mathematical Reasoning chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.