GATE CS 2023 Set 1 — Question 7
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General Aptitude → Analytical Aptitude → Numerical Relations & Reasoning
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Question
Consider two functions of time (),where .Now consider the following two statements:
(i) For some , .
(ii) There exists a , such that for all .Which one of the following options is TRUE?
(i) For some , .
(ii) There exists a , such that for all .Which one of the following options is TRUE?
Correct answer
(C) both (i) and (ii) are correct
Solution
Given functions are and for .Statement (i):
Since , this inequality holds for . For example, at , and , so . Thus, statement (i) is correct.Statement (ii): for all
Since , this holds for . Thus, there exists such that for all , . Thus, statement (ii) is correct.Since both statements are correct, the correct option is (C).
Since , this inequality holds for . For example, at , and , so . Thus, statement (i) is correct.Statement (ii): for all
Since , this holds for . Thus, there exists such that for all , . Thus, statement (ii) is correct.Since both statements are correct, the correct option is (C).
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