GATE ME 2025 Set 1 — Question 4
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+1 / -0.33EasyNumerical Relations & ReasoningAnalytical AptitudeGeneral Aptitude
General Aptitude → Analytical Aptitude → Numerical Relations & Reasoning
Last updated
Question
The ceiling function of a real number , denoted by , is defined as the smallest integer that is greater than or equal to . Similarly, the floor function, denoted by , is defined as the largest integer that is smaller than or equal to . Which one of the following statements is NOT correct for all possible values of ?
Correct answer
(D) fl(x) < ce(x)
Solution
The ceiling function is the smallest integer . The floor function is the largest integer . For any real number , the relationship always holds.
1. is true by definition.
2. is true by definition.
3.Since and , it follows that is always true.
4.If is an integer, then and . In this case, . Therefore, the statement is NOT correct when is an integer. Thus, option (D) is the correct answer.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE ME question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Analytical Aptitude
2026 Set 1 Q1‘The team ____ more than 300 runs in 20 overs _________ rains. However, some players needed to…2026 Set 1 Q2If a positive real satisfies the following equation then…2026 Set 1 Q3The next figure (indicated by ‘?’) in the sequence is [figure]2026 Set 1 Q4‘All the mangoes in the basket are good.’ If the above statement is false, then which one of…2026 Set 1 Q5Consider the following statements about four numbers: (S1) The average of the four numbers is 25…