GATE CE 2026 Set 2 — Question 8
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumMensuration & GeometryQuantitative AptitudeGeneral Aptitude
General Aptitude → Quantitative Aptitude → Mensuration & Geometry
Last updated
Question
Consider a string P of length that is laid out as a straight-line segment. Another string K is laid out as a semicircular arc with string P as its diameter, as represented in Figure (i). When both the strings are shortened by a length they can be re-arranged such that the shortened string K forms a full circle with the shortened string P as its diameter, as represented in Figure (ii). The value of is __________
Correct answer
(C) (π)/(2(π-1))
Solution
Initial state (Figure i):
Length of string P = .
String K is a semicircular arc with diameter . Length of K = .Final state (Figure ii):
Both strings are shortened by .
Length of shortened string P = .
Length of shortened string K = .Shortened string K forms a full circle with diameter equal to the length of shortened string P ().
Circumference of circle = .Equating the length of shortened string K to the circumference:
Length of string P = .
String K is a semicircular arc with diameter . Length of K = .Final state (Figure ii):
Both strings are shortened by .
Length of shortened string P = .
Length of shortened string K = .Shortened string K forms a full circle with diameter equal to the length of shortened string P ().
Circumference of circle = .Equating the length of shortened string K to the circumference:
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 CE 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 Quantitative Aptitude
2026 Set 2 Q1'The team ____ more than 300 runs in 20 overs ____ rains. However, some players needed to…2026 Set 1 Q1‘The shopkeeper sells lemons.’ In this sentence, the word ‘lemons’ is the ________.2026 Set 2 Q2If a positive real satisfies the following equation then…2026 Set 1 Q2The figure below is supposed to show three non-overlapping shapes – one oval and two triangles.…2026 Set 2 Q3The next figure (indicated by ‘?’) in the sequence is