GATE DA 2024 Set 1 — Question 2
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+1 / -0.33MediumSpatial AptitudeGeneral Aptitude2D & 3D Patterns
General Aptitude → Spatial Aptitude → 2D & 3D Patterns
Last updated
Question
The 15 parts of the given figure are to be painted such that no two adjacent parts with shared boundaries (excluding corners) have the same color. The minimum number of colors required is
Correct answer
(A) 4
Solution
This is a planar map-colouring problem: adjacent regions (those sharing a boundary arc, not just a corner) must get different colours.Upper bound. The figure is a map drawn in the plane, so by the Four Colour Theorem at most colours are ever needed. This rules out and .Is enough? No. The figure contains a set of four regions that are pairwise adjacent (each one shares a boundary arc with the other three). Four mutually adjacent regions form a in the adjacency graph, and a needs distinct colours, so colours cannot work.Since colours always suffice for a planar map and are provably not enough here, the minimum number of colours required is .Answer: 4 (option A)
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 DA 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 Spatial Aptitude
2026 Set 1 Q1Verbosity : Brevity :: Insolence :___________ Choose the word that best fills the blank.2026 Set 1 Q2The product of the digits of a three-digit number is 70. The sum of the digits of this three-digit…2026 Set 1 Q3The four pieces of a puzzle are shown in the figure below. [figure] Which one of the figures…2026 Set 1 Q4Consider two distinct positive real numbers , with . Let and…2026 Set 1 Q5‘If his latest movie had been a commercial success, the actor would have made enough money to…