UPSC CAPF (AC) 2026 Paper I · Question 68
Question 68 of the UPSC CAPF (AC) 2026 Paper I (19 July 2026). Try it first, then open the answer and explanation.
A rectangular wall is partitioned into 5 rectangular parts as shown in the following diagram. If you have three different colours to paint the wall and if no two adjacent parts are to be painted with the same colour, in how many different ways can one paint the wall?
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एक आयताकार दीवार को 5 आयताकार भागों में बाँटा गया है, जैसा कि निम्नलिखित आरेख में दर्शाया गया है। यदि आपके पास इस दीवार को रंगने के लिए तीन भिन्न रंग हैं और यदि दो आसन्न भागों को एक ही रंग से रंगा नहीं जाना है, तो दीवार को कितने भिन्न प्रकार से रंगा जा सकता है?
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Show answer
Answer: (3) 18
उत्तर: (3) 18
The wall is a 2 × 2 block of four parts beside one tall right part that touches both middle parts. Colour the right part (3 ways); the two middle parts, touching it and each other, take the other two colours (2 ways); the two left parts must differ from their middle neighbours and from each other, leaving 3 ways, so 3 × 2 × 3 = 18.