UPSC NDA I 2025 Mathematics Paper

⇒ Treat consonants CPTL as a single unit.
⇒ Total "super units" ={CPTL,A,I,A}=4 units.
⇒ Arrangements of super units =4!∕2! (since A repeats).
⇒ Arrangements of super units =24∕2=12.
⇒ Internal arrangements of consonants CPTL =4!.
⇒ Internal arrangements =4×3×2×1=24
⇒ Total arrangements =( Arrangements of super units )×( Internal arrangements of consonants ).
⇒ Total arrangements =12×24.
⇒ Total arrangements =288.
∴ The total number of 7-letter words =288.