If (10) 9 + 2(11) 1 (10) 8 + 3(11) 2 (10) 7 + . . . . . . .…

Maths Sequence and Series ( Progressions ) JEE (Main) / AIEEE Problems ( Previous Year ) Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

If (10) 9 + 2(11) 1 (10) 8 + 3(11) 2 (10) 7 + . . . . . . . . + 10 (11) 9 = k(10) 9 , then k is equal to

100

110

Text Solution

Verified by Experts

The correct answer is:

Let s = (10) 9 + 2(11) 1 (10) 8 + 3 (11) 2 (10) 7 +......................+10(11) 9

∴ s = (11) 1 (10) 8 + 2(11) 2 (10) 7 + .................+9(11) 9 + (11) 10

substract

s = (10) 9 + (11) 1 (10) 8 + (11) 2 (10) 7 + ................+(11) 9 – (11) 10

⇒ – s = – (11) 10 – s =10 9 –(11) 10

⇒ – s = –10 10 + 11 10 – 11 10 ∴ s = 10 11

∴ given 10 11 = k(10) 9 ∴ k = 100

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