JEE Main 2021 — Sequences And Series Question with Solution
From: JEE Main 2021 (Online) 26th August Evening Shift
Question
The sum of all 3-digit numbers less than or equal to 500, that are formed without using the digit "1" and they all are multiple of 11, is _____________.
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Show full solutionCorrect answer: 7744
Correct answer
7744
Step-by-step explanation
209, 220, 231, ..........., 495
Sum = (209 + 495) = 9504
Number containing 1 at unit place \matrix{ {\underline 2 } & {\underline 3 } & {\underline 1 } \cr {\underline 3 } & {\underline 4 } & {\underline 1 } \cr {\underline 4 } & {\underline 5 } & {\underline 1 } \cr }
Number containing 1 at 10th place \matrix{ {\underline 3 } & {\underline 1 } & {\underline 9 } \cr {\underline 4 } & {\underline 1 } & {\underline 8 } \cr }
Required = 9504 (231 + 341 + 451 + 319 + 418)
= 7744
Sum = (209 + 495) = 9504
Number containing 1 at unit place \matrix{ {\underline 2 } & {\underline 3 } & {\underline 1 } \cr {\underline 3 } & {\underline 4 } & {\underline 1 } \cr {\underline 4 } & {\underline 5 } & {\underline 1 } \cr }
Number containing 1 at 10th place \matrix{ {\underline 3 } & {\underline 1 } & {\underline 9 } \cr {\underline 4 } & {\underline 1 } & {\underline 8 } \cr }
Required = 9504 (231 + 341 + 451 + 319 + 418)
= 7744
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This is a previous-year question from JEE Main 2021, covering the Sequences And Series chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.