#IOQMPaperSolutions & Analysis | IOQM Exam | IOQM Questions
IOQM 2022-23 | Solutions | Question No. 10 | Pankaj Baluja Sir

Question 10 :- Consider the 10-digit number M = 9876543210. We obtain a new 10-digit number from M according to the following rule: we can choose one or more disjoint pairs of adjacent digits in M and interchange the digits in these chosen pair, keeping the remaining digits in their own places. For example, from M = 9876543210, by interchanging the 2 underlined pairs, and keeping the others in their places, we get M1 = 9786453210. Note that any number of (disjoint) pairs can be interchanged. Find the number of new numbers that can be so obtained from M.

IOQM 2022-23 Solutions
The first stage of Mathematics Olympiad in India is the Indian Olympiad Qualifier in Mathematics (IOQM), previously known as Pre-Regional Mathematics Olympiad (PRMO). The paper is objective, and OMR based and of duration 3 hours.
• Total marks: 100
• The answer to each question is an integer in the range 00-99.
• No negative marking.
• OMR-based exam.
• Composition of the paper:
1. 10 questions of 2 marks each
2. 12 questions of 5 marks each
3. 2 questions of 10 marks each
The solutions to all the problems of IOQM 2022-23, dated 30th October 2022, are discussed here. It is important for all learners to
• Go through the solutions, try in different ways.
• Foresee what else can be asked in the same lines.
• Anticipate where else, as in IIT JEE Main and/or Advanced, can this concept be used to form a new question
ELIGIBILITY for IOQM
1. Students born between August 1, 2003 and January 1, 2010, and studying in Class VIII, IX, X, XI or XII, are eligible to write IOQM. Please note that NO student born after January 1, 2010 will be allowed to write IOQM.
2. Students satisfying criterion 1 above and studying in Kendriya Vidyalayas (KV) and Jawahar Navodaya Vidyalayas (JNV) are ELIGIBLE to write IOQM. There will be NO separate IOQM for students of Kendriya Vidyalayas (KV) and Jawahar Navodaya Vidyalayas (JNV).
3. The INMO 2022 Awardees are eligible to write INMO 2023 WITHOUT qualifying through IOQM provided they fulfil the eligibility criteria of IMO 2023 and EGMO 2024.

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IOQM Certificate criterion
Any student who scores at least 20% of the total marks of the IOQM paper will receive a certificate.

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