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UPSC Prelims 2025 CSAT, question 40

Topic: Number system

Q40

If N2=12345678987654321N^2=12345678987654321, then how many digits does the number NN have ?

  1. (a) 8
  2. (b) 9Correct answer
  3. (c) 10
  4. (d) 11

Solution.

Answer: (b) 9

  1. Observe the palindrome pattern: 112=12111^2 = 121, 1112=12321111^2 = 12321, and (111,111,111)2=12345678987654321(111,111,111)^2 = 12345678987654321.
  2. Since the middle peak digit of N2=12345678987654321N^2 = 12345678987654321 is 99, NN consists of nine 11's (111,111,111111,111,111) and therefore has 99 digits.