UPSC CSE Prelims
Unit Digit Previous Year Questions (PYQs)
Practice solved questions for Unit Digit with detailed step-by-step solutions, key insights, and trend analysis for UPSC CSE PRELIMS.
Solved Previous Year Questions
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The digit in the unit place of the number $6^{129} \times 7^{307}$ is
Detailed Explanation:
Unit digit of 6^129: Any power of 6 always ends in 6 (since 6×6=36, 36×6=216, etc.). Thus, unit digit = 6.
Unit digit of 7^307: Powers of 7 cycle every 4: 7¹→7, 7²→9, 7³→3, 7⁴→1. Divide 307 by 4: remainder = 3. So unit digit matches 7³ = 3.
Final unit digit: Multiply 6 × 3 = 18, giving unit digit 8.
Therefore, the unit digit is 8, making Option 3 the correct answer.
How many times does $5$ appear in all two-digit positive integers?
Detailed Explanation:
Count the digit 5 in tens place: appears in 50, 51, 52, …, 59 — that's 10 occurrences.
Count the digit 5 in units place: appears in 15, 25, 35, 45, 55, 65, 75, 85, 95 — that's 9 occurrences.
Therefore, total = 10 + 9 = 19, making Option 2 the correct answer.
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