The digit in the unit place of the number 6^129 × 7^307 is (a) 2 (b) 4 (c) 8 (d) 6

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UPSC Prelims 2026 · CSAT Paper 2 · Set DMathematicsQ 22 / 80

UPSC Prelims 2026 CSAT Paper 2 — Question 22

Question

The digit in the unit place of the number 6^129 × 7^307 is

(a)2
(b)4
(c)8
(d)6

UnlockIAS answer: (c)8

Solution

6 raised to any power ends in 6. For 7, the unit-digit cycle is 7, 9, 3, 1 (period 4); 307 mod 4 = 3 → unit digit 3. Then 6 × 3 = 18, so the unit digit is 8.

UnlockIAS expert key, prepared 24 May 2026 and cross-verified by re-deriving the answer — this is our key, not the official UPSC provisional key (awaited).

Section

Mathematics

Topic Reference

Numeracy — Unit digit / cyclicity

Official UPSC key still awaited

UPSC has announced (PIB Release 2262441, 18 May 2026) that the provisional answer key for CSE Prelims 2026 will be released “soon after Exam”. Until then, use the CSAT score calculator for your qualifying-status estimate, and join the per-question discussion below.

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Official Notification

PIB Release 2262441

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