30³⁰ के मान में शून्यों से पहले सबसे दाहिना अंक कौन-सा है?
Read this question in English
What is the rightmost digit preceding the zeros in the value of 30³⁰?
(a) 1 · (b) 3 · (c) 7 · (d) 9
उत्तर और व्याख्या · explanation in English
Answer: (d) 9
30³⁰ = 3³⁰ × 10³⁰, so the digit just before the zeros is the unit digit of 3³⁰. Powers of 3 end in 3, 9, 7, 1 in a cycle of 4, and 30 leaves remainder 2 on division by 4, giving 9.
- 30³⁰ = 3³⁰ × 10³⁰; the factor 10³⁰ supplies the 30 zeros at the end.
- The unit digits of 3¹, 3², 3³, 3⁴ are 3, 9, 7, 1, and then they repeat every 4 powers.
- 30 = 4 × 7 + 2, so 3³⁰ ends like 3², i.e. in 9.
- So the rightmost digit before the zeros is 9.
Remember · Split off the powers of 10 first; then use the four-step unit-digit cycle (remainder 0 means the fourth digit).
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·