CUET · MATHS · PYQ PAPER 2025
The unit's digit in \(13^{61}\) is
- A 1
- B 3
- C 7
- D 9
Answer & Solution
Correct Answer
(B) 3
Step-by-step Solution
Detailed explanation
\(\text{Unit's digits of } 3^n: 3^1 \rightarrow 3, 3^2 \rightarrow 9, 3^3 \rightarrow 7, 3^4 \rightarrow 1\). Cycle length \(4\). \(\text{Exponent modulo cycle length: } 61 \pmod 4 = 1\). \(\text{The unit's digit is the } 1^{\text{st}} \text{ digit in the cycle, which is } 3\).
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