10:[["$","title","0",{"children":"CUET Mathematics - The unit's digit of 13^13 is: | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined When finding the unit's digit of any power, only the unit's digit of the base number matters. Since 13 has unit's digit 3, the pattern of unit's digits when multiplying 3 by itself repeatedly needs to be found.

The first few powers of 3 and their unit's digits: | Power | Calculation | Result | Unit's Digit | |-------|-------------|--------|--------------| | 3^1 | 3 | 3 | 3 | | 3^2 | 3 3 | 9 | 9 | | 3^3 | 9 3 | 27 | 7 | | 3^4 | 27 3 | 81 | 1 | | 3^5 | 81 3 | 243 | 3 | The pattern repeats: 3 9 7 1 3 9 7 1... The cyc<= <=ngth is 4.

To find which position in the cyc<=, divide the power by 4: 13 4 = 3 remainder 1 The remainder determines the position: - Remainder 1 → 1st position in cyc<= → unit's digit is 3 - Remainder 2 → 2nd position in cyc<= → unit's digit is 9 - Remainder 3 → 3rd position in cyc<= → unit's digit is 7 - Remainder 0 → 4th position in cyc<= → unit's digit is 1 Since remainder = 1, the position is 1st in the cyc<=.

The unit's digit of 13^13 is 3."}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$undefined"}],["$","meta","3",{"name":"keywords","content":"CUETMAT,MAT,Arithmetic,Numericals"}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","meta","5",{"name":"category","content":"education"}],["$","meta","6",{"name":"google-site-verification","content":"google"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - The unit's digit of 13^13 is: | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined When finding the unit's digit of any power, only the unit's digit of the base number matters. Since 13 has unit's digit 3, the pattern of unit's digits when multiplying 3 by itself repeatedly needs to be found.

The unit's digit of 13^13 is 3."}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-12/79"}],["$","meta","10",{"property":"og:site_name","content":"AfterBoards | CUET Mathematics Preparation"}],["$","meta","11",{"property":"og:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","meta","12",{"property":"og:type","content":"website"}],["$","meta","13",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","14",{"name":"twitter:site","content":"afterboards.in"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - The unit's digit of 13^13 is: | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined When finding the unit's digit of any power, only the unit's digit of the base number matters. Since 13 has unit's digit 3, the pattern of unit's digits when multiplying 3 by itself repeatedly needs to be found.

The unit's digit of 13^13 is 3."}],"$L17","$L18","$L19","$L1a","$L1b","$L1c","$L1d","$L1e","$L1f","$L20"]

CUET Mathematics 2025 22 May Shift 2 PYQs

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