10:[["$","title","0",{"children":"CUET Mathematics - The least non-negative remainder, when 5^61 is divided by 7, is | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined To find the remainder when 5^61 is divided by 7, calculate the first few powers of 5 modulo 7: 5^1 5 \\±od7 5^2 = 25 4 \\±od7 5^3 = 125 6 \\±od7 5^4 = 625 2 \\±od7 5^5 = 3125 3 \\±od7 5^6 = 15625 1 \\±od7 5^7 = 78125 5 \\±od7 The pattern of remainders is: 5, 4, 6, 2, 3, 1, and then repeats with period 6.

Divide 61 by 6 to determine position in the cyc<=: 61 = 6 10 + 1 The remainder is 1.

Since 5^6 1 \\±od7: 5^61 = 5^6 10 + 1 = (5^6)^10 5^1 1^10 5 \\±od7 5 \\±od7 Therefore, the <=ast non-negative remainder is 5."}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$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"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - The least non-negative remainder, when 5^61 is divided by 7, is | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined To find the remainder when 5^61 is divided by 7, calculate the first few powers of 5 modulo 7: 5^1 5 \\±od7 5^2 = 25 4 \\±od7 5^3 = 125 6 \\±od7 5^4 = 625 2 \\±od7 5^5 = 3125 3 \\±od7 5^6 = 15625 1 \\±od7 5^7 = 78125 5 \\±od7 The pattern of remainders is: 5, 4, 6, 2, 3, 1, and then repeats with period 6.

Divide 61 by 6 to determine position in the cyc<=: 61 = 6 10 + 1 The remainder is 1.

Since 5^6 1 \\±od7: 5^61 = 5^6 10 + 1 = (5^6)^10 5^1 1^10 5 \\±od7 5 \\±od7 Therefore, the <=ast non-negative remainder is 5."}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-20/65"}],["$","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"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - The least non-negative remainder, when 5^61 is divided by 7, is | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined To find the remainder when 5^61 is divided by 7, calculate the first few powers of 5 modulo 7: 5^1 5 \\±od7 5^2 = 25 4 \\±od7 5^3 = 125 6 \\±od7 5^4 = 625 2 \\±od7 5^5 = 3125 3 \\±od7 5^6 = 15625 1 \\±od7 5^7 = 78125 5 \\±od7 The pattern of remainders is: 5, 4, 6, 2, 3, 1, and then repeats with period 6.

Divide 61 by 6 to determine position in the cyc<=: 61 = 6 10 + 1 The remainder is 1.

Since 5^6 1 \\±od7: 5^61 = 5^6 10 + 1 = (5^6)^10 5^1 1^10 5 \\±od7 5 \\±od7 Therefore, the <=ast non-negative remainder is 5."}],["$","meta","17",{"name":"twitter:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","link","18",{"rel":"shortcut icon","href":"https://www.afterboards.in/favicon.ico","type":"image/x-icon","sizes":"48x48"}],["$","link","19",{"rel":"icon","href":"https://www.afterboards.in/favicon.ico","type":"image/x-icon","sizes":"48x48"}],["$","link","20",{"rel":"icon","href":"https://www.afterboards.in/icons/windows11/Square44x44Logo.altform-lightunplated_targetsize-256.png","sizes":"256x256","type":"image/png"}],"$L17","$L18","$L19","$L1a","$L1b","$L1c"]

CUET Mathematics 2025 3 June Shift 2 PYQs

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