Divisibility and Remainders

JEE Main Mathematics · Binomial Theorem · 16 questions, latest first

• Given below are two statements: Statement I: 25^13+20^13+8^13+3^13 is divisible by 7. Statement II: The integral part of (7+4…202628 January, Shift 2 · Q7
• The product of the last two digits of (1919)^1919 is ____20258 April, Shift 2 · Q22
• The remainder when ((64)^(64))^(64) is divided by 7 is equal to20257 April, Shift 1 · Q7
• The remainder, when 7^103 is divided by 23, is equal to:202529 January, Shift 2 · Q7
• The remainder when 428^2024 is divided by 21 is ____.20249 April, Shift 1 · Q25
• Remainder when 64^32^32 is divided by 9 is equal to ____.202429 January, Shift 2 · Q24
• The number of elements in the set {n ∈ N: 10 ≤ n ≤ 100. and 3^n-3 is a multiple of 7\} is ____.202315 April, Shift 1 · Q23
• The remainder, when 7^103 is divided by 17, is ____202313 April, Shift 2 · Q23
• Fractional part of the number (4^2022)/15 is equal to202313 April, Shift 1 · Q13
• Let the number (22)^2022+(2022)^22 leave the remainder α when divided by 3 and β when divided by 7. Then (α^2+β^2) is equal to202310 April, Shift 2 · Q7
• 25^190-19^190-8^190+2^190 is divisible by20238 April, Shift 2 · Q6
• Among the statements: (S1): 2023^2022-1999^2022 is divisible by 8 (S2): 13(13)^n-11 n-13 is divisible by 144 for infinitely many…20236 April, Shift 2 · Q6
• The remainder, when 19^200+23^200 is divided by 49, is ____.20231 February, Shift 1 · Q84
• The remainder on dividing 5^99 by 11 is ____.202331 January, Shift 1 · Q82
• 50^th root of a number x is 12 and 50^th root of another number y is 18. Then the remainder obtained on dividing (x+y) by 25 is…202330 January, Shift 2 · Q84
• The remainder when (2023)^2023 is divided by 35 is ____202325 January, Shift 2 · Q83