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COMEDK20269 May 2026Morning ShiftMathematicsBinomial TheoremActual

The remainder when 7¹⁰³ is divided by 25 is

Options

  1. A7
  2. B18
  3. C1
  4. D-1

Correct answer

B. 18

Step-by-step solution

We need to find the remainder when 7¹⁰³ is divided by 25 . We can write 7¹⁰³ as 7 7¹⁰² = 7 (7^2)⁵¹ . We know that 7^2 = 49 -1 25 . Raising both sides to the power of 51 , we get: (7^2)⁵¹ (-1)⁵¹ 25 7¹⁰² -1 25 Multiplying both sides by 7 , we get: 7¹⁰³ -7 25 To find the positive remainder, we add 25 to -7 : -7 + 25 = 18 Thus, the remainder when 7¹⁰³ is divided by 25 is 18 . Answer: 18

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