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MathsJEE Main 28 Jan 2026, Shift 2·Q1·MCQ·Moderate

Binomial Theorem · Divisibility and integral part

Given below two statements :

Statement I : 2513+2013+813+31325^{13} + 20^{13} + 8^{13} + 3^{13} is divisible by 7.

Statement II : The integral part of (7+43)25\left(7 + 4\sqrt3\right)^{25} is an odd number.

In the light of the above statements, choose the correct answer from the options given below :

  1. (1)Both Statement I and Statement II are false.
  2. (2)Both Statement I and Statement II are true.
  3. (3)Statement I is false but Statement II is true.
  4. (4)Statement I is true but Statement II is false.

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See the full 28 Jan 2026, Shift 2 paper