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JEE Main Mathematics Binomial Theorem 2026 JEE Main 2026 (28 January Shift 2)

JEE Main Mathematics Question (2026) — Solution

Question

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 3 )^ 25 is an odd number. In the light of the above statements, choose the correct answer from the options given below :

Options

  1. A. Statement I is true but Statement II is false
  2. B. Both Statement I and Statement II are true
  3. C. Statement I is false but Statement II is true
  4. D. Both Statement I and Statement II are false

Answer

B. Both Statement I and Statement II are true

Step-by-step solution

Statement I: 25^ 13 + 3^ 13 → divisible by (25 + 3) 20^ 13 + 8^ 13 → divisible by (20 + 8) divisible by 7. TRUE Statement II: For (7+4 3 )^ 25 , let = 7+4 3 and = 7-4 3 (conjugate). Then = 1 and + = 14. Since 0 The fractional part of ^ 25 is 1- ^ 25 , making the integral part odd. TRUE. Both Statement I and Statement II are true.

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