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JEE Main202628 January 2026Evening ShiftMathematicsBinomial TheoremActual

Given below are two statements : Statement I: 25¹³+20¹³+8¹³+3¹³ 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. AStatement I is true but Statement II is false
  2. BBoth Statement I and Statement II are true
  3. CStatement I is false but Statement II is true
  4. DBoth Statement I and Statement II are false

Correct answer

B. Both Statement I and Statement II are true

Step-by-step solution

Statement I: 25¹³ + 3¹³ → divisible by (25 + 3) 20¹³ + 8¹³ → 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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