Integral part of (5 + 11) 2n + 1 is -

Maths Binomial Theorem & Mathematical Induction Mix Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Even

Odd

Even or odd depending upon the value of n

Cannot be determined

Text Solution

Verified by Experts

The correct answer is:

(5 + 11) 2n + 1 = I + f

Now suppose F = (5 – 11) 2n + 1

I + f – F = (5 + 11) 2n + 1 – (5 – 11) 2n + 1

= 2 [ 2n + 1 C 1 (125) n + 2n + 1 C 3 (125) n – 1 11 3 + …]

= 2 even integer

I + f – F = 2k

f – F = 2k – I is an integer

0 ≤ f < 1 0 < F < 1

– 1 < – F < 0

– 1 < f – F < 1

⇒ f – F = 0

I = 2k ⇒ even integer

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