Let a be a positive real number such that where [x] is the…

Maths Definite Integral and Area Under Curves JEE Main 2021 - ( Definite Integration ) Single Correct MCQ

Published on: August 13, 2026

Let a be a positive real number such that where [x] is the greatest integer less than or equal to x. Then a is equal to :

10 − log e (1 + e)

10 + log e 2

10 + log e 3

10 + log e (1 + e)

Text Solution

Verified by Experts

The correct answer is:

a>0

Let n ≤ a < n + 1, n ∈ W

Here [a] = n

Now,

⇒ n(e − 1) + (e a−n − 1) = 10e − 9

∴ n = 0 and {a} = log e 2

So, a = [a] + {a} = (10 + log e 2)

Option (2) is correct.

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