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Maths Functions, Limits, Continuity and Differentiability General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

If [x + [2x]] < 3, where [.] denotes the greatest integer function, then

x ∈ ∈ [0, 1)

x ∈ ∈ (- ∞ ∞ , 2/3]

x ∈ ∈ [0, 3/2)

x ∈ ∈ (- ∞ ∞ , 1)

Text Solution

Verified by Experts

The correct answer is:

[x + [2x]] < 3 ⇒ ⇒ [x] + [2x] ≤ 2.

Any non-positive real number will satisfy this inequality.

Now if x ∈ ∈ ⇒ ⇒ [x] = 0, [2x] = 0

⇒ ⇒ inequality is again satisfied.

For x ∈ ∈ ⇒ ⇒ [x] = 0, [2x] = 1

⇒ ⇒ inequality is still satisfied.

For x ∈ ∈ ⇒ ⇒ [x] = 1, [2x] = 2

⇒ ⇒ inequality doesn't hold true. Thus x ∈ ∈ (- ∞ ∞ , 1).

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