Solve for x (where [•] denotes greatest integer function an…

Maths Fundamental of Mathematics Greatest Integer Function, Fractional Part & Signum Function Matrix Match Questions

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Solve for x (where [•] denotes greatest integer function and {•} represent fractional part function)

(i) [2x] = 1 (ii) {x} 2 + [x] = 2

(iii) 6{x} 2 – 5{x} + 1 = 0 (iv) 6[x] 2 – 5[x] – 1 = 0

Correct Matrix Matching

Text Solution

Verified by Experts

The correct answer is:

(i) (ii); (i) [2x]

(i) (ii) 2

(iii) x ∈ (iv) x ∈ [1,2)

Sol. (i) [2x] = 1 ⇒ 2x ∈ [1,2) ⇒

(ii) {x} 2 + [x] = 2

⇒ {x} = 0, [x] = 2

⇒ x = 2

(iii) 6{x} 2 – 5{x} + 1 = 0 ⇒ {x} =

x = n + , n + where n ∈ I

(iv) 6[x] 2 – 5[x] – 1 = 0

⇒ [x] = 1, (reject ) ⇒ x ∈ [1,2)

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