Match the following:
Column I | Column II |
(i) Set of values of x satisfying < 1 is | [A] [– 3, 6) |
(ii) Value of x satisfying | x | + | x – 3 | > 3 is | [B] (–∞,–1) ∪ (– 1,0) ∪ (3, ∞) |
(iii) Set of solution for ≤ 1 is | [C] (– ∞, 0) ∪ (3, ∞) |
(iv) | 2 – | [x] – 1 | | ≤ 2 then ([⋅⋅] represent greatest integer) | [D] ∪ |
Text Solution
Verified by Experts(i) [B]; (ii) [C]; (iii) [D]; (iv) [A]
Ans.
(i) [B]
(ii) [C]
(iii) [D]
(iv) [A]
Sol. (i) 
< 0 ⇒ – x 2 + 3x < 0, x ≠ –1
⇒ x (x – 3) > 0, x ≠ – 1
⇒ x < 0, x > 3, x ≠ – 1
(ii) | x | + | x – 3 | = 
Now solve
(iii) 
≤ 1
⇒ 0 ≤ x 2 – 
+ 1 ≤ 1
⇒ x ∈ 
∪ 
(iv) | 2 – | [x] – 1 | | ≤ 2
⇒ | | [x]–1| – 2 | ≤ 2
⇒ 0 ≤ | [x] –1 | ≤ 4
⇒ –3 ≤ [x] ≤ 5
⇒ x ∈ [– 3, 6)
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