Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Given : | x – 1| + | x – 2 | = λ where λ ∈ R then answer the following
(i) If λ = 6 then x belongs to
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Ans.
(i)
Sol. | x – 1 | + | x – 2 | = 6
case (i) x < 1 we get 
case (ii) 1 ≤ x < 2
1 = 6 No solution
case (iii) x ≥ 2
x = 
(ii)
Sol. | x – 1| + | x – 2| = 0
∴ L. H. S > 0
R. H. S = 0
∴ No solution
(iii)
Sol. | x –1| + | x – 2 | = 1
case (i) x < 1 we get
x = 1
∴ No solution
case (ii) 1 ≤ x < 2
we get 1 =1
∴ x ∈ [1, 2)
case (iii) x ≥ 2
we get x = 2
∴ from all cases
x ∈ [1, 2]
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