Verified Solution • 2025–26 Session moderate

QJEEM21Maf09d: JEE Main 2021 Mathematics - Class 11 JEEM21Maf09d Solution: If A = {x R :

If A = {x ∈\in R : |x −- 2| > 1},
B = {x ∈\in R : x2−3\sqrt {{x^2} - 3} > 1},
C = {x ∈\in R : |x −- 4| ≥\ge 2} and Z is the set of all integers, then the number of subsets of the
set (A ∩\cap B ∩\cap C)c ∩\cap Z is ________________.

Step-by-Step Verified Solution

A = ( −- ∞\infty , 1) ∪\cup (3, ∞\infty )

B = ( −- ∞\infty , −- 2) ∪\cup (2, ∞\infty )

C = ( −- ∞\infty , 2] ∪\cup [6, ∞\infty )

So, A ∩\cap B ∩\cap C = ( −- ∞\infty , −- 2) ∪\cup [6, ∞\infty )

z ∩\cap (A ∩\cap B ∩\cap C)' = { −- 2, −- 1, 0, −- 1, 2, 3, 4, 5}

Hence, no. of its subsets = 28 = 256.

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